- On the CogAT Verbal Battery, the Verbal Analogies subtest asks a test-taker to do which of the following?
- Figure out the relationship in the first word pair and complete a second pair the same way
- Add two numbers and report the sum
- Choose the picture that is rotated the most
- Spell a vocabulary word correctly
Correct answer: Figure out the relationship in the first word pair and complete a second pair the same way
Figuring out the relationship in the first word pair and completing a second pair the same way is correct. Verbal Analogies presents a complete first pair, and the student must identify the link between those two words, then apply that same link to finish a second pair. The other choices describe quantitative or nonverbal tasks, not verbal reasoning.
- Hot is to cold as up is to ____.
Correct answer: Down
Down is correct. The first pair, hot and cold, are opposites, so the analogy is an antonym relationship; the opposite of up is down. Fast and tall are unrelated directions or qualities, and warm is a near-synonym of hot rather than an opposite of up.
- Puppy is to dog as kitten is to ____.
Correct answer: Cat
Cat is correct. A puppy is a young dog, so the relationship is young animal to its adult form; a kitten is a young cat. A bird is a different animal, milk is something a kitten drinks, and a paw is a body part, none of which match the young-to-adult relationship.
- Finger is to hand as toe is to ____.
Correct answer: Foot
Foot is correct. A finger is a part of a hand, so the relationship is part to whole; a toe is a part of a foot. A shoe covers the foot rather than being a whole containing the toe, a leg is connected but is not the whole the toe is part of, and a nail is another smaller part rather than the whole.
- Author is to book as composer is to ____.
Correct answer: Song
Song is correct. An author creates a book, so the relationship is creator to the work created; a composer creates a song. A piano is a tool a composer might use, a stage is a place, and an orchestra performs the work rather than being the thing created.
- Sentence Completion items on the CogAT Verbal Battery ask the student to do which of the following?
- Rotate a shape until it matches
- Use the meaning of the sentence to choose the word that best fills the blank
- Find the missing number in a series
- Punctuate the sentence correctly
Correct answer: Use the meaning of the sentence to choose the word that best fills the blank
Using the meaning of the sentence to choose the word that best fills the blank is correct. Sentence Completion measures vocabulary and reasoning by giving a sentence with a missing word and asking which choice best fits the context. Rotating shapes and finding missing numbers belong to other batteries, and the task is not about punctuation.
- Choose the word that best completes the sentence: After the long hike, the tired children were eager to ____.
Correct answer: Rest
Rest is correct. The sentence says the children were tired after a long hike, so the context points to wanting to stop and recover, which is to rest. To begin or to run contradicts being tired, and to argue has nothing to do with being worn out from a hike.
- Choose the word that best completes the sentence: The desert receives very little rain, so it is extremely ____.
Correct answer: Dry
Dry is correct. A place that gets very little rain is dry, which fits the cause-and-effect signal of little rain. Crowded and loud describe people or sound rather than rainfall, and green would suggest lush plants, the opposite of a place with little rain.
- Verbal Classification on the CogAT gives the student three words that go together and asks for which of the following?
- A fourth word that belongs to the same group
- The opposite of all three words
- A number that follows the pattern
- A shape that completes a matrix
Correct answer: A fourth word that belongs to the same group
A fourth word that belongs to the same group is correct. In Verbal Classification, the three given words share a category, and the student picks the answer that fits that same category. Choosing an opposite, a number, or a shape would not be classifying a word into the shared group.
- Apple, banana, grape - which word belongs with this group?
Correct answer: Orange
Orange is correct. Apple, banana, and grape are all fruits, so the shared category is fruit, and orange is also a fruit. A carrot is a vegetable, while a spoon and a chair are objects that are not fruits at all.
- Red, blue, green - which word belongs with this group?
Correct answer: Yellow
Yellow is correct. Red, blue, and green are all colors, so the shared category is colors, and yellow is also a color. Round describes a shape, soft describes texture, and loud describes sound, so none of them fit the color category.
- In an analogy such as 'big is to large as small is to little,' which relationship type is being used?
- Antonym
- Part to whole
- Cause and effect
- Synonym
Correct answer: Synonym
Synonym is correct. Big and large mean nearly the same thing, and small and little also mean nearly the same thing, so both pairs are synonyms. The pairs are not opposites, not part-and-whole, and not a cause leading to an effect.
- Day is to night as summer is to ____.
Correct answer: Winter
Winter is correct. Day and night are opposites, making this an antonym relationship; the seasonal opposite of summer is winter. Vacation is an event during summer, warm describes summer, and month names a smaller time unit, so none capture the opposite relationship.
- Pencil is to write as scissors are to ____.
Correct answer: Cut
Cut is correct. A pencil's function is to write, so this is a tool-to-function relationship; the function of scissors is to cut. Sharp and metal describe what scissors are like, and paper is what they might act on, but only cut names what the tool does.
- Rain is to flood as fire is to ____.
Correct answer: Burn
Burn is correct. Rain can cause a flood, so this is a cause-and-effect relationship; fire causes things to burn. A match starts a fire rather than resulting from it, warm describes fire, and smoke is a by-product but burning is the direct effect that parallels flooding.
- On a lower-level CogAT, a Picture Analogy might show a bird with a nest and a dog with an empty box. Which picture completes it?
- A fish
- A tree
- A cloud
- A doghouse
Correct answer: A doghouse
A doghouse is correct. The bird-and-nest pair shows an animal with the place where it lives, so the dog should be paired with where it lives, a doghouse. A fish is another animal, a tree is where the nest sits, and a cloud is unrelated to where a dog lives.
- Teacher is to school as doctor is to ____.
- Hospital
- Medicine
- Patient
- Nurse
Correct answer: Hospital
Hospital is correct. A teacher works at a school, so the relationship is person to their workplace; a doctor works at a hospital. Medicine is a tool, a patient is who the doctor helps, and a nurse is a co-worker, none of which is the workplace.
- Choose the word that best completes the sentence: Because the bridge was unsafe, the workers decided to ____ it.
- Ignore
- Repair
- Decorate
- Photograph
Correct answer: Repair
Repair is correct. The sentence signals a problem, an unsafe bridge, so a sensible response is to fix it, which is to repair. Ignoring an unsafe bridge would be unwise, decorating does not make it safe, and photographing it does nothing to fix the safety problem.
- Bee is to hive as bear is to ____.
Correct answer: Cave
Cave is correct. A bee lives in a hive, so the relationship is animal to its home; a bear often lives in a cave. Honey is something bees make, a forest is too broad to be a specific home, and fur is a body covering, so none matches the specific-home relationship.
- Which relationship best describes the analogy 'glove is to hand as sock is to foot'?
- An item is matched with the body part it covers
- An item is matched with its opposite
- A cause is matched with its effect
- A whole is matched with one of its parts
Correct answer: An item is matched with the body part it covers
An item is matched with the body part it covers is correct. A glove covers a hand and a sock covers a foot, so both pairs connect clothing to the body part it goes on. The pairs are not opposites, not cause and effect, and not whole-and-part relationships.
- Choose the word that best completes the sentence: The scientist recorded each result carefully so her experiment could be repeated ____.
- Loudly
- Accurately
- Sweetly
- Slowly
Correct answer: Accurately
Accurately is correct. Recording results carefully so an experiment can be repeated points to doing it correctly and precisely, which is accurately. Loudly relates to sound, sweetly relates to taste, and slowly relates to speed, none of which fits the idea of careful, correct repetition.
- Brave is to cowardly as generous is to ____.
Correct answer: Stingy
Stingy is correct. Brave and cowardly are opposites, so this is an antonym relationship; the opposite of generous is stingy. Kind and helpful are near-synonyms of generous, and wealthy is unrelated to whether a person shares, so none provides the needed opposite.
- Petal, stem, root - which word belongs with this group?
Correct answer: Leaf
Leaf is correct. Petal, stem, and root are all parts of a plant, so the shared category is plant parts, and a leaf is also a plant part. A garden is a place where plants grow, soil is what they grow in, and rain helps them grow, but none of those is itself a part of the plant.
- Library is to books as garden is to ____.
- Plants
- Fence
- Gardener
- Shovel
Correct answer: Plants
Plants is correct. A library is a place full of books, so the relationship is a place and the main things found there; a garden is full of plants. A fence surrounds a garden, a gardener tends it, and a shovel is a tool, but plants are the things the garden holds.
- Choose the word that best completes the sentence: Although the team practiced for months, they were ____ when they finally won the championship.
- Bored
- Overjoyed
- Confused
- Angry
Correct answer: Overjoyed
Overjoyed is correct. Winning a championship after months of practice would bring great happiness, which is being overjoyed. Bored, confused, and angry are negative or unrelated feelings that do not fit the happy outcome of finally winning.
- Wet is to dry as full is to ____.
Correct answer: Empty
Empty is correct. Wet and dry are opposites, making this an antonym relationship; the opposite of full is empty. Heavy and round describe other qualities, and open is the opposite of closed rather than of full, so empty is the matching opposite.
- Which task is part of the Verbal Battery rather than another CogAT battery?
- Folding paper to predict hole positions
- Balancing two sides of an equation
- Completing a 2x2 figure matrix
- Choosing a word that completes a sentence
Correct answer: Choosing a word that completes a sentence
Choosing a word that completes a sentence is correct. Sentence Completion is one of the three Verbal Battery subtests. Folding paper and completing a figure matrix belong to the Nonverbal Battery, and balancing an equation belongs to the Quantitative Battery.
- Captain is to ship as pilot is to ____.
- Airplane
- Runway
- Ticket
- Passenger
Correct answer: Airplane
Airplane is correct. A captain steers a ship, so the relationship is operator to the vehicle they control; a pilot controls an airplane. A runway is where planes take off, a ticket lets you board, and a passenger rides along, but only the airplane is the vehicle being operated.
- Choose the word that best completes the sentence: The recipe called for fresh herbs, so the cook walked to the garden to ____ some.
Correct answer: Pick
Pick is correct. Getting fresh herbs from a garden means gathering them by hand, which is to pick. Throwing or burning herbs does not get them for the recipe, and buying happens at a store rather than in the garden, so picking fits the garden context.
- Violin, trumpet, drum - which word belongs with this group?
Correct answer: Flute
Flute is correct. A violin, trumpet, and drum are all musical instruments, so the shared category is instruments, and a flute is also a musical instrument. A song is music that is played, a concert is an event, and a stage is a place, none of which is an instrument.
- Thirsty is to drink as hungry is to ____.
Correct answer: Eat
Eat is correct. Being thirsty leads a person to drink, so the relationship is a need and the action that satisfies it; being hungry leads a person to eat. Cooking prepares food but does not directly satisfy hunger, a plate holds food, and sleeping addresses tiredness, not hunger.
- Choose the word that best completes the sentence: The students whispered in the library because they did not want to ____ others who were reading.
Correct answer: Disturb
Disturb is correct. People whisper in a library to avoid bothering others, and to bother someone who is reading is to disturb them. Helping, joining, or thanking others would not be reasons to whisper, so disturb fits the quiet-library context.
- Knife is to cut as broom is to ____.
Correct answer: Sweep
Sweep is correct. A knife's purpose is to cut, so this is a tool-to-function relationship; a broom's purpose is to sweep. The floor is what a broom acts on, a handle is part of the broom, and clean is a result, but sweep names the specific action the tool performs.
- Triangle, square, circle - which word belongs with this group?
Correct answer: Rectangle
Rectangle is correct. A triangle, square, and circle are all shapes, so the shared category is shapes, and a rectangle is also a shape. Red is a color, big is a size, and a ruler is a tool, so none of those belongs to the shape category.
- Caterpillar is to butterfly as tadpole is to ____.
Correct answer: Frog
Frog is correct. A caterpillar grows into a butterfly, so the relationship is an early life stage to its adult form; a tadpole grows into a frog. A pond is where a tadpole lives, a tail is a body part, and a fish is a different animal, so none captures the growth relationship.
- Choose the word that best completes the sentence: Even though it was raining hard, the determined runner refused to ____.
Correct answer: Quit
Quit is correct. A determined runner who keeps going despite hard rain refuses to give up, which is to quit. Winning is a goal rather than something refused, and smiling or stretching are unrelated to the idea of pushing on through bad weather.
- Ear is to hear as eye is to ____.
Correct answer: See
See is correct. An ear is the body part used to hear, so the relationship is a body part and its main function; an eye is used to see. Blinking is a movement of the eye, a tear is a fluid, and a face is where the eye sits, but seeing is the function that parallels hearing.
- Which best states the goal of the entire CogAT Verbal Battery?
- To measure speed at copying shapes
- To measure handwriting neatness
- To measure reasoning with words and language
- To measure how fast a student reads aloud
Correct answer: To measure reasoning with words and language
To measure reasoning with words and language is correct. The Verbal Battery, made up of Verbal Analogies, Sentence Completion, and Verbal Classification, evaluates how well a student reasons using words. It is not a test of copying shapes, handwriting, or reading-aloud speed.
- Choose the word that best completes the sentence: The museum guide spoke quietly so the visitors had to listen ____.
- Rarely
- Angrily
- Quickly
- Carefully
Correct answer: Carefully
Carefully is correct. When a speaker is quiet, listeners must pay close attention, which means listening carefully. Rarely contradicts the need to listen, angrily adds an unrelated emotion, and quickly describes speed rather than the attentive listening the context calls for.
- Pen, marker, crayon - which word belongs with this group?
Correct answer: Chalk
Chalk is correct. A pen, marker, and crayon are all tools used to write or color, and chalk is also used to write or draw. Paper is what you write on, an eraser removes marks, and a desk is furniture, so none of those is a writing-and-coloring tool like chalk.
- Loud is to quiet as fast is to ____.
Correct answer: Slow
Slow is correct. Loud and quiet are opposites, so this is an antonym relationship; the opposite of fast is slow. Bright relates to light, small relates to size, and soft is the opposite of loud rather than of fast, so slow is the matching opposite.
- Baker is to bread as farmer is to ____.
Correct answer: Crops
Crops is correct. A baker produces bread, so the relationship is a worker and what they produce; a farmer produces crops. A tractor is a tool, a barn is a building, and a market is where goods are sold, but crops are what the farmer grows and produces.
- Choose the word that best completes the sentence: The puzzle was so ____ that it took the whole family an entire weekend to finish.
- Easy
- Tiny
- Colorful
- Difficult
Correct answer: Difficult
Difficult is correct. A puzzle that takes a whole weekend for the family is hard, which means difficult. Easy is the opposite of what the long time suggests, tiny describes size, and colorful describes appearance, so difficult best fits the clue of taking a long time.
- Robin, sparrow, eagle - which word belongs with this group?
Correct answer: Owl
Owl is correct. A robin, sparrow, and eagle are all birds, so the shared category is birds, and an owl is also a bird. A nest is where birds live, a feather is a body part, and the sky is where they fly, but only the owl is itself a bird.
- Bird is to fly as fish is to ____.
Correct answer: Swim
Swim is correct. A bird moves by flying, so the relationship is an animal and how it moves; a fish moves by swimming. A scale and a gill are body parts, and water is where the fish lives, but swimming is the action that parallels flying.
- Choose the word that best completes the sentence: She placed the fragile vase carefully on the shelf so it would not ____.
Correct answer: Break
Break is correct. A fragile vase handled carefully is one a person does not want to shatter, which is to break. Growing and floating do not apply to a vase, and shining is not something to avoid, so break fits the careful handling of something fragile.
- Which relationship is shown in 'happy is to glad as sad is to unhappy'?
- Both pairs are antonyms
- Both pairs are cause and effect
- Both pairs are part and whole
- Both pairs are synonyms
Correct answer: Both pairs are synonyms
Both pairs are synonyms is correct. Happy and glad mean nearly the same, and sad and unhappy also mean nearly the same, so each pair is made of synonyms. The pairs are not opposites, not a cause leading to an effect, and not a part with its whole.
- Choose the word that best completes the sentence: The directions were so clear that even a beginner could follow them without feeling ____.
Correct answer: Confused
Confused is correct. Clear directions help a beginner understand, so they would not feel mixed up, which is confused. Happy, ready, and proud are positive feelings that clear directions might cause, but the sentence needs the negative feeling that clear directions prevent.
- Hammer, saw, screwdriver - which word belongs with this group?
Correct answer: Wrench
Wrench is correct. A hammer, saw, and screwdriver are all tools, so the shared category is tools, and a wrench is also a tool. A nail is a material a hammer drives, wood is what is being worked on, and a garage is where tools are kept, but only the wrench is itself a tool.
- Beginning is to end as start is to ____.
Correct answer: Finish
Finish is correct. Beginning and end are opposites, so this is an antonym relationship; the opposite of start is finish. A race is an event, the middle is between start and finish rather than its opposite, and open is the opposite of closed, so finish is the matching opposite.
- Choose the word that best completes the sentence: Because the soup was too hot, the child waited for it to ____ before eating.
Correct answer: Cool
Cool is correct. Soup that is too hot must lose heat before it is safe to eat, which means it should cool. Boiling makes it hotter, spilling wastes it, and freezing makes it cold and solid, so cool is the change that fits waiting before eating.
- Cub is to lion as foal is to ____.
Correct answer: Horse
Horse is correct. A cub is a young lion, so the relationship is a young animal to its adult form; a foal is a young horse. A barn is where horses live, a saddle is equipment, and hay is food, but only the horse is the adult form of a foal.
- Choose the word that best completes the sentence: The new student felt ____ on the first day but soon made many friends.
Correct answer: Nervous
Nervous is correct. A new student on the first day, before making friends, would commonly feel worried or uneasy, which is nervous. Tired relates to rest, famous and tall do not fit a first-day feeling, so nervous matches the situation of being new before fitting in.
- Carrot, potato, onion - which word belongs with this group?
Correct answer: Celery
Celery is correct. A carrot, potato, and onion are all vegetables, so the shared category is vegetables, and celery is also a vegetable. An apple is a fruit, milk is a dairy drink, and bread is a grain product, so none of those belongs to the vegetable category.
- Clock is to time as ruler is to ____.
Correct answer: Length
Length is correct. A clock measures time, so the relationship is an instrument and what it measures; a ruler measures length. Wood is what a ruler might be made of, a line is something you might draw with it, and school is where it is used, but length is what the ruler measures.
- Choose the word that best completes the sentence: The detective looked for any small ____ that might help solve the mystery.
Correct answer: Clue
Clue is correct. A detective solving a mystery searches for hints or evidence, which are clues. A snack is food, a song is music, and a cloud is in the sky, none of which helps solve a mystery, so clue fits the detective context.
- Which pair shows a part-to-whole relationship?
