- Which word means the OPPOSITE of "ancient"?
Correct answer: Modern
The opposite of "ancient" is "modern," because "ancient" describes something very old while "modern" describes something belonging to the present time. "Old," "historic," and "faded" either match or only loosely relate to "ancient," so they are not its opposite.
- Which word means the OPPOSITE of "expand"?
Correct answer: Shrink
"Shrink" is the opposite of "expand," since "expand" means to get larger and "shrink" means to get smaller. "Stretch," "grow," and "widen" all describe increasing in size, so they are synonyms rather than antonyms.
- Which word means the OPPOSITE of "generous"?
Correct answer: Selfish
"Selfish" is the opposite of "generous," because a generous person freely shares while a selfish person keeps things for themselves. "Kind," "giving," and "helpful" describe a generous attitude, not the reverse of it.
- Which word means the OPPOSITE of "victory"?
- Triumph
- Defeat
- Contest
- Reward
Correct answer: Defeat
"Defeat" is the opposite of "victory," since a victory is a win and a defeat is a loss. "Triumph" means the same as victory, while "contest" and "reward" name related ideas rather than the opposite.
- Which word means the OPPOSITE of "permanent"?
- Lasting
- Stable
- Temporary
- Fixed
Correct answer: Temporary
"Temporary" is the opposite of "permanent," because something permanent lasts forever while something temporary lasts only a short time. "Lasting," "stable," and "fixed" all mean enduring, so they match "permanent" instead of opposing it.
- Which word means the OPPOSITE of "transparent"?
Correct answer: Opaque
"Opaque" is the opposite of "transparent," since light passes through a transparent material but cannot pass through an opaque one. "Clear," "glassy," and "thin" describe see-through qualities, making them closer in meaning to transparent.
- Which word means the OPPOSITE of "abundant"?
Correct answer: Scarce
"Scarce" is the opposite of "abundant," because abundant means there is a large supply and scarce means there is very little. "Plentiful," "ample," and "rich" all signal a large amount, so they are synonyms of abundant.
- Which word means the OPPOSITE of "praise"?
- Admire
- Criticize
- Applaud
- Honor
Correct answer: Criticize
"Criticize" is the opposite of "praise," since to praise is to speak well of someone and to criticize is to point out faults. "Admire," "applaud," and "honor" all express approval, which is the same idea as praise.
- Which word means the OPPOSITE of "reveal"?
Correct answer: Conceal
"Conceal" is the opposite of "reveal," because to reveal is to make something known and to conceal is to hide it. "Show," "display," and "expose" all mean to make visible, matching the meaning of reveal.
- Which word means the OPPOSITE of "humble"?
- Modest
- Quiet
- Simple
- Arrogant
Correct answer: Arrogant
"Arrogant" is the opposite of "humble," since a humble person does not boast while an arrogant person thinks too highly of themselves. "Modest," "quiet," and "simple" describe humility rather than oppose it.
- Which word means the OPPOSITE of "fragile"?
- Sturdy
- Delicate
- Brittle
- Weak
Correct answer: Sturdy
"Sturdy" is the opposite of "fragile," because something fragile breaks easily while something sturdy is strong and hard to break. "Delicate," "brittle," and "weak" all share the meaning of being easily damaged, like fragile.
- Which word means the OPPOSITE of "increase"?
Correct answer: Decrease
"Decrease" is the opposite of "increase," since increase means to make larger in amount and decrease means to make smaller. "Raise," "add," and "boost" all mean to make greater, matching increase.
- Which word means the OPPOSITE of "brave"?
- Bold
- Fearless
- Cowardly
- Daring
Correct answer: Cowardly
"Cowardly" is the opposite of "brave," because a brave person faces danger while a cowardly person avoids it out of fear. "Bold," "fearless," and "daring" are all synonyms that describe courage.
- Which word means the OPPOSITE of "artificial"?
- Fake
- Synthetic
- False
- Natural
Correct answer: Natural
"Natural" is the opposite of "artificial," since artificial things are made by people while natural things occur on their own in nature. "Fake," "synthetic," and "false" all describe something manufactured or not genuine, like artificial.
- Which word means the OPPOSITE of "silent"?
Correct answer: Noisy
"Noisy" is the opposite of "silent," because silent means having no sound and noisy means full of sound. "Quiet," "hushed," and "calm" all describe a lack of sound, so they agree with silent.
- In the sentence "Because the bridge was unsafe, the workers decided to ______ it before anyone could cross," which word best completes the sentence?
- Ignore
- Repair
- Decorate
- Photograph
Correct answer: Repair
The word "repair" best completes the sentence, because an unsafe bridge needs fixing before people use it, and repairing it addresses the danger. "Ignore" leaves the danger, while "decorate" and "photograph" do nothing to make the bridge safe.