- Big is to large
- Hot is to cold
- Page is to book
- Rain is to flood
Correct answer: Page is to book
Page is to book is correct. A page is one part of a whole book, which is a part-to-whole relationship. Big and large are synonyms, hot and cold are antonyms, and rain and flood are cause and effect, so only page and book show part to whole.
- Cold is to ice as heat is to ____.
Correct answer: Fire
Fire is correct. Cold is connected to ice, which is something cold, so the relationship pairs a quality with a thing that has it; heat goes with fire, which is something hot. Winter and shade are linked to cold, and a blanket can keep heat in, but fire is the thing that strongly has heat.
- Choose the word that best completes the sentence: The actor practiced his lines many times so he would not ____ them on stage.
Correct answer: Forget
Forget is correct. Practicing lines many times is done to remember them, so the actor wants to avoid forgetting. Enjoying lines is not a problem to prevent, writing and hearing are not what practice for a performance guards against, so forget fits the reason for practicing.
- Monday, Tuesday, Wednesday - which word belongs with this group?
- March
- Thursday
- Morning
- Weekend
Correct answer: Thursday
Thursday is correct. Monday, Tuesday, and Wednesday are all days of the week, so the shared category is days of the week, and Thursday is also a day of the week. March is a month, morning is a time of day, and weekend names a pair of days but is not a single weekday.
- Soft is to hard as light is to ____.
Correct answer: Heavy
Heavy is correct. Soft and hard are opposites, so this is an antonym relationship; here light means not heavy, and its opposite is heavy. Bright relates to a different meaning of light, a lamp gives light, and thin is the opposite of thick, so heavy is the matching opposite.
- Choose the word that best completes the sentence: The garden grew quickly after the gardener began to ____ it every morning.
Correct answer: Water
Water is correct. Plants grow quickly when they get water, so watering the garden each morning explains the fast growth. Ignoring it would slow growth, cutting reduces plants, and painting does not help plants grow, so water fits the cause of quick growth.
- Glove is to hand as hat is to ____.
Correct answer: Head
Head is correct. A glove goes on a hand, so the relationship is clothing to the body part it covers; a hat goes on the head. A coat is another clothing item, wear is the action, and warm describes a result, but the head is the body part a hat covers.
- Which set of three words would best fit a Verbal Classification item about things that are cold?
- Fire, sun, oven
- Ice, snow, frost
- Chair, table, sofa
- Run, jump, hop
Correct answer: Ice, snow, frost
Ice, snow, frost is correct. Ice, snow, and frost are all cold things, so they share the category of cold. Fire, sun, and oven are hot, chair, table, and sofa are furniture, and run, jump, and hop are actions, so only the first set shares the cold category.
- Choose the word that best completes the sentence: Because she studied every night, Maria felt ____ for the big test.
Correct answer: Prepared
Prepared is correct. Studying every night gets a person ready, so Maria would feel prepared for the test. Sleepy and hungry describe physical states unrelated to studying, and lost suggests not understanding, the opposite of what studying produces, so prepared fits.
- Bottle is to milk as jar is to ____.
Correct answer: Jam
Jam is correct. A bottle holds milk, so the relationship is a container and what it commonly holds; a jar holds jam. Glass is what a jar may be made of, a lid covers it, and a kitchen is where it sits, but jam is the contents the jar holds.
- Choose the word that best completes the sentence: The crowd cheered ____ when the home team scored the winning goal.
- Loudly
- Silently
- Sadly
- Slowly
Correct answer: Loudly
Loudly is correct. A cheering crowd celebrating a winning goal would make a lot of noise, which is cheering loudly. Silently contradicts cheering, sadly does not fit a celebration, and slowly describes speed rather than the volume of the cheering.
- Lemon, lime, grapefruit - which word belongs with this group?
- Banana
- Orange
- Strawberry
- Grape
Correct answer: Orange
Orange is correct. A lemon, lime, and grapefruit are all citrus fruits, so the shared category is citrus, and an orange is also citrus. A banana, strawberry, and grape are fruits but not citrus fruits, so orange best fits the specific citrus category these three share.
- Whisper is to shout as walk is to ____.
Correct answer: Run
Run is correct. A whisper is a quiet, low-intensity version and a shout is loud and intense, so the relationship moves from low to high intensity; walking moves to the more intense running. Standing is no motion, a step is part of walking, and a stroll is even gentler, so run matches the higher-intensity action.
- Choose the word that best completes the sentence: The bright flashlight helped the campers ____ their way through the dark woods.
Correct answer: See
See is correct. A flashlight gives light so people can look where they are going in the dark, which means it helps them see. Hearing and tasting are unrelated to light, and throwing is not how a flashlight helps in the woods, so see fits the use of a flashlight.
- Which relationship type connects 'medicine is to cure'?
- A thing and its purpose or function
- A word and its opposite
- A whole and one of its parts
- Two words that mean the same
Correct answer: A thing and its purpose or function
A thing and its purpose or function is correct. Medicine is used to cure illness, so the pair links a thing to what it is meant to do. It is not an opposite pair, not a whole-and-part pair, and the two words do not mean the same thing.
- Picture analogy: a key is shown next to a lock, and a stamp is shown next to an empty space. What completes it?
- A door
- An envelope
- A house
- A pencil
Correct answer: An envelope
An envelope is correct. A key is used with a lock, so the pair shows an item with the thing it is used on; a stamp is used on an envelope. A door goes with the key-and-lock side, a house is unrelated to a stamp, and a pencil is not where a stamp is placed.
- Choose the word that best completes the sentence: The old map was so ____ that the explorers could barely read the faded writing.
Correct answer: Worn
Worn is correct. An old map with faded writing has been used and damaged over time, which means it is worn. New contradicts being old and faded, loud relates to sound, and tasty relates to food, so worn fits a map that is hard to read because it is faded.
- Sand is to beach as snow is to ____.
Correct answer: Mountain
Mountain is correct. Sand is the ground material you find at a beach, so the relationship pairs a material with the place it covers; snow covers a mountain. Rain is different precipitation, and cold and white describe snow rather than naming a place, so mountain best fits as the place.
- Swim, dive, float - which word belongs with this group?
Correct answer: Paddle
Paddle is correct. Swim, dive, and float are all things you do in the water, so the shared category is water activities, and paddling is also done in the water. A towel, a pool, and sunscreen are objects or places related to water, but only paddle is an action done in the water like the others.
- Choose the word that best completes the sentence: After weeks without rain, the farmer was ____ to see dark clouds gathering overhead.
- Bored
- Relieved
- Frightened
- Jealous
Correct answer: Relieved
Relieved is correct. A farmer needing rain after weeks of drought would feel glad and less worried when rain clouds appear, which is feeling relieved. Bored, frightened, and jealous do not fit the welcome arrival of much-needed rain, so relieved matches the context.
- Empty is to full as begin is to ____.
Correct answer: End
End is correct. Empty and full are opposites, so this is an antonym relationship; the opposite of begin is end. Open is the opposite of closed, start is a synonym of begin, and wait is unrelated, so end is the matching opposite of begin.
- Choose the word that best completes the sentence: The chef tasted the sauce and decided it needed more salt to improve its ____.
Correct answer: Flavor
Flavor is correct. Adding salt changes how food tastes, so it improves the sauce's flavor. Color, weight, and shape are not what salt changes when a chef tastes and adjusts a sauce, so flavor fits the idea of seasoning to taste.
- Doctor, nurse, dentist - which word belongs with this group?
- Surgeon
- Hospital
- Patient
- Medicine
Correct answer: Surgeon
Surgeon is correct. A doctor, nurse, and dentist are all people who work in health care, so the shared category is health-care workers, and a surgeon is also a health-care worker. A hospital is a place, a patient is who they help, and medicine is a treatment, but only the surgeon is a health-care worker.
- Seed is to plant as egg is to ____.
Correct answer: Chick
Chick is correct. A seed grows into a plant, so the relationship is a starting form to what it becomes; an egg hatches into a chick. A nest holds the egg, a shell is part of the egg, and a farm is a place, but only the chick is what the egg becomes.
- Choose the word that best completes the sentence: The library was so ____ that you could hear a pin drop.
Correct answer: Silent
Silent is correct. Being able to hear a pin drop describes a place with almost no sound, which is silent. Crowded, messy, and bright describe other qualities and do not explain why a tiny sound could be heard, so silent fits the very quiet library.
- Pilot is to airplane as driver is to ____.
Correct answer: Car
Car is correct. A pilot operates an airplane, so the relationship is an operator and the vehicle they control; a driver operates a car. A road is where the car travels, an engine is a part, and a garage is where it is parked, but only the car is the vehicle being operated.
- Which relationship is shown in 'thirsty is to drink as cold is to warm-up'?
- A condition and the action that relieves it
- Two opposites
- Two synonyms
- A whole and a part
Correct answer: A condition and the action that relieves it
A condition and the action that relieves it is correct. Being thirsty leads you to drink, and being cold leads you to warm up, so each pair links a condition with the action that fixes it. The pairs are not opposites or synonyms, and they are not whole-and-part.
- Choose the word that best completes the sentence: The kitten was so ____ that it chased the ball of yarn all around the room.
Correct answer: Playful
Playful is correct. A kitten that chases yarn around the room is full of energy and fun, which means it is playful. Sleepy would mean resting, angry and shy do not match chasing yarn happily, so playful fits the lively behavior described.
- North, south, east - which word belongs with this group?
Correct answer: West
West is correct. North, south, and east are all compass directions, so the shared category is directions, and west is also a compass direction. A map shows directions, left is relative rather than a compass direction, and near describes distance, so west best fits the group.
- Calf is to cow as lamb is to ____.
Correct answer: Sheep
Sheep is correct. A calf is a young cow, so the relationship is a young animal to its adult form; a lamb is a young sheep. Wool comes from sheep, a field is where they graze, and a shepherd tends them, but only the sheep is the adult form of a lamb.
- Choose the word that best completes the sentence: The instructions said to mix the ingredients ____ so the batter would be smooth.
- Thoroughly
- Rarely
- Loudly
- Secretly
Correct answer: Thoroughly
Thoroughly is correct. To get a smooth batter, you must mix completely and well, which means mixing thoroughly. Rarely would leave it lumpy, loudly relates to sound, and secretly relates to hiding, none of which produces a smooth batter, so thoroughly fits.
- Tall is to short as wide is to ____.
Correct answer: Narrow
Narrow is correct. Tall and short are opposites, so this is an antonym relationship; the opposite of wide is narrow. Long is the opposite of short in length, deep relates to depth, and big relates to overall size, so narrow is the matching opposite of wide.
- Choose the word that best completes the sentence: Even after losing the game, the players showed good ____ by shaking hands with their opponents.
- Hunger
- Speed
- Sportsmanship
- Homework
Correct answer: Sportsmanship
Sportsmanship is correct. Shaking hands with opponents after losing shows fair and respectful behavior in sports, which is good sportsmanship. Hunger, speed, and homework are unrelated to behaving respectfully after a game, so sportsmanship fits the polite gesture.
- Brush, comb, razor - which word belongs with this group?
Correct answer: Scissors
Scissors is correct. A brush, comb, and razor are all grooming tools you use on hair, and scissors are also a tool used to cut hair. A mirror, soap, and towel are bathroom items, but only scissors is a hair-grooming tool like the other three.
- Foot is to shoe as hand is to ____.
Correct answer: Glove
Glove is correct. A shoe covers a foot, so the relationship is a body part and the item that covers it; a glove covers a hand. A finger and a wrist are parts of the hand, and an arm is connected to it, but only a glove is the covering for a hand.
- Choose the word that best completes the sentence: The volcano had been quiet for years, but scientists worried it might ____ again.
Correct answer: Erupt
Erupt is correct. A volcano that has been quiet may become active and burst out lava and ash, which is to erupt. Sleeping is the opposite of becoming active, and freezing or shrinking do not describe what a volcano does, so erupt fits the scientists' worry.
- Which pair shows a cause-and-effect relationship?
- Couch is to sofa
- Big is to small
- Spark is to flame
- Toe is to foot
Correct answer: Spark is to flame
Spark is to flame is correct. A spark can cause a flame, which is a cause-and-effect relationship. Couch and sofa are synonyms, big and small are antonyms, and toe and foot are part and whole, so only spark and flame show cause and effect.
- River, lake, ocean - which word belongs with this group?
Correct answer: Pond
Pond is correct. A river, lake, and ocean are all bodies of water, so the shared category is bodies of water, and a pond is also a body of water. A mountain, desert, and valley are land features rather than water, so pond best fits the group.
- Choose the word that best completes the sentence: The story was so ____ that the children begged to hear it again.
Correct answer: Exciting
Exciting is correct. Children asking to hear a story again means they really enjoyed it, so it was exciting. Boring would make them not want it repeated, while short and quiet describe other features that do not explain why they begged to hear it again, so exciting fits.
- Spider is to web as bee is to ____.
Correct answer: Hive
Hive is correct. A spider builds a web to live in, so the relationship is an animal and the structure it builds as a home; a bee builds a hive. Honey is what bees make, a flower is where they gather nectar, and a sting is a defense, but the hive is the home structure they build.
- Choose the word that best completes the sentence: Because the room was dark, she reached for the switch to turn on the ____.
Correct answer: Light
Light is correct. A dark room is made brighter by turning on a light, so reaching for a switch to fix the darkness means turning on the light. Music, water, and an oven do not solve a dark room, so light fits the cause of reaching for the switch.
- Quick is to rapid as huge is to ____.
Correct answer: Enormous
Enormous is correct. Quick and rapid mean nearly the same, so this is a synonym relationship; a synonym for huge is enormous. Tiny is an opposite, while round and loud describe unrelated qualities, so enormous is the word that means the same as huge.
- Crayon, paint, marker - which word belongs with this group?
- Colored pencil
- Canvas
- Easel
- Artist
Correct answer: Colored pencil
Colored pencil is correct. A crayon, paint, and marker are all things used to add color to a picture, and a colored pencil is also used to color. A canvas is what you draw on, an easel holds the canvas, and an artist is a person, so only the colored pencil is a coloring tool.
- Choose the word that best completes the sentence: The hikers carried plenty of water because the trail was long and the day was very ____.
Correct answer: Hot
Hot is correct. Carrying plenty of water on a long trail makes sense when the weather is hot, since heat makes people thirsty. Cold weather would reduce the need for extra water, and short or easy would not require plenty of water, so hot fits the reason for carrying water.
- Page is to book as room is to ____.
Correct answer: House
House is correct. A page is one part of a whole book, so the relationship is part to whole; a room is one part of a whole house. A door, wall, and floor are smaller parts of a room, so the whole that a room belongs to is the house.
- Choose the word that best completes the sentence: The puppy was ____ to its owner and followed her everywhere.
Correct answer: Loyal
Loyal is correct. A puppy that follows its owner everywhere is faithful and devoted, which is being loyal. Rude and lazy describe negative behaviors that do not match following someone faithfully, and silent describes sound, so loyal fits the devoted puppy.
- Which relationship best fits the analogy 'closed is to open as absent is to present'?
- Both pairs are opposites
- Both pairs are synonyms
- Both pairs are cause and effect
- Both pairs are part and whole
Correct answer: Both pairs are opposites
Both pairs are opposites is correct. Closed and open are opposites, and absent and present are also opposites, so each pair is an antonym pair. The pairs are not synonyms, not cause and effect, and not whole-and-part relationships.
- Mercury, Venus, Earth - which word belongs with this group?
Correct answer: Mars
Mars is correct. Mercury, Venus, and Earth are all planets, so the shared category is planets, and Mars is also a planet. The Moon orbits Earth, the Sun is a star at the center of the system, and a star is not a planet, so Mars best fits the planet category.
- Painter is to brush as writer is to ____.
Correct answer: Pen
Pen is correct. A painter uses a brush as a tool, so the relationship is a worker and the tool they use; a writer uses a pen. A book and a story are what a writer produces, and a desk is furniture, but the pen is the tool the writer uses.
- Choose the word that best completes the sentence: The ice on the pond was too thin, so the sign warned skaters that it was ____.
- Delicious
- Colorful
- Cheerful
- Dangerous
Correct answer: Dangerous
Dangerous is correct. Thin ice that could break under skaters is unsafe, so a warning sign would call it dangerous. Delicious relates to taste, and colorful and cheerful are positive descriptions that do not warn of harm, so dangerous fits a warning about thin ice.
- Wing is to bird as fin is to ____.
Correct answer: Fish
Fish is correct. A wing is a body part of a bird that helps it move, so the relationship is a body part to the animal it belongs to; a fin belongs to a fish. Water and ocean are where a fish lives, and a scale is another fish part, but the animal that has fins is the fish.
- Choose the word that best completes the sentence: The mountain trail was steep, so the climbers had to move ____ to keep from slipping.
- Carelessly
- Cautiously
- Happily
- Loudly
Correct answer: Cautiously
Cautiously is correct. On a steep trail where slipping is a risk, climbers would move carefully to stay safe, which is cautiously. Carelessly would increase the risk, and happily or loudly do not describe safe movement, so cautiously fits the need to avoid slipping.
- Pizza, sandwich, taco - which word belongs with this group?
Correct answer: Burger
Burger is correct. Pizza, a sandwich, and a taco are all foods you eat for a meal, so the shared category is meal foods, and a burger is also a food. A plate holds food, a kitchen is where it is made, and a menu lists foods, but only the burger is itself a food.
- Soap is to clean as glue is to ____.
Correct answer: Stick
Stick is correct. Soap's purpose is to clean, so this is a tool-to-function relationship; glue's purpose is to stick things together. Wet describes what glue feels like, a bottle holds it, and paper is what it might join, but stick names the function glue performs.
- Choose the word that best completes the sentence: The audience grew ____ as the magician slowly revealed his final trick.
Correct answer: Curious
Curious is correct. Slowly revealing a final trick builds interest and makes people want to know what will happen, which is being curious. Sleepy, hungry, and bored are unrelated or opposite to growing interest, so curious fits the suspense of a slow reveal.
- Frame is to picture as cover is to ____.
Correct answer: Book
Book is correct. A frame surrounds and protects a picture, so the relationship is a protective outside part and what it surrounds; a cover surrounds and protects a book. A page and a title are inside parts, and a shelf holds books, but the cover goes around the book.
- Choose the word that best completes the sentence: The toddler was learning to walk and would often ____ before standing back up.
Correct answer: Stumble
Stumble is correct. A toddler learning to walk often trips and falls before getting up again, which is to stumble. Sprinting requires steady walking first, and swimming or singing have nothing to do with learning to walk, so stumble fits the toddler's wobbly steps.
- Happy, excited, cheerful - which word belongs with this group?
Correct answer: Joyful
Joyful is correct. Happy, excited, and cheerful all describe positive, upbeat feelings, so the shared category is happy feelings, and joyful is also a happy feeling. Tired, afraid, and calm describe different states that are not upbeat happiness, so joyful best fits the group.
- Hard is to soft as rough is to ____.
Correct answer: Smooth
Smooth is correct. Hard and soft are opposites, so this is an antonym relationship; the opposite of rough is smooth. Bumpy is similar to rough, sharp relates to edges, and heavy relates to weight, so smooth is the matching opposite of rough.
- Choose the word that best completes the sentence: The bakery smelled ____ because fresh bread had just come out of the oven.
- Terrible
- Wonderful
- Quiet
- Empty
Correct answer: Wonderful
Wonderful is correct. Fresh bread from the oven gives off a pleasant smell, so the bakery would smell wonderful. Terrible is the opposite of a pleasant smell, and quiet and empty describe sound or space rather than smell, so wonderful fits the fresh-bread aroma.
- Which describes how to solve a Verbal Analogy that uses the relationship type 'function'?
- Find the opposite of the first word
- Count the letters in each word
- Find what the first thing is used to do, then match it for the second thing
- Find a word that rhymes with the first
Correct answer: Find what the first thing is used to do, then match it for the second thing
Finding what the first thing is used to do, then matching it for the second thing is correct. In a function analogy, the link is what an object does, so you identify that action and apply the same kind of action to the second item. Finding opposites, counting letters, or finding rhymes does not solve a function analogy.
- Cloud is to rain as seed is to ____.
Correct answer: Plant
Plant is correct. A cloud can produce rain, so the relationship is a source and what it produces or becomes; a seed produces a plant. Soil and sun help a seed grow, and a garden is where it grows, but the plant is what the seed becomes, matching the relationship.
- Choose the word that best completes the sentence: The librarian asked the students to handle the rare books with great ____.
Correct answer: Care
Care is correct. Rare books are valuable and easily damaged, so they should be handled gently and carefully, which is with care. Speed, noise, and anger would risk harming the books, so care fits the librarian's request to protect rare books.
- Circle, oval, sphere - which word belongs with this group?
Correct answer: Ring
Ring is correct. A circle, oval, and sphere are all round shapes with no corners, so the shared category is round shapes, and a ring is also round. A square, triangle, and cube all have straight sides and corners, so they are not round, making ring the best fit.
- Teacher is to student as coach is to ____.
Correct answer: Player
Player is correct. A teacher instructs a student, so the relationship is an instructor and the person being instructed; a coach instructs a player. A team is a group, a field is a place, and a whistle is a tool, but the player is the individual the coach instructs.
- Choose the word that best completes the sentence: After running the race, the athlete was out of breath and needed to ____ for a moment.
Correct answer: Rest
Rest is correct. An athlete out of breath after a race needs to stop and recover, which is to rest. Jumping and shouting use more energy, and studying is unrelated to recovering after running, so rest fits the need to catch one's breath.
- Which pair are synonyms?
- Begin is to start
- Up is to down
- Wheel is to car
- Cloud is to rain
Correct answer: Begin is to start
Begin is to start is correct. Begin and start mean the same thing, so they are synonyms. Up and down are opposites, wheel and car are part and whole, and cloud and rain are cause and effect, so only begin and start are synonyms.
- Choose the word that best completes the sentence: The path through the forest was hidden, so the campers needed a guide to help them ____ the way.
Correct answer: Find
Find is correct. A hidden path means the campers must discover the route, so a guide helps them find the way. Losing, forgetting, or ignoring the way are the opposite of what a guide helps with, so find fits the need to discover a hidden path.
- Whale, dolphin, shark - which word belongs with this group?
Correct answer: Seal
Seal is correct. A whale, dolphin, and shark are all animals that live in the ocean, so the shared category is sea animals, and a seal is also a sea animal. A boat, a wave, and a net are objects or features of the sea but not animals, so seal best fits the group.
- Hot is to warm as freezing is to ____.
Correct answer: Cool
Cool is correct. Hot is a strong version and warm is a milder version of the same idea, so the relationship moves from very hot to a little hot; freezing is very cold and a milder version is cool. Boiling is very hot, wet relates to water, and frozen is as extreme as freezing, so cool matches the milder version.
- Choose the word that best completes the sentence: The clever fox managed to ____ the trap and escape without being caught.
Correct answer: Avoid
Avoid is correct. A fox that escapes without being caught must stay away from the trap, which is to avoid it. Building, painting, or buying a trap are unrelated to escaping, so avoid fits the idea of a clever fox getting away safely.
- Stem is to flower as trunk is to ____.
Correct answer: Tree
Tree is correct. A stem is the main supporting part of a flower, so the relationship is a supporting part to the whole plant; a trunk is the main supporting part of a tree. A leaf and a branch are smaller parts, and a forest is many trees, so the tree is the whole the trunk supports.
- Choose the word that best completes the sentence: The teacher praised the essay for being clear and well ____.
Correct answer: Organized
Organized is correct. An essay praised for being clear is also likely arranged in a sensible order, which is well organized. Torn, wet, and spilled describe physical damage and have nothing to do with the quality of writing, so organized fits the praise for a clear essay.
- Boots, sandals, sneakers - which word belongs with this group?
Correct answer: Slippers
Slippers is correct. Boots, sandals, and sneakers are all types of footwear you wear on your feet, and slippers are also footwear. Socks go on under shoes, laces are part of some shoes, and feet are body parts, so only slippers belong to the footwear category.
- Which relationship type is shown in 'wheel is to bicycle'?
- Part to whole
- Synonym
- Antonym
- Cause and effect
Correct answer: Part to whole
Part to whole is correct. A wheel is one part of a complete bicycle, which is a part-to-whole relationship. The two words do not mean the same, are not opposites, and one does not cause the other, so part to whole is the right relationship.
- Choose the word that best completes the sentence: The young plant grew toward the window because it needed ____ to make food.
- Darkness
- Sunlight
- Silence
- Music
Correct answer: Sunlight
Sunlight is correct. Plants use light to make their food, so a plant grows toward a window to reach sunlight. Darkness would not help it make food, and silence and music are unrelated to a plant's needs, so sunlight fits why the plant leans toward the window.
- Joey is to kangaroo as cub is to ____.
Correct answer: Bear
Bear is correct. A joey is a young kangaroo, so the relationship is a young animal to its adult form; a cub is a young bear. A den is where a bear lives, a claw is a body part, and a forest is a place, but only the bear is the adult form of a cub.
- Choose the word that best completes the sentence: The bridge was strong enough to ____ the weight of heavy trucks.
Correct answer: Support
Support is correct. A strong bridge holds up the weight placed on it, so it can support heavy trucks. Dropping the weight is the opposite of being strong, and melting or coloring are unrelated to holding weight, so support fits a strong bridge.
- Honest, truthful, sincere - which word belongs with this group?
Correct answer: Genuine
Genuine is correct. Honest, truthful, and sincere all describe a person who tells the truth and means what they say, so the shared category is honesty traits, and genuine fits that same idea. Sneaky is the opposite, while fast and quiet describe unrelated qualities, so genuine best fits the group.
- Old is to young as ancient is to ____.
Correct answer: Modern
Modern is correct. Old and young are opposites, so this is an antonym relationship; ancient means very old, and its opposite is modern, meaning new or current. Tired, wise, and broken describe other qualities, so modern is the matching opposite of ancient.
- Choose the word that best completes the sentence: Because the directions were written in a language she did not know, the traveler felt completely ____.
Correct answer: Lost
Lost is correct. Not understanding the directions would leave the traveler unsure of where to go, which means feeling lost. Proud, calm, and rested are positive feelings that do not match being unable to read directions, so lost fits the confusion described.
- Telescope is to stars as microscope is to ____.
- Planets
- Books
- Mountains
- Germs
Correct answer: Germs
Germs is correct. A telescope helps you see faraway stars, so the relationship is a tool and what it helps you see; a microscope helps you see tiny things like germs. Planets are seen through a telescope, books are read, and mountains are seen with the eyes, so germs fit what a microscope reveals.
- Choose the word that best completes the sentence: The class grew ____ when the principal announced an extra recess.
Correct answer: Excited
Excited is correct. Hearing about an extra recess is good news for students, so the class would become happy and eager, which is excited. Upset is a negative reaction, and sleepy or silent do not match the cheerful news, so excited fits the announcement.
- Pebble, boulder, gravel - which word belongs with this group?
Correct answer: Stone
Stone is correct. A pebble, boulder, and gravel are all kinds or pieces of rock, so the shared category is rock, and a stone is also rock. Water, a tree, and a cloud are not rock, so stone best fits the group of rock-related items.
- Which relationship is shown in 'practice is to improvement'?
- Synonym
- Antonym
- Cause and effect
- Part to whole
Correct answer: Cause and effect
Cause and effect is correct. Practicing leads to getting better, so practice causes improvement, which is a cause-and-effect relationship. The two words do not mean the same, are not opposites, and are not a part and a whole, so cause and effect is the relationship.
- Choose the word that best completes the sentence: The campers built a fire to stay ____ during the cold night.
Correct answer: Warm
Warm is correct. A fire gives off heat, so campers build one to keep warm on a cold night. Wet, loud, and tall do not describe what a fire helps with on a cold night, so warm fits the reason for building the fire.
- Leaf is to tree as petal is to ____.
Correct answer: Flower
Flower is correct. A leaf is a part of a tree, so the relationship is a part to the whole plant it belongs to; a petal is a part of a flower. A stem is another part, a garden is where it grows, and a vase holds it, but the flower is the whole the petal belongs to.
- Choose the word that best completes the sentence: The store was having a sale, so the shoes were sold at a lower ____ than usual.
Correct answer: Price
Price is correct. A sale means items cost less money, so the shoes were sold at a lower price. Color, size, and smell are not what a sale lowers, so price fits the idea of items costing less during a sale.
- Choose the word that best completes the sentence: The detective spoke in a calm voice, but inside she was ____ to learn the truth.
Correct answer: Eager
Eager is correct. Wanting very much to learn the truth means being keen and excited to find out, which is eager. Sleepy and bored suggest a lack of interest, and silent describes sound rather than a feeling, so eager fits the detective wanting to know the truth.
- Knee is to leg as elbow is to ____.
Correct answer: Arm
Arm is correct. A knee is a joint in the leg, so the relationship is a joint to the limb it is part of; an elbow is a joint in the arm. A hand and a wrist are other parts of the arm, and a shoulder is a different joint, but the whole limb the elbow belongs to is the arm.
- On the CogAT Quantitative Battery, the Number Analogies subtest asks a test-taker to do which of the following?
- Find a numerical rule shown in completed number pairs and apply that same rule to a new pair
- Choose the picture that does not belong with three others
- Select a word that completes a sentence
- Visualize where holes appear when folded paper is unfolded
Correct answer: Find a numerical rule shown in completed number pairs and apply that same rule to a new pair
Finding a numerical rule in completed number pairs and applying it to a new pair is the Number Analogies task. The subtest presents two or three model pairs that share a hidden rule, then gives a third number and asks for its partner. Choosing odd-one-out pictures, completing sentences, and unfolding paper belong to other batteries.
- A Number Analogies item shows the pairs [2→4] and [3→6]. What number completes the pair [5→00]?
Correct answer: 10
The answer is 10 because each first number is doubled to get its partner: 2 becomes 4 and 3 becomes 6, so 5 becomes 10. Adding (7) or other small offsets does not match both model pairs, so doubling is the only consistent rule.
- A Number Analogies item shows [10→7] and [8→5]. What number completes [6→00]?
Correct answer: 3
The answer is 3 because each partner is found by subtracting 3: 10 minus 3 is 7 and 8 minus 3 is 5, so 6 minus 3 is 3. Subtracting a different amount would break one of the model pairs.
- A Number Analogies item shows [3→9] and [4→12]. What number completes [6→00]?
Correct answer: 18
The answer is 18 because each first number is multiplied by 3: 3 times 3 is 9 and 4 times 3 is 12, so 6 times 3 is 18. The rule is multiply by 3, which only 18 satisfies.
- A Number Analogies item shows [12→6] and [20→10]. What number completes [16→00]?
Correct answer: 8
The answer is 8 because each partner is half of its first number: 12 halved is 6 and 20 halved is 10, so 16 halved is 8. The consistent rule is dividing by 2.
- A Number Analogies item shows [1→3] and [4→6]. What number completes [7→00]?
Correct answer: 9
The answer is 9 because each partner is 2 more than its first number: 1 plus 2 is 3 and 4 plus 2 is 6, so 7 plus 2 is 9. The rule add 2 fits both models.
- A Number Analogies item shows [5→10] and [7→14]. What number completes [9→00]?
Correct answer: 18
The answer is 18 because each first number is doubled: 5 becomes 10 and 7 becomes 14, so 9 becomes 18. Doubling is the only rule that matches both example pairs.
- A Number Analogies item shows [8→4] and [14→7]. What number completes [10→00]?
Correct answer: 5
The answer is 5 because each partner is half the first number: 8 halved is 4 and 14 halved is 7, so 10 halved is 5. The shared rule is divide by 2.
- A Number Analogies item shows [2→5] and [4→7]. What number completes [9→00]?
Correct answer: 12
The answer is 12 because each partner is 3 more than its first number: 2 plus 3 is 5 and 4 plus 3 is 7, so 9 plus 3 is 12. The add-3 rule matches both pairs.
- A Number Analogies item shows [6→2] and [15→5]. What number completes [9→00]?
Correct answer: 3
The answer is 3 because each partner is one-third of the first number: 6 divided by 3 is 2 and 15 divided by 3 is 5, so 9 divided by 3 is 3. Dividing by 3 is the only consistent rule.
- A Number Analogies item shows [4→8] and [6→12]. What number completes [10→00]?
Correct answer: 20
The answer is 20 because each first number is doubled: 4 becomes 8 and 6 becomes 12, so 10 becomes 20. The model pairs both confirm a times-2 rule.
- A Number Analogies item shows [9→6] and [12→9]. What number completes [7→00]?
Correct answer: 4
The answer is 4 because each partner is 3 less than its first number: 9 minus 3 is 6 and 12 minus 3 is 9, so 7 minus 3 is 4. Subtracting 3 fits both models.
- A Number Analogies item shows [3→12] and [5→20]. What number completes [6→00]?
Correct answer: 24
The answer is 24 because each first number is multiplied by 4: 3 times 4 is 12 and 5 times 4 is 20, so 6 times 4 is 24. The times-4 rule is the only one that works for both examples.
- A Number Analogies item shows [11→9] and [20→18]. What number completes [15→00]?
Correct answer: 13
The answer is 13 because each partner is 2 less than its first number: 11 minus 2 is 9 and 20 minus 2 is 18, so 15 minus 2 is 13. The shared rule is subtract 2.
- A Number Analogies item shows [2→6] and [3→9]. What number completes [8→00]?
Correct answer: 24
The answer is 24 because each first number is tripled: 2 times 3 is 6 and 3 times 3 is 9, so 8 times 3 is 24. Tripling is the rule confirmed by both pairs.
- A Number Analogies item shows [16→8] and [24→12]. What number completes [40→00]?
Correct answer: 20
The answer is 20 because each partner is half the first number: 16 halved is 8 and 24 halved is 12, so 40 halved is 20. The divide-by-2 rule holds for all the pairs.
- A Number Analogies item shows [1→4] and [2→5]. What number completes [10→00]?
Correct answer: 13
The answer is 13 because each partner is 3 more than the first number: 1 plus 3 is 4 and 2 plus 3 is 5, so 10 plus 3 is 13. The add-3 rule fits both examples.
- A Number Analogies item shows [5→25] and [2→10]. What number completes [4→00]?
Correct answer: 20
The answer is 20 because each first number is multiplied by 5: 5 times 5 is 25 and 2 times 5 is 10, so 4 times 5 is 20. The times-5 rule matches both model pairs.
- A Number Analogies item shows [18→15] and [10→7]. What number completes [6→00]?
Correct answer: 3
The answer is 3 because each partner is 3 less than its first number: 18 minus 3 is 15 and 10 minus 3 is 7, so 6 minus 3 is 3. Subtracting 3 is the consistent rule.
- A Number Analogies item shows [7→14] and [10→20]. What number completes [12→00]?
Correct answer: 24
The answer is 24 because each first number is doubled: 7 becomes 14 and 10 becomes 20, so 12 becomes 24. The doubling rule is confirmed by both pairs.
- A Number Analogies item shows [4→7] and [9→12]. What number completes [11→00]?
Correct answer: 14
The answer is 14 because each partner is 3 more than its first number: 4 plus 3 is 7 and 9 plus 3 is 12, so 11 plus 3 is 14. The add-3 rule matches both examples.
- A Number Analogies item shows [20→4] and [25→5]. What number completes [35→00]?
Correct answer: 7
The answer is 7 because each partner is one-fifth of the first number: 20 divided by 5 is 4 and 25 divided by 5 is 5, so 35 divided by 5 is 7. Dividing by 5 is the only consistent rule.
- A Number Analogies item shows [3→5] and [8→10]. What number completes [14→00]?
Correct answer: 16
The answer is 16 because each partner is 2 more than its first number: 3 plus 2 is 5 and 8 plus 2 is 10, so 14 plus 2 is 16. The add-2 rule fits both pairs.
- A Number Analogies item shows [6→18] and [4→12]. What number completes [7→00]?
Correct answer: 21
The answer is 21 because each first number is multiplied by 3: 6 times 3 is 18 and 4 times 3 is 12, so 7 times 3 is 21. The times-3 rule matches both examples.
- A Number Analogies item shows [30→25] and [12→7]. What number completes [20→00]?
Correct answer: 15
The answer is 15 because each partner is 5 less than its first number: 30 minus 5 is 25 and 12 minus 5 is 7, so 20 minus 5 is 15. The subtract-5 rule fits both pairs.
- A Number Analogies item shows [2→8] and [3→12]. What number completes [5→00]?
Correct answer: 20
The answer is 20 because each first number is multiplied by 4: 2 times 4 is 8 and 3 times 4 is 12, so 5 times 4 is 20. The times-4 rule is the only consistent one.
- In a Number Analogies item, the first model pair adds 5 and the new pair starts with 13. If the same rule must apply, what is the partner of 13?
Correct answer: 18
The answer is 18 because the rule from the model pair, add 5, must be applied to the new number: 13 plus 5 is 18. The whole point of a number analogy is to carry the same operation to the new pair, so subtracting (8) is wrong.