- In the sentence "The scientist needed more evidence, so she chose to ______ the experiment several more times," which word best completes the sentence?
Correct answer: Repeat
The word "repeat" best completes the sentence, since gathering more evidence requires doing the experiment again. "Forget," "cancel," and "avoid" would all stop the experiment, which contradicts the need for more evidence.
- In the sentence "Although the directions seemed ______, the students still managed to assemble the model without any mistakes," which word best completes the sentence?
- Simple
- Colorful
- Short
- Confusing
Correct answer: Confusing
The word "confusing" best completes the sentence, because the word "although" signals a contrast: despite hard directions, the students still succeeded. "Simple" and "short" would not create a contrast, and "colorful" does not relate to how hard the directions were.
- In the sentence "The hikers carried extra water because they knew the trail would be long and ______," which word best completes the sentence?
- Exhausting
- Shady
- Brief
- Downhill
Correct answer: Exhausting
The word "exhausting" best completes the sentence, since carrying extra water makes sense for a long, tiring trail. "Shady," "brief," and "downhill" describe easier conditions that would not require extra water.
- In the sentence "The new employee was so ______ that she finished every task ahead of schedule," which word best completes the sentence?
- Lazy
- Efficient
- Tired
- Forgetful
Correct answer: Efficient
The word "efficient" best completes the sentence, because finishing tasks ahead of schedule shows someone who works quickly and well. "Lazy," "tired," and "forgetful" would lead to falling behind, not finishing early.
- In the sentence "The audience grew ______ as the magician revealed the surprising end of his trick," which word best completes the sentence?
Correct answer: Amazed
The word "amazed" best completes the sentence, since a surprising magic trick is most likely to fill an audience with wonder. "Bored" and "sleepy" contradict a surprising moment, and "angry" does not fit an entertaining trick.
- In the sentence "Since the recipe called for fresh herbs, the cook decided to ______ some from the garden," which word best completes the sentence?
Correct answer: Gather
The word "gather" best completes the sentence, because needing fresh herbs leads logically to collecting them from a garden. "Burn," "sell," and "drop" would not provide herbs for the recipe.
- In the sentence "The museum guide spoke in a ______ voice so that every visitor could hear the explanation clearly," which word best completes the sentence?
- Clear
- Whispered
- Mumbled
- Faint
Correct answer: Clear
The word "clear" best completes the sentence, since being heard by everyone requires speaking distinctly. "Whispered," "mumbled," and "faint" describe quiet or unclear speech that would be hard to hear.
- In the sentence "The storm was so ______ that the city canceled all outdoor events for the weekend," which word best completes the sentence?
Correct answer: Severe
The word "severe" best completes the sentence, because only a serious, dangerous storm would cause an entire weekend of events to be canceled. "Mild," "gentle," and "brief" describe weak storms that would not require cancellations.
- In the sentence "Even though the puzzle had hundreds of pieces, the determined child refused to ______," which word best completes the sentence?
Correct answer: Quit
The word "quit" best completes the sentence, since a determined child working on a hard puzzle would refuse to give up. "Continue," "try," and "finish" describe persistence, but the sentence says the child "refused to," so the missing word must mean stopping.
- In the sentence "The librarian asked the noisy students to be ______ so others could study," which word best completes the sentence?
Correct answer: Quiet
The word "quiet" best completes the sentence, because helping others study means reducing noise. "Louder" is the opposite of what is needed, and "faster" and "busier" do not relate to noise.
- In the sentence "The athlete trained every day, which is why his improvement was so ______," which word best completes the sentence?
- Remarkable
- Slow
- Invisible
- Sudden
Correct answer: Remarkable
The word "remarkable" best completes the sentence, since daily training over time would produce impressive, noticeable progress. "Slow" and "invisible" contradict steady hard work, and "sudden" does not match gradual daily effort.
- In the sentence "Because the instructions were ______, the team completed the project without asking a single question," which word best completes the sentence?
- Unclear
- Precise
- Misleading
- Missing
Correct answer: Precise
The word "precise" best completes the sentence, because needing no questions means the instructions were exact and easy to follow. "Unclear," "misleading," and "missing" would all force the team to ask questions.
- In the sentence "The chef tasted the soup and added more salt because it was too ______," which word best completes the sentence?
Correct answer: Bland
The word "bland" best completes the sentence, since adding salt is the usual fix for food that lacks flavor. "Spicy," "hot," and "thick" describe problems that salt would not solve.
- In the sentence "The volunteers worked together to ______ the trash from the beach until it looked spotless," which word best completes the sentence?
Correct answer: Remove
The word "remove" best completes the sentence, because making a beach spotless requires taking the trash away. "Scatter," "create," and "hide" would leave or add trash rather than clean it up.
- Rearrange the words "garden / the / waters / gardener / every / morning" to form a meaningful sentence. Which word would come FIRST?