- In a Number Analogies item, the model pairs all subtract 4. What is the partner of 22 under this rule?
Correct answer: 18
The answer is 18 because applying the rule subtract 4 to 22 gives 22 minus 4, which is 18. The new pair must follow the same operation found in the models, so adding (26) would be incorrect.
- A student notices that in a Number Analogies item the partner numbers are always triple the first numbers. Under this rule, what partners 8?
Correct answer: 24
The answer is 24 because the established rule triple it means 8 times 3, which is 24. Recognizing and reapplying the multiply-by-3 relationship is exactly what the Number Analogies subtest measures.
- A Number Analogies item shows [9→3] and [21→7]. What number completes [27→00]?
Correct answer: 9
The answer is 9 because each partner is one-third of the first number: 9 divided by 3 is 3 and 21 divided by 3 is 7, so 27 divided by 3 is 9. The divide-by-3 rule fits both models.
- On the CogAT Quantitative Battery, the Number Puzzles subtest asks a test-taker to do which of the following?
- Match a number pair to a relationship rule
- Pick the next number in a sequence
- Find the value that makes both sides of an equation equal
- Select the figure that completes a matrix
Correct answer: Find the value that makes both sides of an equation equal
Finding the value that balances both sides of an equation is the Number Puzzles task, an equation-balancing skill. The subtest shows an open sentence such as a box plus a number equals another expression and asks what value the box stands for. Choosing the next number, matching pairs, and completing matrices belong to other subtests.
- In a Number Puzzles item, the box must make both sides equal: □+4=9. What value belongs in the box?
Correct answer: 5
The answer is 5 because 5 plus 4 equals 9, balancing the equation. Number Puzzles asks for the value that makes both sides equal, and only 5 does that here.
- In a Number Puzzles item, the box balances the equation: □+7=15. What value belongs in the box?
Correct answer: 8
The answer is 8 because 8 plus 7 equals 15, making both sides equal. The Number Puzzles task is to find the value that balances the equation, and 8 is that value.
- In a Number Puzzles item: □−3=6. What value belongs in the box?
Correct answer: 9
The answer is 9 because 9 minus 3 equals 6, balancing both sides. To undo the subtraction you add 3 to 6, which gives 9.
- In a Number Puzzles item: □−5=10. What value belongs in the box?
Correct answer: 15
The answer is 15 because 15 minus 5 equals 10, making the equation balance. Adding 5 back to 10 recovers the box value of 15.
- In a Number Puzzles item: □×2=12. What value belongs in the box?
Correct answer: 6
The answer is 6 because 6 times 2 equals 12, balancing the equation. Dividing 12 by 2 finds the box value, which is 6.
- In a Number Puzzles item: □×3=18. What value belongs in the box?
Correct answer: 6
The answer is 6 because 6 times 3 equals 18, making both sides equal. Dividing 18 by 3 gives the box value of 6.
- In a Number Puzzles item: 8=□+3. What value belongs in the box?
Correct answer: 5
The answer is 5 because 5 plus 3 equals 8, balancing the equation. The box can sit on either side; here 8 minus 3 gives the box value of 5.
- In a Number Puzzles item: 20=□+12. What value belongs in the box?
Correct answer: 8
The answer is 8 because 8 plus 12 equals 20, making both sides equal. Subtracting 12 from 20 yields the box value of 8.
- In a Number Puzzles item, the two sides must match: □+2=3+4. What value belongs in the box?
Correct answer: 5
The answer is 5 because the right side, 3 plus 4, equals 7, so the box plus 2 must also equal 7, meaning the box is 5. Balancing both sides is the core Number Puzzles skill.
- In a Number Puzzles item: □+6=5+5. What value belongs in the box?
Correct answer: 4
The answer is 4 because the right side, 5 plus 5, equals 10, so the box plus 6 must equal 10, making the box 4. Only 4 keeps both sides equal.
- In a Number Puzzles item: □+1=2+6. What value belongs in the box?
Correct answer: 7
The answer is 7 because the right side, 2 plus 6, equals 8, so the box plus 1 must equal 8, making the box 7. Balancing the equation gives 7.
- In a Number Puzzles item: □−2=4+1. What value belongs in the box?
Correct answer: 7
The answer is 7 because the right side, 4 plus 1, equals 5, so the box minus 2 must equal 5, meaning the box is 7. Adding 2 back to 5 recovers the box value.
- In a Number Puzzles item, two shapes stand for numbers. A star equals 3. The equation is star + box = 10. What value belongs in the box?
Correct answer: 7
The answer is 7 because the star equals 3, so the equation becomes 3 plus box equals 10, making the box 7. Substituting the known shape value first is how shape-and-number puzzles are solved.
- In a Number Puzzles item, a circle equals 5. The equation is circle + box = 12. What value belongs in the box?
Correct answer: 7
The answer is 7 because the circle equals 5, so the equation becomes 5 plus box equals 12, making the box 7. Replacing the shape with its value reveals the answer.
- In a Number Puzzles item, a triangle equals 4. The equation is triangle + triangle = box. What value belongs in the box?
Correct answer: 8
The answer is 8 because each triangle equals 4, so triangle plus triangle is 4 plus 4, which is 8. The box must equal the total of both triangles.
- In a Number Puzzles item, a square equals 2. The equation is square + square + box = 9. What value belongs in the box?
Correct answer: 5
The answer is 5 because the two squares total 2 plus 2, which is 4, so 4 plus box equals 9, making the box 5. Substituting the shape value before solving gives 5.
- In a Number Puzzles item: □+□=14. What value belongs in each box?
Correct answer: 7
The answer is 7 because two equal boxes that sum to 14 must each be half of 14, which is 7. Since both boxes hold the same value, dividing 14 by 2 gives 7.
- In a Number Puzzles item: □+□+□=18. What value belongs in each box?
Correct answer: 6
The answer is 6 because three equal boxes summing to 18 must each be one-third of 18, which is 6. Dividing 18 by 3 gives the value of each box.
- In a Number Puzzles item: 10+□=6+9. What value belongs in the box?
Correct answer: 5
The answer is 5 because the right side, 6 plus 9, equals 15, so 10 plus box must equal 15, making the box 5. Comparing the totals of both sides gives 5.
- In a Number Puzzles item: 7+□=4+8. What value belongs in the box?
Correct answer: 5
The answer is 5 because the right side, 4 plus 8, equals 12, so 7 plus box must equal 12, making the box 5. Balancing the two sides yields 5.
- In a Number Puzzles item: □×4=20. What value belongs in the box?
Correct answer: 5
The answer is 5 because 5 times 4 equals 20, balancing the equation. Dividing 20 by 4 finds the box value of 5.
- In a Number Puzzles item: □÷2=6. What value belongs in the box?
Correct answer: 12
The answer is 12 because 12 divided by 2 equals 6, making both sides equal. Multiplying 6 by 2 recovers the box value of 12.
- In a Number Puzzles item: □÷3=4. What value belongs in the box?
Correct answer: 12
The answer is 12 because 12 divided by 3 equals 4, balancing the equation. Multiplying 4 by 3 gives the box value of 12.
- In a Number Puzzles item: 16=□+□. What value belongs in each box?
Correct answer: 8
The answer is 8 because two equal boxes that total 16 must each be half of 16, which is 8. Dividing 16 by 2 gives each box value.
- In a Number Puzzles item, a heart equals 6. The equation is box + 2 = heart. What value belongs in the box?
Correct answer: 4
The answer is 4 because the heart equals 6, so box plus 2 equals 6, making the box 4. Substituting the shape value before solving reveals 4.
- In a Number Puzzles item, a moon equals 9. The equation is box + box = moon + 1. What value belongs in each box?
Correct answer: 5
The answer is 5 because moon plus 1 equals 9 plus 1, which is 10, and two equal boxes summing to 10 must each be 5. Substituting then halving gives 5.
- In a Number Puzzles item: □+9=6+6. What value belongs in the box?
Correct answer: 3
The answer is 3 because the right side, 6 plus 6, equals 12, so box plus 9 must equal 12, making the box 3. Balancing both sides gives 3.
- In a Number Puzzles item: 5+5=□+4. What value belongs in the box?
Correct answer: 6
The answer is 6 because the left side, 5 plus 5, equals 10, so box plus 4 must equal 10, making the box 6. Matching the totals of both sides yields 6.
- On the CogAT Quantitative Battery, the Number Series subtest asks a test-taker to do which of the following?
- Choose the picture that does not belong
- Solve for the value that balances an equation
- Apply a rule from one number pair to another
- Find the pattern in a row of numbers and choose the next number
Correct answer: Find the pattern in a row of numbers and choose the next number
Finding the pattern in a row of numbers and choosing what comes next is the Number Series task. The subtest shows a sequence with a hidden rule, such as adding the same amount each step, and asks for the next term. Balancing equations, applying pair rules, and odd-one-out pictures belong to other subtests.
- What number comes next in the series 2, 4, 6, 8, ____?
Correct answer: 10
The answer is 10 because each number increases by 2: 2, 4, 6, 8, so the next is 8 plus 2, which is 10. Recognizing the constant step of plus 2 is the key to the series.
- What number comes next in the series 5, 10, 15, 20, ____?
Correct answer: 25
The answer is 25 because each number increases by 5: 5, 10, 15, 20, so the next is 20 plus 5, which is 25. The pattern is counting by fives.
- What number comes next in the series 3, 6, 9, 12, ____?
Correct answer: 15
The answer is 15 because each number increases by 3: 3, 6, 9, 12, so the next is 12 plus 3, which is 15. The series counts by threes.
- What number comes next in the series 20, 18, 16, 14, ____?
Correct answer: 12
The answer is 12 because each number decreases by 2: 20, 18, 16, 14, so the next is 14 minus 2, which is 12. The pattern is a constant step of minus 2.
- What number comes next in the series 30, 25, 20, 15, ____?
Correct answer: 10
The answer is 10 because each number decreases by 5: 30, 25, 20, 15, so the next is 15 minus 5, which is 10. The series counts down by fives.
- What number comes next in the series 1, 2, 4, 8, ____?
Correct answer: 16
The answer is 16 because each number is doubled: 1, 2, 4, 8, so the next is 8 times 2, which is 16. The pattern is multiply by 2 each step.
- What number comes next in the series 2, 6, 18, 54, ____?
Correct answer: 162
The answer is 162 because each number is tripled: 2, 6, 18, 54, so the next is 54 times 3, which is 162. The pattern is multiply by 3 each step.
- What number comes next in the series 1, 4, 7, 10, ____?
Correct answer: 13
The answer is 13 because each number increases by 3: 1, 4, 7, 10, so the next is 10 plus 3, which is 13. The constant step is plus 3.
- What number comes next in the series 100, 90, 80, 70, ____?
Correct answer: 60
The answer is 60 because each number decreases by 10: 100, 90, 80, 70, so the next is 70 minus 10, which is 60. The pattern is minus 10 each step.
- What number comes next in the series 1, 3, 5, 7, ____?
Correct answer: 9
The answer is 9 because the series lists odd numbers increasing by 2: 1, 3, 5, 7, so the next is 7 plus 2, which is 9. The step is plus 2.
- What number comes next in the series 4, 8, 12, 16, ____?
Correct answer: 20
The answer is 20 because each number increases by 4: 4, 8, 12, 16, so the next is 16 plus 4, which is 20. The series counts by fours.
- What number comes next in the series 50, 45, 40, 35, ____?
Correct answer: 30
The answer is 30 because each number decreases by 5: 50, 45, 40, 35, so the next is 35 minus 5, which is 30. The pattern is minus 5 each step.
- What number comes next in the series 2, 4, 8, 16, ____?
Correct answer: 32
The answer is 32 because each number is doubled: 2, 4, 8, 16, so the next is 16 times 2, which is 32. The pattern is multiply by 2.
- A series alternates its steps: 1, 2, 4, 5, 7, 8, ____. What comes next?
Correct answer: 10
The answer is 10 because the pattern alternates plus 1 then plus 2: from 8 the next step adds 2, giving 10. Spotting the repeating add-1, add-2 rhythm is what reveals the next number.
- A series alternates its steps: 2, 4, 6, 8, 10, ____, then keeps going by 2. What comes next after 10?
Correct answer: 12
The answer is 12 because the series adds 2 each time: 2, 4, 6, 8, 10, so the next is 10 plus 2, which is 12. The constant step of plus 2 continues.
- A series alternates steps: 3, 5, 9, 11, 15, ____. What comes next?
Correct answer: 17
The answer is 17 because the steps alternate plus 2 then plus 4: from 15 the next step adds 2, giving 17. Reading the repeating add-2, add-4 pattern reveals 17.
- What number comes next in the series 1, 2, 3, 5, 8, ____?
Correct answer: 13
The answer is 13 because each number is the sum of the two before it: 3 plus 5 is 8, and 5 plus 8 is 13. This add-the-previous-two pattern gives 13.
- What number comes next in the series 25, 20, 15, 10, ____?
Correct answer: 5
The answer is 5 because each number decreases by 5: 25, 20, 15, 10, so the next is 10 minus 5, which is 5. The pattern is minus 5 each step.
- What number comes next in the series 6, 12, 18, 24, ____?
Correct answer: 30
The answer is 30 because each number increases by 6: 6, 12, 18, 24, so the next is 24 plus 6, which is 30. The series counts by sixes.
- What number comes next in the series 81, 27, 9, 3, ____?
Correct answer: 1
The answer is 1 because each number is divided by 3: 81, 27, 9, 3, so the next is 3 divided by 3, which is 1. The pattern is divide by 3 each step.
- A Quantitative Battery item gives the pairs [4→16] and [5→25]. What number completes [6→00]?
Correct answer: 36
The answer is 36 because each first number is squared, or multiplied by itself: 4 times 4 is 16 and 5 times 5 is 25, so 6 times 6 is 36. Recognizing the multiply-by-itself rule across both pairs is quantitative reasoning at work.
- The CogAT Quantitative Battery measures which underlying ability across all three of its subtests?
- Reading comprehension of long passages
- Quantitative reasoning and number-pattern recognition
- Spatial rotation of three-dimensional shapes
- Vocabulary knowledge from sentence context
Correct answer: Quantitative reasoning and number-pattern recognition
Quantitative reasoning and number-pattern recognition is the common ability the battery measures, because Number Analogies, Number Puzzles, and Number Series all require working with numerical relationships. Reading, spatial rotation, and vocabulary are measured by the Verbal and Nonverbal batteries instead.
- Which three subtests make up the CogAT Quantitative Battery?
- Figure Matrices, Paper Folding, and Figure Classification
- Verbal Analogies, Sentence Completion, and Verbal Classification
- Number Analogies, Number Puzzles, and Number Series
- Picture Analogies, Number Puzzles, and Paper Folding
Correct answer: Number Analogies, Number Puzzles, and Number Series
Number Analogies, Number Puzzles, and Number Series are the three Quantitative Battery subtests. The verbal trio and the figure trio belong to the Verbal and Nonverbal batteries, so any list mixing those in is incorrect.
- A student must identify the rule behind a row of numbers to predict the next one. Which Quantitative Battery subtest is this?
- Figure Matrices
- Number Puzzles
- Number Analogies
- Number Series
Correct answer: Number Series
Number Series is the subtest where a student identifies the rule behind a row of numbers and predicts the next one. Number Puzzles balances equations, Number Analogies applies a pair rule, and Figure Matrices is a nonverbal task.
- A student must figure out which value makes both sides of a number sentence equal. Which Quantitative Battery subtest is this?
- Number Puzzles
- Number Series
- Number Analogies
- Verbal Classification
Correct answer: Number Puzzles
Number Puzzles is the equation-balancing subtest, where a student finds the value that makes both sides equal. Number Series predicts the next term, Number Analogies applies a pair rule, and Verbal Classification is a verbal task.
- A Number Analogies item shows [10→100] and [3→30]. What number completes [7→00]?
Correct answer: 70
The answer is 70 because each first number is multiplied by 10: 10 times 10 is 100 and 3 times 10 is 30, so 7 times 10 is 70. The times-10 rule matches both pairs.
- A Number Analogies item shows [40→4] and [70→7]. What number completes [90→00]?
Correct answer: 9
The answer is 9 because each partner is one-tenth of the first number: 40 divided by 10 is 4 and 70 divided by 10 is 7, so 90 divided by 10 is 9. Dividing by 10 is the consistent rule.
- A Number Analogies item shows [2→7] and [5→10]. What number completes [8→00]?
Correct answer: 13
The answer is 13 because each partner is 5 more than its first number: 2 plus 5 is 7 and 5 plus 5 is 10, so 8 plus 5 is 13. The add-5 rule fits both pairs.
- In a Number Puzzles item: □+8=20. What value belongs in the box?
Correct answer: 12
The answer is 12 because 12 plus 8 equals 20, balancing the equation. Subtracting 8 from 20 finds the box value of 12.
- In a Number Puzzles item: □−6=14. What value belongs in the box?
Correct answer: 20
The answer is 20 because 20 minus 6 equals 14, making both sides equal. Adding 6 back to 14 recovers the box value of 20.
- In a Number Puzzles item: □×5=25. What value belongs in the box?
Correct answer: 5
The answer is 5 because 5 times 5 equals 25, balancing the equation. Dividing 25 by 5 gives the box value of 5.
- In a Number Puzzles item, a diamond equals 7 and a circle equals 2. The equation is diamond + box = circle + 9. What value belongs in the box?
Correct answer: 4
The answer is 4 because the right side becomes 2 plus 9, which is 11, and the left side is 7 plus box, so box must be 4 to reach 11. Substituting both shapes before solving gives 4.
- What number comes next in the series 7, 14, 21, 28, ____?
Correct answer: 35
The answer is 35 because each number increases by 7: 7, 14, 21, 28, so the next is 28 plus 7, which is 35. The series counts by sevens.
- What number comes next in the series 64, 32, 16, 8, ____?
Correct answer: 4
The answer is 4 because each number is halved: 64, 32, 16, 8, so the next is 8 divided by 2, which is 4. The pattern is divide by 2 each step.
- What number comes next in the series 9, 12, 15, 18, ____?
Correct answer: 21
The answer is 21 because each number increases by 3: 9, 12, 15, 18, so the next is 18 plus 3, which is 21. The constant step is plus 3.
- A Number Analogies item shows [6→11] and [9→14]. What number completes [12→00]?
Correct answer: 17
The answer is 17 because each partner is 5 more than its first number: 6 plus 5 is 11 and 9 plus 5 is 14, so 12 plus 5 is 17. The add-5 rule fits both pairs.
- A Number Analogies item shows [14→7] and [18→9]. What number completes [22→00]?
Correct answer: 11
The answer is 11 because each partner is half the first number: 14 halved is 7 and 18 halved is 9, so 22 halved is 11. The divide-by-2 rule holds for all pairs.
- A Number Analogies item shows [3→7] and [6→13]. What number completes [4→00]?
Correct answer: 9
The answer is 9 because each partner is double the first number plus 1: 3 doubled plus 1 is 7 and 6 doubled plus 1 is 13, so 4 doubled plus 1 is 9. The two-step rule fits both models.
- In a Number Puzzles item: 12=□+□+□+□. What value belongs in each box?
Correct answer: 3
The answer is 3 because four equal boxes summing to 12 must each be one-fourth of 12, which is 3. Dividing 12 by 4 gives each box value.
- In a Number Puzzles item: □+3=3+3+3. What value belongs in the box?
Correct answer: 6
The answer is 6 because the right side, 3 plus 3 plus 3, equals 9, so box plus 3 must equal 9, making the box 6. Balancing both sides gives 6.
- A Number Analogies item shows [5→1] and [9→5]. What number completes [12→00]?
Correct answer: 8
The answer is 8 because each partner is 4 less than the first number: 5 minus 4 is 1 and 9 minus 4 is 5, so 12 minus 4 is 8. The subtract-4 rule fits both pairs.
- A student sees a row of numbers increasing by the same amount each time and is asked what comes next. To answer, the student should first do which of the following?
- Add all the numbers together
- Find the constant difference between each pair of neighbors
- Square the first number
- Balance both sides of an equation
Correct answer: Find the constant difference between each pair of neighbors
Finding the constant difference between neighbors is the right first step, because once the step size is known, you add it to the last term to get the next number. Summing the row, squaring, or balancing equations are not how a Number Series is solved.
- A student looks at two model number pairs to discover one rule, then applies it to a third number. Which Quantitative Battery subtest is being described?
- Number Puzzles
- Number Series
- Number Analogies
- Figure Classification
Correct answer: Number Analogies
Number Analogies is the subtest where a student finds one rule in model pairs and applies it to a new number. Number Series predicts the next term, Number Puzzles balances equations, and Figure Classification is a nonverbal task.
- In a Number Puzzles item, why must the box value make both sides of the number sentence equal?
- Because the box must equal zero in every puzzle
- Because the box always equals the largest number shown
- Because Number Puzzles are solved by adding every number in the row
- Because a Number Puzzle is an equation, and an equation is true only when both sides have the same total
Correct answer: Because a Number Puzzle is an equation, and an equation is true only when both sides have the same total
A Number Puzzle is an equation, and an equation holds only when both sides share the same total, so the box value is whatever makes that balance true. The box is not fixed at the largest number or zero, and the task is balancing rather than summing the whole row.
- A Number Analogies item shows [7→21] and [10→30]. What number completes [4→00]?
Correct answer: 12
The answer is 12 because each first number is tripled: 7 times 3 is 21 and 10 times 3 is 30, so 4 times 3 is 12. The times-3 rule fits both model pairs.
- What number comes next in the series 11, 9, 7, 5, ____?
Correct answer: 3
The answer is 3 because each number decreases by 2: 11, 9, 7, 5, so the next is 5 minus 2, which is 3. The constant step is minus 2.
- In a Number Puzzles item, a cloud equals 8. The equation is cloud - box = 3. What value belongs in the box?
Correct answer: 5
The answer is 5 because the cloud equals 8, so 8 minus box equals 3, making the box 5. Substituting the shape value first turns the puzzle into a simple balance.
- A Number Analogies item shows [8→16] and [11→22]. What number completes [15→00]?
Correct answer: 30
The answer is 30 because each first number is doubled: 8 becomes 16 and 11 becomes 22, so 15 becomes 30. The doubling rule matches both pairs.
- What number comes next in the series 3, 7, 11, 15, ____?
Correct answer: 19
The answer is 19 because each number increases by 4: 3, 7, 11, 15, so the next is 15 plus 4, which is 19. The constant step is plus 4.
- A Number Analogies item shows [12→4] and [18→6]. What number completes [24→00]?
Correct answer: 8
The answer is 8 because each partner is one-third of the first number: 12 divided by 3 is 4 and 18 divided by 3 is 6, so 24 divided by 3 is 8. The divide-by-3 rule fits both pairs.
- In a Number Puzzles item: 4+4=□+□. What value belongs in each box?
Correct answer: 4
The answer is 4 because the left side, 4 plus 4, equals 8, and two equal boxes summing to 8 must each be 4. Halving the total of 8 gives each box value.
- What number comes next in the series 1, 10, 100, 1000, ____?
Correct answer: 10000
The answer is 10000 because each number is multiplied by 10: 1, 10, 100, 1000, so the next is 1000 times 10, which is 10000. The pattern is multiply by 10 each step.
- A Number Analogies item shows [9→18] and [7→16]. What number completes [5→00]?
Correct answer: 14
The answer is 14 because each partner is the first number plus 9: 9 plus 9 is 18 and 7 plus 9 is 16, so 5 plus 9 is 14. The add-9 rule fits both pairs.
- In a Number Puzzles item: □×2=6+4. What value belongs in the box?
Correct answer: 5
The answer is 5 because the right side, 6 plus 4, equals 10, so box times 2 must equal 10, making the box 5. Dividing 10 by 2 finds the box value.
- What number comes next in the series 2, 5, 8, 11, ____?
Correct answer: 14
The answer is 14 because each number increases by 3: 2, 5, 8, 11, so the next is 11 plus 3, which is 14. The constant step is plus 3.
- A Number Analogies item shows [4→1] and [12→3]. What number completes [20→00]?
Correct answer: 5
The answer is 5 because each partner is one-fourth of the first number: 4 divided by 4 is 1 and 12 divided by 4 is 3, so 20 divided by 4 is 5. The divide-by-4 rule fits both pairs.
- In a Number Puzzles item, a key equals 5 and a bell equals 3. The equation is key + bell = box. What value belongs in the box?
Correct answer: 8
The answer is 8 because the key equals 5 and the bell equals 3, so key plus bell is 5 plus 3, which is 8. The box must equal the total of the two shapes.
- What number comes next in the series 40, 36, 32, 28, ____?
Correct answer: 24
The answer is 24 because each number decreases by 4: 40, 36, 32, 28, so the next is 28 minus 4, which is 24. The constant step is minus 4.
- A Number Analogies item shows [5→8] and [10→13]. What number completes [20→00]?
Correct answer: 23
The answer is 23 because each partner is 3 more than the first number: 5 plus 3 is 8 and 10 plus 3 is 13, so 20 plus 3 is 23. The add-3 rule fits both pairs.
- In a Number Puzzles item: □+10=25. What value belongs in the box?
Correct answer: 15
The answer is 15 because 15 plus 10 equals 25, balancing the equation. Subtracting 10 from 25 gives the box value of 15.
- On the CogAT Nonverbal Battery, the Figure Matrices subtest asks a test-taker to do which of the following?
- Find the rule that turns the top-left figure into the top-right figure, then apply it to complete the bottom row
- Add two numbers and report the sum
- Choose the word that completes a sentence
- Pick the word that best matches a category
Correct answer: Find the rule that turns the top-left figure into the top-right figure, then apply it to complete the bottom row
Finding the rule that turns the top-left figure into the top-right figure and applying it to the bottom row is the Figure Matrices task. The subtest shows a 2x2 grid with three figures filled in and asks for the figure that completes the pattern. Completing sentences, adding numbers, and matching word categories belong to other batteries, not the Nonverbal Battery.
- In a 2x2 Figure Matrix, the top row shows a small circle then a large circle, and the bottom row shows a small square then a blank. Which figure completes the matrix?
- A small triangle
- A large square
- A large circle
- A small square
Correct answer: A large square
A large square is correct. Across the top row the shape stays a circle but grows from small to large, so the rule is the shape gets bigger; applying that to the bottom-row square gives a large square. A small square keeps the size, a large circle changes the shape, and a small triangle changes both.
- In a 2x2 Figure Matrix, the top row shows a white star then a black star, and the bottom row shows a white heart then a blank. Which figure completes the matrix?
- A black star
- A white circle
- A black heart
- A white heart
Correct answer: A black heart
A black heart is correct. In the top row the shape stays a star but its color changes from white to black, so the rule is fill the shape in; applying that to the white heart gives a black heart. A white heart ignores the color change, a black star changes the shape, and a white circle changes both shape and color.
- In a 2x2 Figure Matrix, the top row shows an arrow pointing up then an arrow pointing down, and the bottom row shows a triangle pointing up then a blank. Which figure completes the matrix?
- A triangle pointing left
- An arrow pointing down
- A triangle pointing up
- A triangle pointing down
Correct answer: A triangle pointing down
A triangle pointing down is correct. In the top row the arrow flips from pointing up to pointing down, so the rule is turn it upside down; applying that to the upward triangle gives a triangle pointing down. Keeping it upward ignores the flip, pointing left is the wrong turn, and an arrow changes the shape.
- In a 2x2 Figure Matrix, the top row shows one dot then two dots, and the bottom row shows three dots then a blank. Which figure completes the matrix?
- Four dots
- Six dots
- Three dots
- Two dots
Correct answer: Four dots
Four dots is correct. Across the top row the count rises by one, from one dot to two dots, so the rule is add one more; applying that to three dots gives four dots. Three dots ignores the change, six dots doubles instead of adding one, and two dots repeats an earlier count.
- In a 2x2 Figure Matrix, the top row shows a square then a square with an X inside it, and the bottom row shows a circle then a blank. Which figure completes the matrix?
- A plain circle
- A circle with an X inside it
- A square with an X inside it
- A circle with a dot inside it
Correct answer: A circle with an X inside it
A circle with an X inside it is correct. In the top row an X is added inside the shape while the shape stays the same, so the rule is put an X inside; applying that to the circle gives a circle with an X inside it. A plain circle skips the added X, a square changes the shape, and a dot is the wrong added mark.
- In a 2x2 Figure Matrix, the top row shows a single line then two parallel lines, and the bottom row shows a single curve then a blank. Which figure completes the matrix?
- One curve
- Three curves
- Two parallel curves
- One straight line
Correct answer: Two parallel curves
Two parallel curves is correct. In the top row one shape becomes two of the same shape side by side, so the rule is make a matching pair; applying that to the single curve gives two parallel curves. One curve ignores the doubling, a straight line changes the shape, and three curves adds too many.
- In a 2x2 Figure Matrix, the top row shows a large shaded circle then a small shaded circle, and the bottom row shows a large shaded square then a blank. Which figure completes the matrix?
- A small white square
- A small shaded circle
- A large shaded square
- A small shaded square
Correct answer: A small shaded square
A small shaded square is correct. In the top row the shape and shading stay the same while the size shrinks from large to small, so the rule is make it smaller; applying that to the large shaded square gives a small shaded square. Keeping it large ignores the shrink, removing the shading changes the fill, and a circle changes the shape.
- A Figure Matrices item changes the top-left figure into the top-right figure by rotating it a quarter turn. To complete the matrix, what must a test-taker do to the bottom-left figure?
- Rotate it the same quarter turn
- Make it larger only
- Add a new shape beside it
- Change its color only
Correct answer: Rotate it the same quarter turn
Rotating the bottom-left figure the same quarter turn is correct. The matrix rule is whatever transformation links the top pair, so if the top changes by a quarter turn, the bottom figure must change the same way. Changing only color, only size, or adding a shape would not match the rotation rule shown on top.
- In a 2x2 Figure Matrix, the top row shows an empty box then a box with a single dot, and the bottom row shows an empty triangle then a blank. Which figure completes the matrix?
- A box with a single dot
- A triangle with a single dot
- An empty triangle
- A triangle with two dots
Correct answer: A triangle with a single dot
A triangle with a single dot is correct. In the top row a single dot is added inside the shape, so the rule is place one dot inside; applying that to the triangle gives a triangle with one dot. An empty triangle skips the dot, a box changes the shape, and two dots adds too many.
- A student is shown a 2x2 grid of figures with one cell empty and must pick the figure that completes the pattern. Which Nonverbal Battery subtest is this?
- Paper Folding
- Figure Classification
- Figure Matrices
- Number Series
Correct answer: Figure Matrices
Figure Matrices is correct. It is the subtest that presents a 2x2 grid with one cell empty and asks for the figure that completes the pattern. Paper Folding deals with punched holes, Figure Classification groups figures by a shared property, and Number Series is a quantitative task.
- In a 2x2 Figure Matrix, the top row shows a shape then the same shape rotated a half turn, and the bottom row shows a flag pointing right then a blank. Which figure completes the matrix?
- A larger flag pointing right
- A flag pointing up
- A flag pointing right
- A flag pointing left
Correct answer: A flag pointing left
A flag pointing left is correct. The top row shows a half turn, which flips a shape to face the opposite way, so a right-pointing flag turned halfway points left. Keeping it right ignores the rotation, pointing up is a quarter turn, and a larger flag adds a size change that is not part of the rule.
- In a 2x2 Figure Matrix, the top row shows two circles then three circles, and the bottom row shows two squares then a blank. Which figure completes the matrix?
- Three squares
- Two squares
- Four squares
- Three circles
Correct answer: Three squares
Three squares is correct. Across the top row the count goes up by one, from two to three, so the rule is add one more; applying that to two squares gives three squares. Two squares ignores the change, four squares adds too many, and three circles changes the shape.
- In a 2x2 Figure Matrix, the top row shows a thin rectangle then a thin rectangle with a circle on top of it, and the bottom row shows a thin triangle then a blank. Which figure completes the matrix?
- A thin rectangle with a circle on top
- A thin triangle with a circle on top of it
- A thin triangle with a square on top
- A plain thin triangle
Correct answer: A thin triangle with a circle on top of it
A thin triangle with a circle on top of it is correct. The top row adds a circle on top of the base shape, so the rule is place a circle above it; applying that to the triangle gives a triangle with a circle on top. A plain triangle skips the circle, a rectangle changes the base shape, and a square on top is the wrong added shape.
- In a 2x2 Figure Matrix, the top row shows a white triangle then a gray triangle, and the bottom row shows a white pentagon then a blank. Which figure completes the matrix?
- A white pentagon
- A gray triangle
- A gray pentagon
- A black pentagon
Correct answer: A gray pentagon
A gray pentagon is correct. The top row keeps the shape but changes the color from white to gray, so the rule is shade it gray; applying that to the white pentagon gives a gray pentagon. A white pentagon ignores the color change, a triangle changes the shape, and a black pentagon uses the wrong shade.
- In a 2x2 Figure Matrix, the top row shows a shape with one stripe then the same shape with two stripes, and the bottom row shows a circle with one stripe then a blank. Which figure completes the matrix?
- A circle with one stripe
- A circle with three stripes
- A square with two stripes
- A circle with two stripes
Correct answer: A circle with two stripes
A circle with two stripes is correct. The top row adds one stripe, going from one to two, so the rule is add a stripe; applying that to the one-stripe circle gives a two-stripe circle. One stripe ignores the change, a square changes the shape, and three stripes adds one too many.
- In a 2x2 Figure Matrix, the top row shows a small shape then a large version of the same shape, and the bottom row shows a small moon then a blank. Which figure completes the matrix?
- A large moon
- A large sun
- A small star
- A small moon
Correct answer: A large moon
A large moon is correct. The top row keeps the shape the same while making it larger, so the rule is make it bigger; applying that to the small moon gives a large moon. A small moon ignores the size change, a sun and a star change the shape entirely.
- In a 2x2 Figure Matrix, the top row shows a shape then the shape with a circle around it, and the bottom row shows a heart then a blank. Which figure completes the matrix?
- A circle with a heart around it
- A heart with a circle around it
- A plain heart
- A heart with a square around it
Correct answer: A heart with a circle around it
A heart with a circle around it is correct. The top row adds a circle surrounding the shape, so the rule is draw a circle around it; applying that to the heart gives a heart inside a circle. A plain heart skips the added circle, a square around it is the wrong enclosure, and swapping which shape is inside reverses the rule.
- In a 2x2 Figure Matrix, the top row shows a single small square then four small squares forming a larger square, and the bottom row shows a single small circle then a blank. Which figure completes the matrix?
- Four small squares
- Two small circles
- Four small circles grouped together
- One small circle
Correct answer: Four small circles grouped together
Four small circles grouped together is correct. The top row multiplies one shape into four of the same shape, so the rule is make four; applying that to the circle gives four circles grouped together. One circle ignores the change, two circles is too few, and four squares changes the shape.
- In a 2x2 Figure Matrix, the top row shows a clock hand pointing to 12 then a clock hand pointing to 3, and the bottom row shows an arrow pointing to 12 then a blank. Which figure completes the matrix?
- An arrow pointing to 9
- An arrow pointing to 6
- An arrow pointing to 12
- An arrow pointing to 3
Correct answer: An arrow pointing to 3
An arrow pointing to 3 is correct. The top row turns the hand a quarter turn clockwise, from the 12 position to the 3 position, so the rule is a quarter turn clockwise; applying that to the arrow at 12 brings it to 3. Staying at 12 ignores the turn, the 6 position is a half turn, and the 9 position is the wrong direction.
- In a 2x2 Figure Matrix, the top row shows a face looking left then a face looking right, and the bottom row shows a fish facing left then a blank. Which figure completes the matrix?
- A fish facing right
- A fish facing left
- A face facing right
- A fish facing up
Correct answer: A fish facing right
A fish facing right is correct. The top row flips the figure to face the opposite direction, from left to right, so the rule is flip it horizontally; applying that to the left-facing fish gives a fish facing right. Facing left ignores the flip, facing up is the wrong direction, and a face changes the figure.
- In a 2x2 Figure Matrix, the top row shows a small dot then a small dot with a ring around it, and the bottom row shows a small square then a blank. Which figure completes the matrix?
- A large square
- A small square with a ring around it
- A small dot with a ring
- A small square alone
Correct answer: A small square with a ring around it
A small square with a ring around it is correct. The top row adds a ring around the central mark, so the rule is surround it with a ring; applying that to the square gives a square with a ring around it. The plain square skips the ring, a dot changes the central shape, and a large square adds a size change that is not part of the rule.
- In a 2x2 Figure Matrix, the top row shows a tall thin rectangle then a short wide rectangle, and the bottom row shows a tall thin oval then a blank. Which figure completes the matrix?
- A short wide rectangle
- A tall thin oval
- A short wide oval
- A tall thin rectangle
Correct answer: A short wide oval
A short wide oval is correct. The top row changes a tall narrow shape into a short wide one while keeping it a rectangle, so the rule is turn it from tall-thin to short-wide; applying that to the oval gives a short wide oval. A tall thin oval ignores the change, and the rectangle options change the shape from an oval.