- Gardener
- Garden
- Waters
- Morning
Correct answer: Gardener
The first word is "gardener," because the only sensible sentence is "The gardener waters the garden every morning," and after the opening "the," the subject "gardener" comes first among the choices. Starting with "garden," "waters," or "morning" would not form a clear, complete thought.
- Rearrange the words "loudly / dog / the / barked / at / stranger / the" to form a meaningful sentence. Which word would come LAST?
Correct answer: Stranger
The last word is "stranger," because the only meaningful sentence is "The dog barked loudly at the stranger," which ends with the person being barked at. "Dog," "barked," and "loudly" all belong earlier in the sentence.
- Rearrange the words "book / interesting / read / I / an / yesterday" to form a meaningful sentence. Which word should come SECOND?
Correct answer: Read
The second word is "read," because the sentence "I read an interesting book yesterday" places the verb "read" right after the subject "I." Putting "book," "interesting," or "I" in the second spot would break the natural subject-verb order.
- Rearrange the words "snow / the / mountains / covered / tall" to form a meaningful sentence. Which word would come FIRST?
Correct answer: Snow
The first word is "snow," because the clearest sentence is "Snow covered the tall mountains," where "snow" is the subject doing the action. Beginning with "mountains," "tall," or "covered" would not produce a logical sentence.
- Rearrange the words "team / won / our / championship / the" to form a meaningful sentence. Which word should directly follow "our"?
Correct answer: Team
The word "team" directly follows "our," because the sentence "Our team won the championship" pairs "our" with "team" as the subject. "Won," "championship," and "the" all belong later in the sentence, not right after "our."
- Rearrange the words "melted / quickly / the / sun / ice / the / in" to form a meaningful sentence. Which word would come FIRST?
Correct answer: The
The first word is "the," because the meaningful sentence is "The ice melted quickly in the sun," which must begin with the article "the" before the subject "ice." Starting with "melted," "quickly," or "ice" alone would leave the sentence ungrammatical.
- Rearrange the words "painted / artist / a / the / beautiful / picture" to form a meaningful sentence. Which word comes immediately BEFORE "picture"?
Correct answer: Beautiful
The word "beautiful" comes immediately before "picture," because the sentence "The artist painted a beautiful picture" places the adjective directly in front of the noun it describes. "Artist," "painted," and "a" appear earlier, not just before "picture."
- Rearrange the words "children / playground / the / on / played / the" to form a meaningful sentence. Which word would come LAST?
- Playground
- Children
- Played
- On
Correct answer: Playground
The last word is "playground," because the sentence "The children played on the playground" ends with the place where the action happens. "Children," "played," and "on" all appear earlier, leaving "playground" at the end.
- Rearrange the words "a / wrote / letter / she / long" to form a meaningful sentence. Which word should come SECOND?
Correct answer: Wrote
The second word is "wrote," because the sentence "She wrote a long letter" places the verb "wrote" right after the subject "she." Putting "letter," "a," or "long" in the second position would scramble the natural word order.
- Rearrange the words "to / store / drove / father / the / my" to form a meaningful sentence. Which word would come FIRST?
Correct answer: My
The first word is "my," because the sentence "My father drove to the store" begins with the possessive word that introduces the subject "father." Starting with "drove," "store," or "to" would not form a complete, logical sentence.
- Rearrange the words "rang / loudly / the / bell / school" to form a meaningful sentence. Which word comes immediately BEFORE "bell"?
Correct answer: School
The word "school" comes immediately before "bell," because the sentence "The school bell rang loudly" uses "school" to describe which bell rang. "Rang," "loudly," and "the" do not directly precede "bell" in this arrangement.
- Finch is to bird as salmon is to ______. Which word completes the analogy?
Correct answer: Fish
The answer is "fish," because a finch is a type of bird, so the matching pair must name a category that a salmon belongs to, and a salmon is a type of fish. "River" is where a salmon lives, "scale" is a body part, and "swim" is an action, so none of those name the category the way "bird" does.
- Author is to novel as composer is to ______. Which word completes the analogy?
- Audience
- Piano
- Stage
- Symphony
Correct answer: Symphony
The answer is "symphony," because an author creates a novel, so the matching pair must name what a composer creates, and a composer creates a symphony. "Audience" listens, "piano" is an instrument, and "stage" is a place, so none of them is the thing the composer produces.
- Thirsty is to drink as tired is to ______. Which word completes the analogy?
Correct answer: Sleep
The answer is "sleep," because being thirsty leads a person to drink, so the matching pair must name what a tired person does to fix that state, and a tired person sleeps. "Run" and "eat" do not relieve tiredness, and "awake" is the opposite of resting.
- Library is to books as orchard is to ______. Which word completes the analogy?