- In a 2x2 Figure Matrix, the top row shows a shape with a plus sign inside then a shape with a minus sign inside, and the bottom row shows a circle with a plus sign then a blank. Which figure completes the matrix?
- A circle with an X inside
- A circle with a plus sign inside
- A square with a minus sign inside
- A circle with a minus sign inside
Correct answer: A circle with a minus sign inside
A circle with a minus sign inside is correct. The top row changes the inner mark from a plus sign to a minus sign, so the rule is swap the plus for a minus; applying that to the circle gives a circle with a minus sign. Keeping the plus ignores the change, a square changes the outer shape, and an X is the wrong inner mark.
- In a 2x2 Figure Matrix, the top row shows a shape with a flat top then the same shape with a pointed top, and the bottom row shows a flat-topped tower then a blank. Which figure completes the matrix?
- A tower with a pointed top
- A tower with a flat top
- A pointed shape with no tower
- A wider flat-topped tower
Correct answer: A tower with a pointed top
A tower with a pointed top is correct. The top row changes a flat top into a pointed top, so the rule is make the top come to a point; applying that to the flat-topped tower gives a pointed-top tower. Keeping the flat top ignores the change, removing the tower drops part of the figure, and widening it adds an unrelated change.
- In a 2x2 Figure Matrix, the top row shows two stacked boxes then three stacked boxes, and the bottom row shows two stacked balls then a blank. Which figure completes the matrix?
- Two stacked balls
- Three stacked balls
- Four stacked balls
- Three stacked boxes
Correct answer: Three stacked balls
Three stacked balls is correct. The top row adds one item to the stack, going from two boxes to three, so the rule is add one more; applying that to the two stacked balls gives three stacked balls. Two balls ignores the change, four balls adds too many, and three boxes changes the shape.
- In a 2x2 Figure Matrix, the top row shows a black shape then a white outline of the same shape, and the bottom row shows a black diamond then a blank. Which figure completes the matrix?
- A white outline of a circle
- A black diamond
- A white outline of a diamond
- A gray diamond
Correct answer: A white outline of a diamond
A white outline of a diamond is correct. The top row changes a filled black shape into a white outline of the same shape, so the rule is empty out the fill; applying that to the black diamond gives a white diamond outline. Keeping it black ignores the change, a circle changes the shape, and gray is the wrong fill.
- In a 2x2 Figure Matrix, the top row shows an L shape then the L shape flipped to face the other way, and the bottom row shows a boot shape facing left then a blank. Which figure completes the matrix?
- A boot shape upside down
- A boot shape facing left
- An L shape facing right
- A boot shape facing right
Correct answer: A boot shape facing right
A boot shape facing right is correct. The top row flips the figure to face the opposite way, so the rule is mirror it left to right; applying that to the left-facing boot gives a boot facing right. Facing left ignores the flip, upside down is a different change, and an L shape changes the figure.
- In a 2x2 Figure Matrix, the top row shows a happy face then a happy face wearing a hat, and the bottom row shows a star then a blank. Which figure completes the matrix?
- A star wearing a hat
- A happy face wearing a hat
- A star wearing shoes
- A plain star
Correct answer: A star wearing a hat
A star wearing a hat is correct. The top row adds a hat on top of the figure, so the rule is put a hat on it; applying that to the star gives a star with a hat. A plain star skips the hat, a happy face changes the base figure, and shoes are the wrong added item.
- In a 2x2 Figure Matrix, the top row shows a left-leaning slash then a right-leaning slash, and the bottom row shows a left-leaning arrow then a blank. Which figure completes the matrix?
- A right-leaning slash
- A right-leaning arrow
- A left-leaning arrow
- A vertical arrow
Correct answer: A right-leaning arrow
A right-leaning arrow is correct. The top row flips the lean from left to right, so the rule is reverse the lean; applying that to the left-leaning arrow gives a right-leaning arrow. Keeping the left lean ignores the change, a vertical arrow loses the lean, and a slash changes the figure into a plain line.
- In a 2x2 Figure Matrix, the top row shows a balloon on a long string then a balloon on a short string, and the bottom row shows a kite on a long string then a blank. Which figure completes the matrix?
- A balloon on a short string
- A kite with no string
- A kite on a short string
- A kite on a long string
Correct answer: A kite on a short string
A kite on a short string is correct. The top row keeps the object the same while shortening the string from long to short, so the rule is shorten the string; applying that to the kite gives a kite on a short string. A long string ignores the change, a balloon changes the object, and no string removes the string entirely.
- In a 2x2 Figure Matrix, the top row shows a shape outlined with a thin line then the same shape outlined with a thick line, and the bottom row shows a thin-outlined hexagon then a blank. Which figure completes the matrix?
- A thin-outlined hexagon
- A shaded hexagon
- A thick-outlined circle
- A thick-outlined hexagon
Correct answer: A thick-outlined hexagon
A thick-outlined hexagon is correct. The top row keeps the shape but thickens the outline from thin to thick, so the rule is make the outline thicker; applying that to the hexagon gives a thick-outlined hexagon. A thin outline ignores the change, a circle changes the shape, and shading is a different kind of change.
- In a 2x2 Figure Matrix, the top row shows a tree with two branches then a tree with four branches, and the bottom row shows a tree with three branches then a blank. Which figure completes the matrix?
- A tree with five branches
- A tree with three branches
- A tree with one branch
- A tree with six branches
Correct answer: A tree with five branches
A tree with five branches is correct. Across the top row the branch count grows by two, from two to four, so the rule is add two more; applying that to three branches gives five branches. Three branches ignores the change, six branches adds too many, and one branch decreases instead of adding.
- In a 2x2 Figure Matrix, the top row shows a single triangle then two triangles joined point to point, and the bottom row shows a single square then a blank. Which figure completes the matrix?
- Three squares in a row
- Two squares joined corner to corner
- Two squares far apart
- One square
Correct answer: Two squares joined corner to corner
Two squares joined corner to corner is correct. The top row joins two of the same shape at a point, so the rule is connect a matching pair at the corner; applying that to the square gives two squares joined corner to corner. One square ignores the doubling, squares far apart are not joined, and three squares is the wrong count.
- In a 2x2 Figure Matrix, the top row shows a cup that is empty then a cup that is full, and the bottom row shows an empty jar then a blank. Which figure completes the matrix?
- A broken jar
- An empty jar
- A full jar
- A full cup
Correct answer: A full jar
A full jar is correct. The top row changes the container from empty to full while keeping it the same object, so the rule is fill it; applying that to the empty jar gives a full jar. An empty jar ignores the change, a cup changes the object, and a broken jar is an unrelated change.
- In a 2x2 Figure Matrix, the top row shows one window on a house then two windows on a house, and the bottom row shows one window on a barn then a blank. Which figure completes the matrix?
- A barn with one window
- A house with two windows
- A barn with three windows
- A barn with two windows
Correct answer: A barn with two windows
A barn with two windows is correct. The top row adds one window, going from one to two, so the rule is add a window; applying that to the one-window barn gives a barn with two windows. One window ignores the change, a house changes the building, and three windows adds too many.
- In a 2x2 Figure Matrix, the top row shows a shape pointing up then the shape pointing up with a second copy below it pointing down, and the bottom row shows a single up-pointing triangle then a blank. Which figure completes the matrix?
- An up-pointing triangle with a down-pointing triangle below it
- Two up-pointing triangles
- A single up-pointing triangle
- A single down-pointing triangle
Correct answer: An up-pointing triangle with a down-pointing triangle below it
An up-pointing triangle with a down-pointing triangle below it is correct. The top row adds a flipped copy beneath the original, so the rule is place a mirrored copy below; applying that to the up-pointing triangle gives an up triangle with a down triangle under it. A single triangle ignores the added copy, two up triangles forget the flip, and a lone down triangle drops the original.
- In a 2x2 Figure Matrix, the top row shows a circle split by one line then a circle split by two crossing lines, and the bottom row shows a square split by one line then a blank. Which figure completes the matrix?
- A circle split by two lines
- A square split by two crossing lines
- A square split by one line
- A plain square
Correct answer: A square split by two crossing lines
A square split by two crossing lines is correct. The top row adds a second dividing line that crosses the first, so the rule is add a crossing line; applying that to the once-split square gives a square split by two crossing lines. One line ignores the addition, a circle changes the shape, and a plain square removes the lines.
- In a 2x2 Figure Matrix, the top row shows a ladder with two rungs then a ladder with three rungs, and the bottom row shows a ladder with four rungs then a blank. Which figure completes the matrix?
- A ladder with six rungs
- A ladder with four rungs
- A ladder with five rungs
- A ladder with three rungs
Correct answer: A ladder with five rungs
A ladder with five rungs is correct. The top row adds one rung, going from two to three, so the rule is add one rung; applying that to the four-rung ladder gives a five-rung ladder. Four rungs ignores the change, six rungs adds too many, and three rungs is fewer than the start.
- In a 2x2 Figure Matrix, the top row shows a shaded shape then the shaded shape with a white dot punched out of its center, and the bottom row shows a shaded heart then a blank. Which figure completes the matrix?
- A shaded circle with a white dot
- A white heart outline
- A fully shaded heart
- A shaded heart with a white dot in its center
Correct answer: A shaded heart with a white dot in its center
A shaded heart with a white dot in its center is correct. The top row adds a white dot in the center of the shaded shape, so the rule is punch a white dot in the middle; applying that to the shaded heart gives a shaded heart with a white center dot. A fully shaded heart skips the dot, a white outline empties the whole shape, and a circle changes the shape.
- On the CogAT Nonverbal Battery, the Paper Folding subtest asks a test-taker to do which of the following?
- Picture where the holes will appear after a folded, hole-punched paper is unfolded
- Find the missing number in a series
- Pick the word with the same meaning
- Choose the picture that does not belong
Correct answer: Picture where the holes will appear after a folded, hole-punched paper is unfolded
Picturing where the holes will appear after a folded, hole-punched paper is unfolded is the Paper Folding task. The subtest shows paper being folded and a hole punched through it, then asks which unfolded sheet shows the correct hole pattern. Finding numbers, choosing odd-one-out pictures, and matching word meanings belong to other subtests.
- A square sheet is folded once in half, and one hole is punched through both layers. When the paper is unfolded, how many holes appear?
- Three holes
- Two holes
- One hole
- Four holes
Correct answer: Two holes
Two holes is correct. A single fold creates two layers, so one punch passes through both layers and makes a hole in each; unfolding reveals two holes. One hole forgets the second layer, while three or four holes would require more folds or more punches.
- A square sheet is folded in half once, and two holes are punched through both layers. When unfolded, how many holes appear?
- Two holes
- Three holes
- Four holes
- Six holes
Correct answer: Four holes
Four holes is correct. One fold makes two layers, and each of the two punches passes through both layers, so each punch makes two holes, giving two times two, which is four. Two holes counts only one punch, three holes is not possible from this even doubling, and six holes would need three layers.
- A square sheet is folded in half and then folded in half again, making four layers, and one hole is punched. When unfolded, how many holes appear?
- One hole
- Eight holes
- Two holes
- Four holes
Correct answer: Four holes
Four holes is correct. Folding in half twice stacks four layers, so a single punch goes through all four and creates four holes when unfolded. Two holes counts only one fold, one hole ignores the layers, and eight holes would require eight layers.
- A paper is folded in half from left to right, so the right edge lands on the left edge. A hole is punched near the folded right side. When the paper is unfolded, where do the holes appear?
- One hole on each side, mirrored across the center fold
- One hole exactly in the center
- Three holes spread across the page
- Only one hole on the right
Correct answer: One hole on each side, mirrored across the center fold
One hole on each side, mirrored across the center fold, is correct. The single punch passes through both layers, and when unfolded the second hole appears as a mirror image of the first across the fold line. Only one hole forgets the second layer, three holes adds too many, and a single center hole would only happen if the punch were on the fold itself.
- When you unfold a paper that was folded once before being punched, the holes always appear in what arrangement relative to the fold line?
- All stacked exactly on the fold line
- As mirror images on opposite sides of the fold line
- Only on the side that was on top
- Randomly scattered with no relation to the fold
Correct answer: As mirror images on opposite sides of the fold line
As mirror images on opposite sides of the fold line is correct. A fold acts like a mirror, so each hole punched on one layer has a matching hole the same distance away on the other side when unfolded. The holes are not all on the fold, not random, and not limited to the top side, because the punch went through both layers.
- A square sheet is folded in half top to bottom, and one hole is punched in the upper-left area of the folded paper. When unfolded, the two holes appear where?
- In the upper-left and upper-right areas
- Only in the lower-left area
- In the upper-left and lower-left areas, mirrored across the horizontal fold
- Both in the upper-left corner
Correct answer: In the upper-left and lower-left areas, mirrored across the horizontal fold
The upper-left and lower-left areas, mirrored across the horizontal fold, is correct. A top-to-bottom fold creates a horizontal mirror line, so a hole in the upper-left reflects to the lower-left when unfolded. Two holes both in the upper-left ignore the reflection, an upper-right hole would come from a vertical fold, and only one lower hole forgets the original punch.
- A square sheet is folded in half and then in half again into four layers, and two holes are punched. When unfolded, how many holes appear?
- Four holes
- Six holes
- Two holes
- Eight holes
Correct answer: Eight holes
Eight holes is correct. Two folds create four layers, and each of the two punches passes through all four layers, so each punch makes four holes, giving two times four, which is eight. Four holes counts only one punch, six holes does not match the doubling, and two holes ignores the layers entirely.
- The number of holes seen after unfolding depends on which two factors in a Paper Folding item?
- How many layers the folds create and how many punches are made
- The thickness of the pencil and the room temperature
- How long the paper is folded and who folds it
- The color of the paper and the size of the holes
Correct answer: How many layers the folds create and how many punches are made
How many layers the folds create and how many punches are made is correct. Each punch passes through every stacked layer, so total holes equal the number of layers multiplied by the number of punches. Paper color, hole size, folding time, and other physical conditions do not change how many holes the punches produce.
- A square sheet is folded once and a hole is punched exactly on the fold line. When the paper is unfolded, how many holes appear?
- Two separate holes
- One hole on the fold line
- Four holes
- Three holes
Correct answer: One hole on the fold line
One hole on the fold line is correct. When the punch lands directly on the fold, the two layers share the same spot at the crease, so unfolding shows a single hole sitting on the fold line rather than a mirrored pair. Two, three, or four holes would appear only if the punch were away from the fold or more folds were made.
- A student watches a paper get folded and punched, then chooses how the unfolded sheet will look. Which Nonverbal Battery subtest is this?
- Verbal Classification
- Figure Classification
- Paper Folding
- Figure Matrices
Correct answer: Paper Folding
Paper Folding is correct. It is the subtest that shows a paper being folded and punched and asks which unfolded sheet shows the right hole pattern. Figure Matrices completes a grid, Figure Classification groups figures, and Verbal Classification is a word task.
- A square sheet is folded in half once, and three holes are punched in a row through both layers. When unfolded, how many holes appear?
- Nine holes
- Four holes
- Three holes
- Six holes
Correct answer: Six holes
Six holes is correct. One fold makes two layers, and each of the three punches passes through both, so three punches times two layers gives six holes. Three holes counts only one layer, nine holes is not a product of two and three, and four holes does not match the count.
- A square sheet is folded into four layers, and one hole is punched in a corner area. When unfolded, the holes appear where?
- One hole in each of the four corner areas
- Only one hole in the original corner
- Two holes along one edge
- Three holes in a triangle shape
Correct answer: One hole in each of the four corner areas
One hole in each of the four corner areas is correct. Folding into four layers stacks the sheet so a single corner punch passes through all four, and unfolding mirrors the hole into all four corners. Only one hole forgets the layers, and two or three holes do not match the four-layer doubling.
- A paper is folded once and a hole is punched near the top edge, far from the fold. After unfolding, the two holes will be located where?
- Both near the bottom edge
- Both near the top edge, one on each side of the fold
- One near the top and one near the bottom
- Both exactly in the center
Correct answer: Both near the top edge, one on each side of the fold
Both near the top edge, one on each side of the fold, is correct. A fold mirrors the punch across the crease at the same distance from the fold, so a hole near the top reflects to another hole near the top on the other side. The holes do not move to the bottom or center, since the reflection keeps each hole the same distance from the fold line.
- A square sheet is folded in half top to bottom, then in half left to right, making four layers. One hole is punched. When unfolded, how many holes appear?
- Two holes
- Eight holes
- Four holes
- One hole
Correct answer: Four holes
Four holes is correct. Two folds, one each direction, stack four layers, so a single punch passes through all four and makes four holes when unfolded. Two holes counts only one fold, eight holes would need two punches, and one hole ignores the layers.
- A square sheet is folded in half and a hole is punched, then it is folded again and a second hole is punched in the four-layer stack. Counting all punches, the unfolded sheet will clearly show what?
- Holes only on the fold lines
- Exactly one hole only
- No holes at all
- More than one hole because every punch went through more than one layer
Correct answer: More than one hole because every punch went through more than one layer
More than one hole because every punch went through more than one layer is correct. Each punch passed through stacked layers, so unfolding reveals several mirrored holes rather than a single one. There cannot be exactly one hole or no holes when multiple layers are punched, and the holes are not limited to the fold lines.
- A square sheet is folded in half twice into four layers, and two holes are punched in the stack. When unfolded, the eight holes will appear how?
- As a symmetric pattern mirrored across both fold lines
- Randomly with no pattern
- In a single straight line on one edge
- All crowded in one corner
Correct answer: As a symmetric pattern mirrored across both fold lines
A symmetric pattern mirrored across both fold lines is correct. Each fold acts as a mirror, so the punched holes reflect across both crease lines, producing a balanced, symmetric arrangement of eight holes. The holes are not crowded in one corner, lined up on one edge, or random, because folding forces a mirrored layout.
- A square sheet is folded in half once, and four holes are punched through both layers. When unfolded, how many holes appear?
- Six holes
- Eight holes
- Sixteen holes
- Four holes
Correct answer: Eight holes
Eight holes is correct. One fold creates two layers, and each of the four punches passes through both, so four punches times two layers gives eight holes. Four holes counts only one layer, six holes does not match the doubling, and sixteen holes would require four layers.
- A paper is folded in half and a single hole is punched. A student claims the unfolded paper shows three holes. Why must this be wrong?