Correct answer: Fruit
The answer is "fruit," because a library is a place that holds many books, so the matching pair must name what an orchard holds in large numbers, and an orchard holds fruit on its trees. "Farmer" works there, "shade" is an effect of the trees, and "fence" surrounds it, so none names what the place is full of.
- Cub is to bear as foal is to ______. Which word completes the analogy?
Correct answer: Horse
The answer is "horse," because a cub is the young of a bear, so the matching pair must name the adult animal whose young is a foal, and a foal is a young horse. "Barn" is where it lives, "saddle" is equipment, and "gallop" is a movement, so none names the grown animal.
- Whisper is to shout as walk is to ______. Which word completes the analogy?
Correct answer: Sprint
The answer is "sprint," because a whisper is a quiet, low-intensity version of a shout, so the matching pair must be a high-intensity version of walking, and a sprint is a fast, intense form of moving on foot. "Stroll" is gentler than walking, "stand" is no movement, and "step" is just one part of walking, so none increases the intensity the way "shout" does.
- Glove is to hand as sock is to ______. Which word completes the analogy?
Correct answer: Foot
The answer is "foot," because a glove covers a hand, so the matching pair must name the body part a sock covers, and a sock covers a foot. "Shoe" also covers the foot but is another piece of clothing, not a body part, while "warm" and "wool" describe a sock rather than what it covers.
- Knife is to cut as broom is to ______. Which word completes the analogy?
Correct answer: Sweep
The answer is "sweep," because a knife is a tool used to cut, so the matching pair must name the action a broom is used to do, and a broom is used to sweep. "Sharp" describes a knife, "floor" is what gets swept, and "handle" is a part of the broom, so none names the broom's action.
- Petal is to flower as page is to ______. Which word completes the analogy?
Correct answer: Book
The answer is "book," because a petal is one part of a whole flower, so the matching pair must name the whole that a page is part of, and a page is part of a book. "Read" is an action, "paper" is the material, and "library" is where books are kept, so none names the whole made of pages.
- Sun is to day as moon is to ______. Which word completes the analogy?
Correct answer: Night
The answer is "night," because the sun is the bright object seen during the day, so the matching pair must name the time when the moon is most seen, and the moon is seen at night. "Star" is another object in the sky, "sky" is where both appear, and "round" describes a shape, so none names the matching time of day.
- Which word does NOT belong with the others: maple, oak, pine, granite?
Correct answer: Granite
The word that does not belong is "granite," because maple, oak, and pine are all kinds of trees, while granite is a kind of rock. Grouping by category, the three trees share a class that granite is not part of.
- Which word does NOT belong with the others: copper, silver, gold, oxygen?
Correct answer: Oxygen
The word that does not belong is "oxygen," because copper, silver, and gold are all metals, while oxygen is a gas. The three metals share a property that oxygen does not have.
- Which word does NOT belong with the others: triangle, square, circle, pentagon?
- Square
- Circle
- Triangle
- Pentagon
Correct answer: Circle
The word that does not belong is "circle," because a triangle, square, and pentagon are all shapes made of straight sides, while a circle has no straight sides at all. The three straight-sided shapes share a feature the circle lacks.
- Which word does NOT belong with the others: violin, trumpet, guitar, cello?
Correct answer: Trumpet
The word that does not belong is "trumpet," because the violin, guitar, and cello all make sound from vibrating strings, while a trumpet makes sound from blown air. The three string instruments share a way of producing sound that the trumpet does not.
- Which word does NOT belong with the others: hammer, screwdriver, wrench, nail?
- Nail
- Hammer
- Screwdriver
- Wrench
Correct answer: Nail
The word that does not belong is "nail," because a hammer, screwdriver, and wrench are all tools that a person uses to do work, while a nail is a fastener that the tools act upon. The three tools share a role that the nail does not.
- Which word does NOT belong with the others: Tuesday, Friday, March, Sunday?
Correct answer: March
The word that does not belong is "March," because Tuesday, Friday, and Sunday are all days of the week, while March is a month of the year. The three days share a category that March is not a member of.
- Which word does NOT belong with the others: shout, whisper, murmur, mutter?
Correct answer: Shout
The word that does not belong is "shout," because to whisper, murmur, and mutter all mean to speak softly and quietly, while to shout means to speak very loudly. The three quiet ways of speaking share a volume that shouting is the opposite of.
- Which word does NOT belong with the others: lake, pond, river, desert?
Correct answer: Desert
The word that does not belong is "desert," because a lake, pond, and river are all bodies of water, while a desert is a dry land area with very little water. The three watery places share a feature the desert lacks.
- All of the marbles in a bag are blue. Maria pulls one marble out of the bag without looking. Which statement must be true?
- The marble Maria pulled out is blue.
- The marble Maria pulled out is the largest one.