- Folding always removes holes
- Holes only appear if the paper is colored
- One punch through two layers can only make two holes, not three
- A punch never makes more than one hole
Correct answer: One punch through two layers can only make two holes, not three
One punch through two layers can only make two holes is correct. A single fold stacks exactly two layers, so one punch produces exactly two mirrored holes, never an odd number like three. A punch can make more than one hole through layers, folding does not remove holes, and paper color has nothing to do with the count.
- A square sheet is folded into eight layers, and one hole is punched. When unfolded, how many holes appear?
- Two holes
- Four holes
- One hole
- Eight holes
Correct answer: Eight holes
Eight holes is correct. Eight stacked layers mean a single punch passes through all eight, creating eight holes when the paper is opened. Four holes would come from four layers, two holes from two layers, and one hole would ignore the stacking entirely.
- A paper folded once shows a hole punched halfway between the fold and the far edge. After unfolding, how far from the fold is each of the two holes?
- The same distance from the fold on each side
- Different distances from the fold
- Both touching the fold line
- Both at the far edge
Correct answer: The same distance from the fold on each side
The same distance from the fold on each side is correct. A fold mirrors the punch, so each hole sits the same distance away from the crease, like a reflection. The holes are not at different distances, not on the fold itself, and not pushed to the far edge, because the reflection preserves the original distance.
- A square sheet is folded in half once and a hole is punched in the exact center of the folded paper. When unfolded, where is the hole?
- Four holes in the corners
- A single hole on the fold line at the paper's center
- Two holes far apart
- No holes at all
Correct answer: A single hole on the fold line at the paper's center
A single hole on the fold line at the paper's center is correct. When folded in half, the center of the folded sheet lies on the fold line, so a punch there sits on the crease and shows as one hole at the center after unfolding. Two far-apart holes, four corner holes, and no holes do not match a single center punch on the fold.
- A square sheet is folded in half twice into four layers, and one hole is punched in the middle of one edge. When unfolded, how many holes appear along the edges?
- Two holes
- Eight holes
- Four holes
- One hole
Correct answer: Four holes
Four holes is correct. Folding twice stacks four layers, so a single punch passes through all four and yields four holes when unfolded, mirrored across both folds. Two holes counts only one fold, one hole ignores the layers, and eight holes would require a second punch or more layers.
- A square sheet is folded in half top to bottom and a hole is punched, then it is unfolded. The student sees two holes. What would adding a second top-to-bottom fold before punching change?
- It would make the holes disappear
- It would keep the count at exactly two holes
- It would turn the holes into a single line
- It would increase the number of layers, so one punch would make more holes
Correct answer: It would increase the number of layers, so one punch would make more holes
Increasing the number of layers is correct. Each extra fold doubles the layers a punch goes through, so more folds mean one punch produces more holes when unfolded. The holes would not disappear, would not stay at two, and would not merge into a line, because adding layers multiplies the punch count.
- A square sheet is folded in half and a hole is punched. Could the unfolded sheet ever show an odd number of holes from a single off-fold punch?
- No, because the punch goes through two layers and makes a mirrored pair
- Yes, it usually shows three holes
- Yes, it always shows one hole
- Yes, it shows five holes
Correct answer: No, because the punch goes through two layers and makes a mirrored pair
No, because the punch goes through two layers and makes a mirrored pair is correct. A single fold gives two layers, so one off-fold punch always produces two mirrored holes, an even number. It cannot show three, one, or five holes from a single off-fold punch through two layers, since the result is always a pair.
- A square sheet is folded into four layers and one hole is punched in the very center of the folded stack. When unfolded, the holes form what pattern around the middle of the sheet?
- A line of holes across the bottom
- A small symmetric cluster of holes near the center
- A single hole at one corner
- No holes at all
Correct answer: A small symmetric cluster of holes near the center
A small symmetric cluster of holes near the center is correct. With four layers, a center punch creates holes that mirror across both fold lines, producing a balanced cluster around the middle when unfolded. A single corner hole, a bottom line of holes, and no holes do not match a center punch through four mirrored layers.
- A square sheet is folded twice into four layers and a hole is punched, producing four holes when unfolded. If only one fold had been used instead, how many holes would one punch make?
- One hole
- Four holes
- Two holes
- Eight holes
Correct answer: Two holes
Two holes is correct. A single fold makes only two layers, so one punch passes through two layers and creates two holes. Four holes would come from two folds, one hole would ignore the second layer, and eight holes would need even more layers, so two is right for a single fold.
- A square sheet is folded in half once and a hole is punched, making two holes when unfolded. A student wants exactly four holes using a single fold. How can this be done?
- Fold the paper a third time
- Use a bigger hole punch
- Color the paper before punching
- Punch two holes instead of one before unfolding
Correct answer: Punch two holes instead of one before unfolding
Punching two holes instead of one is correct. With a single fold giving two layers, each punch makes two holes, so two punches make two times two, which is four holes. Adding folds changes the layer count rather than keeping a single fold, and a bigger punch or coloring does not change how many holes appear.
- On the CogAT Nonverbal Battery, the Figure Classification subtest asks a test-taker to do which of the following?
- Find the property shared by three given figures and choose a fourth figure that fits the set
- Balance both sides of an equation
- Complete a sentence with the right word
- Apply a number rule to a new pair
Correct answer: Find the property shared by three given figures and choose a fourth figure that fits the set
Finding the property shared by three figures and choosing a fourth that fits is the Figure Classification task. The subtest shows three figures that go together and asks which option belongs with them. Balancing equations, completing sentences, and applying number rules belong to other subtests, not the Nonverbal Battery.
- Three figures are shown: a triangle, a square, and a pentagon. All are figures with straight sides. Which figure belongs with this set?
- A crescent
- A hexagon
- An oval
- A circle
Correct answer: A hexagon
A hexagon is correct. The three given figures all have straight sides and corners, so the shared property is being made of straight sides; a hexagon also has straight sides. A circle, an oval, and a crescent are all curved, so none of them shares the straight-sided property.
- Three figures are shown, each a shape fully shaded black: a black circle, a black square, and a black star. Which figure belongs with this set?
- A white circle
- A white triangle
- A black triangle
- A striped square
Correct answer: A black triangle
A black triangle is correct. The three given figures are all completely shaded black, so the shared property is being fully black; a black triangle is also fully black. A white triangle and a white circle are unshaded, and a striped square is only partly filled, so none matches the all-black property.
- Three figures are shown, each containing exactly one dot inside: a circle with one dot, a square with one dot, and a triangle with one dot. Which figure belongs with this set?
- A square with two dots inside
- A star with three dots inside
- An empty star
- A star with one dot inside
Correct answer: A star with one dot inside
A star with one dot inside is correct. The shared property is having exactly one dot inside the shape, regardless of the shape itself; a star with one dot matches that. Three dots, no dots, and two dots all have the wrong number of dots, so only the single-dot star fits the set.
- Three figures are shown, all small: a small circle, a small square, and a small triangle. Which figure belongs with this set?
- A small star
- A large star
- A large circle
- A large square
Correct answer: A small star
A small star is correct. The three given figures are all small, so the shared property is small size; a small star matches that size. A large star, a large circle, and a large square are all big, so none of them shares the small-size property even though they are common shapes.
- Three figures are shown, each divided into two equal halves by a line: a circle split in two, a square split in two, and a rectangle split in two. Which figure belongs with this set?
- A circle split into four parts
- A triangle split into two halves
- A whole triangle with no line
- A square with a dot inside
Correct answer: A triangle split into two halves
A triangle split into two halves is correct. The shared property is being divided into two equal halves by a single line; a triangle split in two matches that. A whole triangle has no dividing line, a circle split into four has too many parts, and a square with a dot is not divided, so only the two-part triangle fits.
- Three figures are shown, each with four sides: a square, a rectangle, and a diamond. Which figure belongs with this set?
- A pentagon
- A triangle
- A trapezoid
- A circle
Correct answer: A trapezoid
A trapezoid is correct. The shared property is having exactly four sides; a trapezoid is also a four-sided shape. A triangle has three sides, a pentagon has five sides, and a circle has no straight sides, so only the trapezoid has the four sides the set shares.
- Three figures are shown, each an arrow pointing to the right. Which figure belongs with this set?
- An arrow pointing left
- An arrow pointing up
- A circle with no arrow
- A fourth arrow pointing right
Correct answer: A fourth arrow pointing right
A fourth arrow pointing right is correct. The shared property is being an arrow that points to the right, so another right-pointing arrow fits the set. Arrows pointing left or up face the wrong way, and a circle is not an arrow at all, so only the right-pointing arrow belongs.
- Three figures are shown, each shape outlined with a dashed line: a dashed circle, a dashed square, and a dashed triangle. Which figure belongs with this set?
- A dashed star
- A fully shaded star
- A solid-outline star
- A dotted-fill square
Correct answer: A dashed star
A dashed star is correct. The shared property is having a dashed outline; a dashed star matches that style. A solid-outline star uses a continuous line, a fully shaded star is filled rather than outlined, and a dotted-fill square has the wrong style, so only the dashed star fits the set.
- Three figures are shown, each containing a smaller copy of itself inside: a square inside a square, a circle inside a circle, and a triangle inside a triangle. Which figure belongs with this set?
- A star next to a star
- A star inside a star
- A circle inside a square
- A single plain star
Correct answer: A star inside a star
A star inside a star is correct. The shared property is a shape holding a smaller copy of the same shape inside it; a star inside a star matches that. A single plain star has nothing inside, a circle inside a square mixes shapes, and a star next to a star places them side by side rather than nested, so only the nested star fits.
- A student is shown three figures that go together and must choose a fourth that belongs. Which Nonverbal Battery subtest is this?
- Paper Folding
- Number Analogies
- Figure Classification
- Figure Matrices
Correct answer: Figure Classification
Figure Classification is correct. It is the subtest that shows three figures sharing a property and asks for a fourth that fits the group. Figure Matrices completes a grid pattern, Paper Folding predicts hole positions, and Number Analogies is a quantitative task.
- Three figures are shown, each a shape with exactly one curved side and the rest straight: a half-circle shape, a shape like a capital D, and a quarter-circle wedge. Which figure belongs with this set?
- A full circle with no straight sides
- A square with four straight sides
- A triangle with three straight sides
- A shape with one curved side and one straight side
Correct answer: A shape with one curved side and one straight side
A shape with one curved side and one straight side is correct. The set shares the property of mixing a curve with straight edges, so a figure with one curved side and one straight side fits. A full circle has no straight side, and a square or triangle has no curved side, so none of those matches the mix the set shows.
- Three figures are shown, each with an upward-pointing arrow inside a box. Which figure belongs with this set?
- An upward arrow inside a box
- A box with no arrow
- A downward arrow inside a box
- An upward arrow with no box
Correct answer: An upward arrow inside a box
An upward arrow inside a box is correct. The shared property is an arrow that points up enclosed within a box, so another upward arrow inside a box fits. A downward arrow points the wrong way, an arrow with no box is missing the enclosure, and an empty box has no arrow, so none of those matches both features.
- Three figures are shown, each made of exactly three small circles: three circles in a row, three circles in a triangle shape, and three circles stacked in a column. Which figure belongs with this set?
- Five circles in a row
- Three circles arranged in an L shape
- Two circles side by side
- Four circles in a row
Correct answer: Three circles arranged in an L shape
Three circles arranged in an L shape is correct. The shared property is being made of exactly three circles, no matter how they are arranged, so three circles in an L fits. Four circles, two circles, and five circles all have the wrong number, so only the three-circle group belongs.
- Three figures are shown, each a plain outline with no shading: an empty circle, an empty square, and an empty triangle. Which figure belongs with this set?
- A black circle
- A fully shaded star
- An empty star
- A half-shaded square
Correct answer: An empty star
An empty star is correct. The shared property is being an unshaded outline, so an empty star fits the set. A fully shaded star and a black circle are filled in, and a half-shaded square is partly filled, so none of those matches the empty outline the set shares.
- Three figures are shown, each split into exactly four equal parts: a circle cut into four, a square cut into four, and a rectangle cut into four. Which figure belongs with this set?
- A whole square with no cuts
- A triangle cut into three parts
- A circle cut into two parts
- A triangle cut into four equal parts
Correct answer: A triangle cut into four equal parts
A triangle cut into four equal parts is correct. The shared property is being divided into exactly four equal parts, so a triangle in four parts fits. A circle in two parts and a triangle in three parts have the wrong number of parts, and a whole square has no cuts at all, so only the four-part triangle matches.
- Three figures are shown, each a striped shape: a striped circle, a striped square, and a striped triangle. Which figure belongs with this set?
- A striped pentagon
- An empty pentagon
- A solid black pentagon
- A dotted pentagon
Correct answer: A striped pentagon
A striped pentagon is correct. The shared property is having a striped fill, so a striped pentagon matches the set. A solid black pentagon is fully filled, an empty pentagon has no fill, and a dotted pentagon uses dots instead of stripes, so only the striped pentagon fits the pattern.
- Three figures are shown, each a shape with a small black dot in its center: a circle with a center dot, a square with a center dot, and a star with a center dot. Which figure belongs with this set?
- A triangle with two dots
- A triangle with a center dot
- A plain triangle
- A triangle with a dot in its corner
Correct answer: A triangle with a center dot
A triangle with a center dot is correct. The shared property is having a single dot placed in the center of the shape, so a triangle with a center dot fits. A corner dot is in the wrong place, a plain triangle has no dot, and two dots is the wrong count, so only the center-dotted triangle matches.
- Three figures are shown, each a large shape: a large circle, a large square, and a large triangle. Which figure belongs with this set?
- A small circle
- A small square
- A large hexagon
- A small hexagon
Correct answer: A large hexagon
A large hexagon is correct. The shared property is large size, so a large hexagon fits the set. A small hexagon, a small circle, and a small square are all small, so none of them shares the large size that the three given figures have in common.
- Three figures are shown, each a shape resting on a short flat base line: a triangle on a line, a square on a line, and a circle on a line. Which figure belongs with this set?
- A star tilted on its side
- A line with no shape
- A star floating with no line
- A star resting on a short flat line
Correct answer: A star resting on a short flat line
A star resting on a short flat line is correct. The shared property is a shape sitting upright on a short base line, so a star on a line fits. A floating star has no line, a bare line has no shape, and a tilted star is not resting upright, so only the upright star on a line matches the set.
- Three figures are shown, each with two shapes overlapping to share a small region: two overlapping circles, two overlapping squares, and two overlapping triangles. Which figure belongs with this set?
- Two overlapping stars
- A single star
- Two stars far apart
- Three stars in a row
Correct answer: Two overlapping stars
Two overlapping stars is correct. The shared property is two of the same shape overlapping so they share a region, so two overlapping stars fits. Two stars far apart do not overlap, a single star has nothing to overlap, and three stars in a row changes the count, so only the overlapping pair matches.
- Three figures are shown, each a five-pointed star of a different size and color. What property do all three share?
- They are all the same size
- They are all stars
- They are all circles
- They are all the same color
Correct answer: They are all stars
They are all stars is correct. The figures differ in size and color but each is a five-pointed star, so the only property they share is being a star. They are not the same size or color, and none of them is a circle, so the star shape is the common trait.
- Three figures are shown, each pointing diagonally toward the upper-right corner: an arrow, a triangle, and a finger shape, all aimed upper-right. Which figure belongs with this set?
- A pencil shape aimed toward the lower-left
- A flat horizontal pencil shape
- A pencil shape aimed toward the upper-right
- A pencil shape aimed straight down
Correct answer: A pencil shape aimed toward the upper-right
A pencil shape aimed toward the upper-right is correct. The shared property is pointing diagonally toward the upper-right corner, so a pencil aimed that way fits the set. Aiming straight down, toward the lower-left, or flat horizontally all point the wrong direction, so only the upper-right pencil matches.
- Three figures are shown, each shape rotated so it tilts to one side rather than sitting upright: a tilted square, a tilted triangle, and a tilted rectangle. Which figure belongs with this set?
- An upright pentagon
- A pentagon lying perfectly flat and level
- An upright square
- A tilted pentagon
Correct answer: A tilted pentagon
A tilted pentagon is correct. The shared property is being tilted to one side rather than upright, so a tilted pentagon fits the set. An upright pentagon and an upright square are not tilted, and a perfectly level pentagon is also not tilted, so only the tilted pentagon matches the set.
- Three figures are shown, each having a small shape sitting inside a larger shape: a small dot in a big circle, a small dot in a big square, and a small dot in a big triangle. Which figure belongs with this set?
- A small dot inside a big star
- A big dot with nothing around it
- Two dots side by side
- A big star inside a small dot
Correct answer: A small dot inside a big star
A small dot inside a big star is correct. The shared property is a small dot placed inside a larger outer shape, so a small dot in a big star fits. A lone big dot has no outer shape, putting a big star inside a small dot reverses the sizes, and two side-by-side dots are not nested, so only the dot-in-star matches.
- Three figures are shown, each made of a single unbroken loop: a circle, an oval, and a rounded rectangle with no gaps. Which figure belongs with this set?
- A capital letter C with a gap
- A closed heart outline
- A straight line
- A horseshoe shape with an opening
Correct answer: A closed heart outline
A closed heart outline is correct. The shared property is being a single closed loop with no opening, so a closed heart outline fits. A letter C, a horseshoe, and a straight line all have a gap or open ends, so none of them forms the unbroken loop the set shares.
- Three figures are shown, each containing two dots: a circle with two dots, a square with two dots, and a triangle with two dots. Which figure belongs with this set?
- A star with three dots
- An empty star
- A star with two dots
- A star with one dot
Correct answer: A star with two dots
A star with two dots is correct. The shared property is having exactly two dots inside, so a star with two dots fits the set. One dot, three dots, and no dots all have the wrong number, so only the star with two dots matches the count the set shows.
- Three figures are shown, each a shape with rounded corners: a rounded square, a rounded triangle, and a rounded rectangle. Which figure belongs with this set?
- A sharp-cornered square
- A perfect circle
- A pentagon with sharp pointed corners
- A rounded-corner pentagon
Correct answer: A rounded-corner pentagon
A rounded-corner pentagon is correct. The shared property is having rounded corners, so a pentagon with rounded corners fits the set. A pentagon with sharp corners and a sharp-cornered square have pointed corners, and a circle has no corners at all, so only the rounded pentagon matches.
- Three figures are shown, each shape cut exactly in half with one half shaded: a half-shaded circle, a half-shaded square, and a half-shaded triangle. Which figure belongs with this set?
- A half-shaded pentagon
- A pentagon shaded in tiny dots
- A fully shaded pentagon
- An empty pentagon
Correct answer: A half-shaded pentagon
A half-shaded pentagon is correct. The shared property is having exactly half of the shape shaded, so a half-shaded pentagon fits. A fully shaded pentagon and a dotted pentagon are filled differently, and an empty pentagon has no shading, so only the half-shaded pentagon matches the set.