- There are exactly ten marbles in the bag.
- Maria will put the marble back.
Correct answer: The marble Maria pulled out is blue.
The statement that must be true is that the marble Maria pulled out is blue, because every marble in the bag is blue, so any marble she takes has to be blue. The size, the total number of marbles, and whether she returns it are not stated, so those cannot be known for certain.
- Every student in Mr. Lee's class plays a musical instrument. Devon is a student in Mr. Lee's class. Which conclusion follows?
- Devon plays the violin.
- Devon plays a musical instrument.
- Devon is the best musician in the class.
- Devon also sings in the choir.
Correct answer: Devon plays a musical instrument.
The conclusion that follows is that Devon plays a musical instrument, because all students in the class play one and Devon is a student in that class. Which instrument he plays, how skilled he is, and whether he sings are details the statements never give, so they cannot be concluded.
- Whenever it rains, the school cancels outdoor recess. Today the school did not cancel outdoor recess. Which conclusion follows?
- It rained today.
- Recess was held indoors.
- The school will cancel recess tomorrow.
- It did not rain today.
Correct answer: It did not rain today.
The conclusion that follows is that it did not rain today, because rain always causes recess to be canceled, so if recess was not canceled, rain could not have happened. The other choices either contradict this reasoning or guess about tomorrow, which the statements do not address.
- All the cookies on the top shelf have chocolate chips. The cookie Sam grabbed has no chocolate chips. Which conclusion follows?
- Sam's cookie did not come from the top shelf.
- Sam's cookie came from the top shelf.
- Sam baked the cookies himself.
- There are no cookies left on the top shelf.
Correct answer: Sam's cookie did not come from the top shelf.
The conclusion that follows is that Sam's cookie did not come from the top shelf, because every cookie on that shelf has chocolate chips, so a cookie with no chips cannot be from there. Who baked the cookies and how many remain are not stated, so those cannot be concluded.
- Some of the books on the table are about animals. Every book about animals on the table has pictures. Which statement must be true?
- At least one book on the table has pictures.
- Every book on the table has pictures.
- None of the books on the table has pictures.
- All the books on the table are about animals.
Correct answer: At least one book on the table has pictures.
The statement that must be true is that at least one book on the table has pictures, because some books are about animals and every animal book has pictures, so those animal books guarantee at least one picture book. The other choices claim more or less than the facts support, so they cannot be certain.
- If the train is on time, then Aisha will catch it. Aisha did not catch the train. Which conclusion follows?
- The train was on time.
- Aisha missed the bus instead.
- The train was not on time.
- Aisha arrived early.
Correct answer: The train was not on time.
The conclusion that follows is that the train was not on time, because being on time guarantees Aisha catches it, so the fact that she did not catch it means the train could not have been on time. The other choices either reverse the logic or add information the statements never provide.
- A farmer has only chickens and cows in a pen. He counts 7 heads and 20 legs in all. How many cows are in the pen?
Correct answer: 3
The answer is 3 cows, because if all 7 animals were chickens there would be 14 legs, but there are 20 legs, leaving 6 extra legs; each cow adds 2 legs beyond a chicken's 2, so 6 divided by 2 gives 3 cows. Checking, 3 cows have 12 legs and 4 chickens have 8 legs, which totals 20 legs and 7 heads.
- Lena is twice as old as her brother. In 4 years, Lena will be 16. How old is her brother now?
Correct answer: 6
The answer is 6 years old, because if Lena will be 16 in 4 years then she is 12 now, and since she is twice her brother's age, he is half of 12, which is 6. Reasoning through the relationship rather than just computing gives the brother's current age.
- A baker puts cookies into boxes of 6. After filling as many full boxes as possible from 40 cookies, how many cookies are left over?
Correct answer: 4
The answer is 4 cookies, because 6 cookies fit in each box and 6 times 6 equals 36, which fills six full boxes using 36 of the 40 cookies, leaving 40 minus 36, or 4 cookies. The leftover is found by reasoning about how many groups of six fit before any remainder.
- Three friends share the cost of a $24 gift equally. Then a fourth friend joins and they split the same $24 cost among all four. How much less does each person now pay?
Correct answer: $2
The answer is $2 less, because $24 split three ways is $8 each, and $24 split four ways is $6 each, so each person now pays $8 minus $6, which is $2 less. The problem is solved by comparing the two share amounts rather than by a single calculation.
- A water tank fills at a steady rate and becomes one-quarter full after 5 minutes. How many total minutes will it take to fill completely?
Correct answer: 20
The answer is 20 minutes, because filling one-quarter of the tank takes 5 minutes, so filling all four quarters takes 4 times 5 minutes, which equals 20 minutes. Recognizing that a quarter is one of four equal parts makes the steady rate easy to extend to the whole tank.
- Tom reads 15 pages each day. He has read 45 pages of a 90-page book. How many more days will he need to finish the book?
Correct answer: 3
The answer is 3 days, because 90 pages minus the 45 already read leaves 45 pages, and at 15 pages a day, 45 divided by 15 equals 3 days. The key step is finding the pages remaining before applying the daily reading rate.
- A class has 28 students. There are 6 more girls than boys. How many boys are in the class?
Correct answer: 11
The answer is 11 boys, because removing the 6 extra girls from 28 leaves 22 to split evenly into boys and an equal number of girls, giving 11 boys; adding back the 6 makes 17 girls, and 11 plus 17 equals 28. Reasoning about the difference before dividing finds the smaller group.
- Look at the word grid. The top row reads HOT, COLD; the bottom row reads UP, ____. What word belongs in the empty box?
Correct answer: DOWN
The answer is "DOWN," because each row pairs a word with its opposite: HOT pairs with COLD, so UP must pair with its opposite, which is DOWN. "High," "over," and "fast" are not opposites of "up," so they do not follow the row's relationship.
- In the letter grid, the top row reads A, B, C; the bottom row reads C, D, ____. What letter belongs in the empty box?
Correct answer: E
The answer is "E," because each row lists three letters in alphabetical order, so the bottom row starting C, D must continue with the next letter, E. The letters F and G skip ahead, and D simply repeats, so none keeps the row's step-by-step order.
- Look at the word grid. The top row reads DOG, PUPPY; the bottom row reads CAT, ____. What word belongs in the empty box?
Correct answer: KITTEN
The answer is "KITTEN," because each row pairs an adult animal with its young: DOG goes with PUPPY, so CAT must go with its young, which is KITTEN. "Mouse" is a different animal, "paw" is a body part, and "pet" is a general term, so none matches the young-animal relationship.
- In the letter grid, the top row reads M, N, O; the bottom row reads ____, S, T. What letter belongs in the empty box?
Correct answer: R
The answer is "R," because each row lists three letters in alphabetical order, and the bottom row ending S, T must be preceded by the letter just before S, which is R. The letter Q comes two places before S, U comes after T, and P is far earlier, so none fits right before S.
- Look at the word grid. The top row reads TEACHER, SCHOOL; the bottom row reads DOCTOR, ____. What word belongs in the empty box?
- HOSPITAL
- PATIENT
- MEDICINE
- NURSE
Correct answer: HOSPITAL
The answer is "HOSPITAL," because each row pairs a worker with the place that worker usually works: a TEACHER works in a SCHOOL, so a DOCTOR works in a HOSPITAL. "Patient," "medicine," and "nurse" relate to a doctor but do not name the workplace the way "school" does.
- A shape is described as something that has exactly three straight sides. Which choice must be an example of this shape?
- A square
- A circle
- A triangle
- A cube
Correct answer: A triangle
The answer is "a triangle," because the description requires exactly three straight sides, and only a triangle has three sides. A square has four sides, a circle has no straight sides, and a cube is a solid figure rather than a flat three-sided shape.
- Which of the following is something that every island must have?
- Palm trees on it
- People living on it
- A sandy beach
- Water all around it
Correct answer: Water all around it
The answer is "water all around it," because by definition an island is land completely surrounded by water, so that feature must always be present. Palm trees, people, and a sandy beach appear on some islands but are not required for a piece of land to be an island.
- Which of the following is something a forest must always include?
- A river
- Trees
- Bears
- A hiking trail
Correct answer: Trees
The answer is "trees," because a forest is by definition a large area covered mainly with trees, so trees are a necessary part of any forest. A river, bears, and a hiking trail may be found in some forests but are not required for an area to be a forest.
- A teacher says a "square" is a shape with four equal sides and four right angles. Which of these must always be true of a square?
- It is colored red.
- All four of its sides are the same length.
- It is larger than a triangle.
- It is made of paper.
Correct answer: All four of its sides are the same length.
The answer is that all four of its sides are the same length, because the given definition states a square has four equal sides, making equal side lengths a required feature. Color, size compared to a triangle, and material are not part of the definition, so they need not be true.
- Which of the following must be true of any clock that is working correctly?
- It is round in shape.
- It hangs on a wall.
- It makes a ticking sound.
- It shows the time.
Correct answer: It shows the time.
The answer is that it shows the time, because the purpose of a clock is to tell the time, so a correctly working clock must do that. Being round, hanging on a wall, and ticking describe only some clocks and are not required for a clock to work.
- Which of the following is something that every triangle must have?
- Three angles
- A right angle
- Three equal sides
- Sides of one inch
Correct answer: Three angles
The answer is "three angles," because every triangle has three sides that meet to form exactly three angles, making three angles a required feature. A right angle, three equal sides, and a fixed side length describe only certain triangles, so they are not required for all of them.