- Three figures are shown, each having exactly one corner cut off so a slanted edge replaces it: a square with a clipped corner, a rectangle with a clipped corner, and a triangle with a clipped corner. Which figure belongs with this set?
- A pentagon with every corner clipped
- A pentagon with one corner clipped
- A pentagon with all corners sharp
- A perfect circle
Correct answer: A pentagon with one corner clipped
A pentagon with one corner clipped is correct. The shared property is having exactly one corner cut off, so a pentagon with one clipped corner fits. A pentagon with all sharp corners has none clipped, clipping every corner is too many, and a circle has no corners, so only the single-clipped pentagon matches.
- Three figures are shown, each an open shape with two free ends: a letter C, a letter U, and a horseshoe. Which figure belongs with this set?
- A closed square
- A closed circle
- A letter V with two open ends
- A filled black dot
Correct answer: A letter V with two open ends
A letter V with two open ends is correct. The shared property is being an open shape with two free ends, so a V fits the set. A closed circle and a closed square have no open ends, and a filled dot has no ends at all, so only the V matches the open-ended pattern.
- Three figures are shown, each a shape touching a wall on its left side: a circle touching a left wall, a square touching a left wall, and a triangle touching a left wall. Which figure belongs with this set?
- A star touching a wall on its right side
- A star at the top of the box
- A star floating in the middle
- A star touching a wall on its left side
Correct answer: A star touching a wall on its left side
A star touching a wall on its left side is correct. The shared property is having the shape pressed against the left wall, so a star against the left wall fits. A floating star touches nothing, a right-wall star is on the wrong side, and a star at the top is in the wrong place, so only the left-wall star matches.
- Three figures are shown, each pair of identical shapes with the second one larger than the first: small-then-large circles, small-then-large squares, and small-then-large triangles. Which figure belongs with this set?
- A small star followed by a large star
- Two stars the same size
- A large star followed by a small star
- A single star
Correct answer: A small star followed by a large star
A small star followed by a large star is correct. The shared property is a pair where the second shape is bigger than the first, so a small star then a large star fits. Reversing the order, using equal sizes, or showing a single star all break the small-then-large pattern, so only the growing star pair matches.
- Three figures are shown, each a shape made entirely of dotted lines: a dotted circle, a dotted square, and a dotted star. Which figure belongs with this set?
- A fully shaded triangle
- A triangle drawn with dotted lines
- A triangle drawn with a thick bold line
- A triangle drawn with a solid line
Correct answer: A triangle drawn with dotted lines
A triangle drawn with dotted lines is correct. The shared property is being drawn with dotted lines, so a dotted triangle fits the set. A solid-line triangle, a shaded triangle, and a thick bold triangle all use a different line style, so only the dotted triangle matches the set.
- Three figures are shown, each a shape with an X drawn through its center: a circle with an X, a square with an X, and a hexagon with an X. Which figure belongs with this set?
- A pentagon with a plus sign
- A plain pentagon
- A pentagon with an X through its center
- A pentagon with a single dot
Correct answer: A pentagon with an X through its center
A pentagon with an X through its center is correct. The shared property is having an X drawn through the middle of the shape, so a pentagon with an X fits. A single dot, an empty interior, and a plus sign are all different inner marks, so only the pentagon with an X matches the set.
- Three figures are shown, each having two parts of equal size: a circle split into two equal halves, an hourglass shape with two equal triangles, and a domino with two equal squares. Which figure belongs with this set?
- A whole undivided rectangle
- A rectangle with a tiny corner cut off
- A rectangle split into three unequal parts
- A rectangle split into two equal halves
Correct answer: A rectangle split into two equal halves
A rectangle split into two equal halves is correct. The shared property is being made of two equal parts, so a rectangle in two equal halves fits. Three unequal parts has the wrong number and uneven sizes, a whole rectangle has no parts, and a cut corner does not create two equal halves, so only the evenly halved rectangle matches.
- Three figures are shown, each a shape with a tail sticking out to the right: a circle with a tail, a square with a tail, and a triangle with a tail. Which figure belongs with this set?
- A star with a tail sticking out to the right
- A star with no tail
- A lone tail with no shape
- A star with a tail sticking out to the left
Correct answer: A star with a tail sticking out to the right
A star with a tail sticking out to the right is correct. The shared property is a shape with a tail extending to the right, so a star with a right-side tail fits. A tailless star is missing the tail, a left-side tail points the wrong way, and a lone tail has no shape, so only the right-tailed star matches the set.
- Three figures are shown, each shape divided into stripes that run sideways: a circle with horizontal stripes, a square with horizontal stripes, and a triangle with horizontal stripes. Which figure belongs with this set?
- A pentagon with diagonal stripes
- A pentagon with horizontal stripes
- A plain pentagon
- A pentagon with vertical stripes
Correct answer: A pentagon with horizontal stripes
A pentagon with horizontal stripes is correct. The shared property is having stripes that run sideways, or horizontally, so a pentagon with horizontal stripes fits. Vertical and diagonal stripes run the wrong way, and a plain pentagon has no stripes, so only the horizontally striped pentagon matches the set.
- The Nonverbal Battery of the CogAT is best described as measuring which of the following?
- Knowledge of vocabulary and grammar rules
- Speed at solving long word problems
- Reasoning with shapes and figures that does not rely on reading words or numbers
- Memory for historical dates
Correct answer: Reasoning with shapes and figures that does not rely on reading words or numbers
Reasoning with shapes and figures that does not rely on reading words or numbers is correct. The Nonverbal Battery, made of Figure Matrices, Paper Folding, and Figure Classification, tests visual and spatial reasoning without language. It is not about vocabulary, solving word problems, or memorizing dates, which involve reading or recall rather than figure reasoning.
- Which three subtests make up the CogAT Nonverbal Battery?
- Picture Analogies, Number Series, and Sentence Completion
- Number Analogies, Number Puzzles, and Number Series
- Verbal Analogies, Sentence Completion, and Verbal Classification
- Figure Matrices, Paper Folding, and Figure Classification
Correct answer: Figure Matrices, Paper Folding, and Figure Classification
Figure Matrices, Paper Folding, and Figure Classification are the three Nonverbal Battery subtests. The verbal trio and the quantitative trio belong to the Verbal and Quantitative batteries, so any list mixing those in is incorrect.
- Why is the CogAT Nonverbal Battery especially useful for students who are still learning English?
- It uses shapes and figures instead of words, so reading ability does not affect the score
- It is graded by a different scale than the other batteries
- It allows students to use a dictionary during the test
- It only asks about familiar vocabulary words
Correct answer: It uses shapes and figures instead of words, so reading ability does not affect the score
Using shapes and figures instead of words is correct. Because the Nonverbal Battery relies on visual reasoning rather than language, a student who is still learning English can show reasoning ability without being held back by reading. It does not involve dictionaries, vocabulary recall, or a special grading scale.
- The Nonverbal Battery measures reasoning without words. Which of these would NOT appear on the Nonverbal Battery?
- A folded paper with punched holes
- A sentence with a missing word to fill in
- Three figures that share a property
- A 2x2 grid of figures with one cell empty
Correct answer: A sentence with a missing word to fill in
A sentence with a missing word to fill in is correct as the one that would not appear. That is a Verbal Battery task involving words, while the Nonverbal Battery uses figure grids, folded paper, and shared-property figure sets. The three figure-based items all belong to the Nonverbal Battery, so only the sentence task does not.
- A test booklet section shows only shapes, figures, and folded papers with no words or numbers to read. Which CogAT battery is this section?
- The Verbal Battery
- The Quantitative Battery
- The Nonverbal Battery
- The Reading Battery
Correct answer: The Nonverbal Battery
The Nonverbal Battery is correct. A section made entirely of shapes, figures, and folded papers with no reading is the Nonverbal Battery, which tests figure reasoning without language or numbers. The Verbal Battery uses words and the Quantitative Battery uses numbers, while a Reading Battery is not one of the three CogAT batteries.
- Why does the CogAT include a Nonverbal Battery alongside the Verbal and Quantitative batteries?
- To make the test longer
- To replace the need for any verbal questions
- To test how neatly a student can draw
- To measure reasoning ability through figures, giving a fuller picture of a student's thinking beyond words and numbers
Correct answer: To measure reasoning ability through figures, giving a fuller picture of a student's thinking beyond words and numbers
Measuring reasoning through figures for a fuller picture is correct. The Nonverbal Battery captures reasoning that does not depend on words or numbers, so the three batteries together show a more complete view of a student's abilities. It is not there to lengthen the test, judge drawing neatness, or replace the verbal questions, which remain part of the CogAT.
- Spatial reasoning on the Nonverbal Battery often involves rotation. If a shape shaped like the letter L is rotated a quarter turn clockwise, the part that pointed up will now point in which direction?
- To the right
- To the left
- Still straight up
- Straight down
Correct answer: To the right
To the right is correct. A quarter turn clockwise moves whatever was pointing up so that it now points to the right. Pointing left would be a counterclockwise turn, pointing down would be a half turn, and staying up would mean no rotation at all.
- A figure is described as symmetrical. What does that mean about the figure?
- It is always shaded black
- One half is a mirror image of the other half
- It has more than four sides
- It can never be rotated
Correct answer: One half is a mirror image of the other half
One half being a mirror image of the other half is correct. Symmetry means a figure can be split by a line so that the two halves match like a reflection. Having many sides, being shaded black, or never rotating are unrelated to whether the two halves mirror each other.
- Which of these shapes has the most sides?
- A square
- A triangle
- A hexagon
- A pentagon
Correct answer: A hexagon
A hexagon is correct because it has six sides, more than the others. A triangle has three sides, a square has four, and a pentagon has five, so the hexagon has the greatest number of sides.
- If a triangle pointing up is rotated a half turn, which way will it point?
- To the right
- To the left
- Up
- Down
Correct answer: Down
Down is correct. A half turn flips a shape completely upside down, so a triangle that pointed up will then point down. It will not still point up, and pointing left or right would only happen after a quarter turn, not a half turn.
- If a shape that looks like the letter F faces to the right, what does its mirror image look like?
- The same letter F facing to the left
- The letter F turned upside down
- The letter E
- The letter L
Correct answer: The same letter F facing to the left
The same letter F facing to the left is correct. A mirror image flips a shape left to right, so an F facing right becomes an F facing left, like a reflection in a mirror. Turning it upside down is a rotation rather than a reflection, and the E and L are different letters, not mirror images of F.
- A figure has a line of symmetry running straight down its middle. Folding the figure along that line would do what?
- Turn the figure upside down
- Make the two halves match up exactly
- Change the figure into a circle
- Make the figure twice as large
Correct answer: Make the two halves match up exactly
Making the two halves match up exactly is correct. A line of symmetry means that folding along it lines the two halves up perfectly, like mirror images. Folding does not enlarge the figure, flip it upside down, or change it into a circle, since the halves simply overlap.
- When a square is rotated by a quarter turn, how does its appearance change?
- It becomes much larger
- It turns into a circle
- It looks exactly the same because a square has matching sides and corners
- It becomes a triangle
Correct answer: It looks exactly the same because a square has matching sides and corners
Looking exactly the same is correct. A square has four equal sides and equal corners, so turning it a quarter turn lands every side and corner in a spot identical to before. Rotation never changes a shape into a triangle or circle, and it does not change the size, so the square appears unchanged.
- Which figure has a line of symmetry?
- A scribble with no matching halves
- The number seven written normally
- A shape with all different sides
- A square
Correct answer: A square
A square is correct. A square can be divided by a line so its two halves mirror each other, which means it has a line of symmetry. A random scribble, the number seven, and a shape with all different sides cannot be split into two matching halves, so they lack symmetry.
- A shape pointing to the left is rotated a quarter turn counterclockwise. Which way does it point now?
Correct answer: Down
Down is correct. A quarter turn counterclockwise moves something pointing left so that it points down. Pointing up would be a clockwise quarter turn, pointing right would be a half turn, and staying left would mean no rotation occurred.
- Which statement about a circle's symmetry is true?
- A circle has exactly two lines of symmetry
- A circle has many lines of symmetry because any line through its center divides it into matching halves
- A circle has exactly one line of symmetry
- A circle has no lines of symmetry
Correct answer: A circle has many lines of symmetry because any line through its center divides it into matching halves
Having many lines of symmetry is correct. Any straight line drawn through the center of a circle splits it into two matching halves, so a circle has countless lines of symmetry. Saying it has none, exactly one, or exactly two undercounts the symmetry a circle actually has.
- A shape that points up is reflected across a horizontal line (flipped top to bottom). Which way does it point after the flip?
Correct answer: Down
Down is correct. Reflecting across a horizontal line flips a shape top to bottom, so something pointing up ends up pointing down, like its image in water. It does not stay up, and pointing left or right would require a flip across a vertical line instead.
- Counting sides is a useful spatial skill. How many sides does a pentagon have?
Correct answer: Five
Five is correct. A pentagon is defined as a shape with five straight sides. Three sides describes a triangle, four sides describes a quadrilateral such as a square, and six sides describes a hexagon, so only five matches a pentagon.
- If a figure looks the same after being rotated a half turn, the figure is said to have what kind of symmetry?
- Rotational symmetry
- Only color symmetry
- No symmetry at all
- Only size symmetry
Correct answer: Rotational symmetry
Rotational symmetry is correct. A figure has rotational symmetry when it appears unchanged after being turned, such as after a half turn. Saying it has no symmetry contradicts the unchanged look, and color or size symmetry are not the terms for matching after a rotation.
- Which shape would look exactly the same after a quarter turn?
- A scalene triangle with three different sides
- A square
- An arrow pointing right
- A capital letter R
Correct answer: A square
A square is correct. Because a square has four equal sides and corners, turning it a quarter turn leaves it looking identical. A capital letter R, a triangle with three unequal sides, and a right-pointing arrow each look different after a quarter turn, so only the square stays the same.
- A letter b is reflected across a vertical line (flipped left to right). What letter does its mirror image most resemble?
- The letter q
- The letter b unchanged
- The letter d
- The letter p
Correct answer: The letter d
The letter d is correct. Flipping a lowercase b left to right swaps the bump from the right side to the left, producing a shape that looks like a d. Flipping it top to bottom would make a p, a different flip makes a q, and it does not stay unchanged because reflection moves the bump.
- How many lines of symmetry does an equilateral triangle, which has three equal sides, have?
Correct answer: Three
Three is correct. An equilateral triangle can be folded into matching halves along a line from each corner to the middle of the opposite side, and there are three corners, so it has three lines of symmetry. One, two, or zero would undercount the symmetry of a triangle with three equal sides.
- When a figure is rotated, which feature always stays the same?
- Its size and shape
- Its position on the page
- Nothing stays the same
- The direction it points
Correct answer: Its size and shape
Its size and shape is correct. Rotation only turns a figure; it does not stretch, shrink, or reshape it, so the size and shape are kept. The direction it points usually changes with rotation, its place on the page can shift, and saying nothing stays the same ignores that the figure itself is unchanged.
- Which pair of letters are mirror images of each other across a vertical line?
- E and W
- B and d
- N and u
- B and p
Correct answer: B and d
b and d is correct. Flipping a lowercase b left to right across a vertical line produces a d, so they are vertical mirror images. The letters b and p mirror top to bottom, n and u mirror top to bottom, and E and W are not mirror images at all, so only b and d match across a vertical line.
- A figure with no line of symmetry would look like which of the following?
- A circle
- A capital letter A
- A random blob whose two sides do not match no matter where you draw a line
- A perfect square
Correct answer: A random blob whose two sides do not match no matter where you draw a line
A random blob is correct. Lacking symmetry means there is no line that splits the figure into two matching halves, which describes an irregular blob. A square, a circle, and a capital letter A each have at least one line that divides them into mirror halves, so they do have symmetry.
- A rectangle that is twice as long as it is wide is rotated a quarter turn. How does it look afterward?
- It turns into a triangle
- It becomes a square
- It stays exactly the same as before
- It now stands tall instead of lying flat, swapping its long and short directions
Correct answer: It now stands tall instead of lying flat, swapping its long and short directions
Standing tall instead of lying flat is correct. A quarter turn rotates the rectangle so its long side, once horizontal, becomes vertical, swapping which way is long and short. It does not become a square or triangle, since rotation keeps the shape, and it does not look the same because its proportions are not equal in both directions.
- If a shape pointing right is rotated three-quarters of a turn clockwise, which way will it point?
Correct answer: Up
Up is correct. Starting pointing right, a quarter turn clockwise points it down, a half turn points it left, and three-quarters of a turn brings it to point up. Down and left are earlier stages of the turn, and right would mean no turn at all, so up is the result after three-quarters.
- How many sides does an octagon, like a common stop sign shape, have?
Correct answer: Eight
Eight is correct. An octagon, the shape of a stop sign, has eight straight sides. Six sides describes a hexagon, five describes a pentagon, and ten describes a decagon, so only eight matches an octagon.
- A capital letter T is rotated a half turn. What does it look like afterward?
- The same upright T
- A plus sign
- An upside-down T with the crossbar at the bottom
- A capital letter L
Correct answer: An upside-down T with the crossbar at the bottom
An upside-down T with the crossbar at the bottom is correct. A half turn flips the letter completely, so the crossbar that was on top moves to the bottom. It does not stay upright, and it does not become an L or a plus sign, since rotation keeps the same parts but turns them around.
- Which of these capital letters looks the same when reflected across a vertical line down its middle?
- The letter G
- The letter R
- The letter F
- The letter A
Correct answer: The letter A
The letter A is correct. A capital A is symmetric left to right, so its mirror image across a vertical center line looks identical. The letters F, G, and R are not the same on both sides, so their mirror images would look different, leaving A as the symmetric one.
- When a shape is reflected, or flipped, the result is best described as which of the following?
- A mirror image of the original
- A shape turned a quarter turn
- A larger copy of the original
- A shape with one more side
Correct answer: A mirror image of the original
A mirror image of the original is correct. Reflecting a shape flips it to produce its mirror image, like looking at it in a mirror. Reflection does not change its size, add sides, or rotate it a quarter turn, so the mirror-image description is the accurate one.
- Which figure would NOT look the same after being rotated a half turn?
- A capital letter H
- A capital letter P
- A capital letter X
- A capital letter O
Correct answer: A capital letter P
A capital letter P is correct. Turning a P a half turn moves its bump to the bottom, so it no longer looks like a P. The letters O, H, and X each look the same after a half turn because they are balanced top and bottom, so only the P changes appearance.