- On the OLSAT, a Figural Classification item asks you to find the odd one out among pictures. What feature do you compare the figures by to decide which one does NOT belong?
- A shared visual property such as shape, shading, size, or number
- The meaning of a written word beside each figure
- How the figures sound when read aloud
- The alphabetical order of the figures
Correct answer: A shared visual property such as shape, shading, size, or number
The correct answer is a shared visual property such as shape, shading, size, or number, because Figural Classification gives a group of figures that are alike in one visual way and asks for the one that breaks that pattern. Written words, alphabetical order, and sound are not part of a nonverbal figure item, which relies only on what the pictures look like.
- Four figures are shown: a black diamond, a black oval, a black crescent, and a white diamond. Which figure does NOT belong with the others?
- The white diamond
- The black oval
- The black crescent
- The black diamond
Correct answer: The white diamond
The figure that does not belong is the white diamond, because the other three figures are all filled in black, while the white diamond is left unshaded. The shared feature among the others is the black coloring, which the white diamond lacks even though its shape matches one of them.
- Four figures are shown: a shape with exactly two square corners, a shape with exactly two square corners, a shape with exactly two square corners, and a shape with no square corners at all. Which figure does NOT belong with the others?
- The shape with no square corners at all
- The third shape with two square corners
- The second shape with two square corners
- The first shape with two square corners
Correct answer: The shape with no square corners at all
The figure that does not belong is the shape with no square corners at all, because each of the other three figures contains two right-angle corners, while this shape has none. The shared rule among the others is having square corners, which the cornerless shape does not follow.
- Four figures are shown: a shape with an X drawn inside it, a shape with an X drawn inside it, a shape with an X drawn inside it, and a shape with a plus sign drawn inside it. Which figure does NOT belong with the others?
- The second shape with an X inside
- The first shape with an X inside
- The shape with a plus sign inside
- The third shape with an X inside
Correct answer: The shape with a plus sign inside
The figure that does not belong is the shape with a plus sign inside, because the other three figures each contain an X formed by two slanted crossing lines, while this one holds an upright plus sign. The common mark among the others is the slanted X, which the upright plus sign does not match.
- Four figures are shown: a kite, a cloud, a balloon, and a feather. If three of these float or fly in the air, which figure does NOT belong with the others?
- The kite
- The cloud
- The balloon
- The feather
Correct answer: The feather
The figure that does not belong is the feather, because a kite, a cloud, and a balloon all rise and stay up high in the sky, while a feather drifts gently down toward the ground. The shared idea among the others is staying aloft, which the falling feather does not share.
- Four figures are shown: a circle resting on a flat base, a square resting on a flat base, a triangle resting on a flat base, and a triangle balanced on a single point. Which figure does NOT belong with the others?
- The circle resting on a flat base
- The square resting on a flat base
- The triangle resting on a flat base
- The triangle balanced on a single point
Correct answer: The triangle balanced on a single point
The figure that does not belong is the triangle balanced on a single point, because the other three figures each sit steadily on a flat bottom edge, while this triangle stands on just one tip. The shared feature among the others is resting on a flat base, which the point-balanced triangle does not.
- Four figures are shown: a shape filled with horizontal stripes, a shape filled with horizontal stripes, a shape filled with horizontal stripes, and a shape filled with polka dots. Which figure does NOT belong with the others?
- The first striped shape
- The second striped shape
- The polka-dot shape
- The third striped shape
Correct answer: The polka-dot shape
The figure that does not belong is the polka-dot shape, because the other three figures are all filled with horizontal stripes, while this one is filled with scattered dots. The common pattern among the others is the striped fill, which the dotted shape does not share.
- Four figures are shown: a shape made of exactly six small squares, a shape made of exactly six small squares, a shape made of exactly six small squares, and a shape made of exactly four small squares. Which figure does NOT belong with the others?
- The shape made of four small squares
- The second shape made of six small squares
- The first shape made of six small squares
- The third shape made of six small squares
Correct answer: The shape made of four small squares
The figure that does not belong is the shape made of four small squares, because the other three figures are each built from six small squares, while this one uses only four. The shared count among the others is six squares, which the smaller figure does not match.
- Four figures are shown: an open box with its lid up, an open jar with its lid off, an open envelope with its flap up, and a sealed closed box. Which figure does NOT belong with the others?
- The open jar with its lid off
- The open envelope with its flap up
- The open box with its lid up
- The sealed closed box
Correct answer: The sealed closed box
The figure that does not belong is the sealed closed box, because the other three figures are all shown open with a lid or flap lifted, while this box is completely shut. The shared feature among the others is being open, which the sealed box does not share.
- Four figures are shown: a shape with a smooth wavy outline, a shape with a smooth wavy outline, a shape with a smooth wavy outline, and a shape with a sharp zigzag outline. Which figure does NOT belong with the others?
- The third shape with a wavy outline
- The first shape with a wavy outline
- The shape with a sharp zigzag outline
- The second shape with a wavy outline
Correct answer: The shape with a sharp zigzag outline
The figure that does not belong is the shape with a sharp zigzag outline, because the other three figures have smooth curving wavy edges, while this one has sharp pointed zigzags. The common feature among the others is the smooth wavy outline, which the jagged shape does not have.
- On the OLSAT, a Figural Analogy reads 'figure A is to figure B as figure C is to ?'. To choose the missing figure, what must you do first?
- Pick the figure that looks the most colorful
- Figure out the change that turns the first figure into the second, then apply it to the third
- Choose the figure that is largest on the page
- Count how many figures appear in the whole problem
Correct answer: Figure out the change that turns the first figure into the second, then apply it to the third
The correct answer is to figure out the change that turns the first figure into the second, then apply it to the third, because a figural analogy hides a single rule in the first pair that the second pair must repeat. Counting figures, choosing the most colorful, or picking the largest ignores the relationship that the analogy is built on.
- Look at this figure analogy: a small heart is to a large heart as a small star is to ______. Which figure completes the analogy?
- A large heart
- A tiny star
- A large star
- A small moon
Correct answer: A large star
The answer is a large star, because the first pair keeps the same shape and only makes it bigger, so the matching pair must take the small star and enlarge it into a large star. A large heart changes the shape, a small moon changes the shape, and a tiny star does not grow at all.
- Look at this figure analogy: a shape pointing right is to the same shape pointing left as a fish pointing right is to ______. Which figure completes the analogy?
- A fish pointing up
- A fish pointing left
- A larger fish pointing right
- A fish pointing right
Correct answer: A fish pointing left
The answer is a fish pointing left, because the first pair flips the figure so it faces the opposite side, so the matching pair must flip the fish to face left instead of right. A fish pointing up turns the wrong way, a fish pointing right stays the same, and a larger fish changes the size instead of the direction.
- Look at this figure analogy: a plain square is to a square with a circle on top as a plain triangle is to ______. Which figure completes the analogy?
- A triangle with a square on top
- A triangle with a circle on top
- A square with a circle on top
- A plain triangle
Correct answer: A triangle with a circle on top
The answer is a triangle with a circle on top, because the first pair keeps the base shape the same and adds a circle resting on top of it, so the matching pair must place a circle on top of the triangle. A plain triangle adds nothing, a square changes the base shape, and a square on top adds the wrong topper.
- Look at this figure analogy: a figure made of 2 circles is to a figure made of 4 circles as a figure made of 3 circles is to ______. Which figure completes the analogy?
- A figure made of 9 circles
- A figure made of 5 circles
- A figure made of 6 circles
- A figure made of 4 circles
Correct answer: A figure made of 6 circles
The answer is a figure made of 6 circles, because the first pair doubles the number of circles, going from 2 to 4, so the matching pair must double 3 circles to make 6. A figure of 5 circles adds two, 4 circles adds one, and 9 circles triples the amount instead of doubling it.
- Look at this figure analogy: a circle is to a half-circle as a square is to ______. Which figure completes the analogy?
- A whole square
- A half-circle
- A doubled square
- A half-square
Correct answer: A half-square
The answer is a half-square, because the first pair cuts the shape in half and keeps only one half, so the matching pair must cut the square in half and keep one half. A whole square is not cut at all, a half-circle changes the shape, and a doubled square goes the wrong way by adding instead of halving.
- Look at this figure analogy: a white arrow is to a striped arrow as a white moon is to ______. Which figure completes the analogy?
- A white moon
- A striped arrow
- A black moon
- A striped moon
Correct answer: A striped moon
The answer is a striped moon, because the first pair keeps the shape the same and changes the fill from white to stripes, so the matching pair must give the moon a striped fill. A white moon does not change the fill, a black moon uses a solid fill instead of stripes, and a striped arrow changes the shape.
- Look at this figure analogy: a small dot inside a big circle is to a big dot inside a small circle as a small dot inside a big square is to ______. Which figure completes the analogy?
- A big dot inside a big square
- A small dot inside a big square
- A small dot inside a small square
- A big dot inside a small square
Correct answer: A big dot inside a small square
The answer is a big dot inside a small square, because the first pair swaps the sizes so the dot grows large and the outer shape shrinks, so the matching pair must enlarge the dot and shrink the square. The other choices keep one of the two sizes unchanged instead of swapping both.
- Look at this figure analogy: a shape with 1 dot is to a shape with 3 dots as a shape with 2 dots is to ______. Which figure completes the analogy?
- A shape with 5 dots
- A shape with 4 dots
- A shape with 3 dots
- A shape with 6 dots
Correct answer: A shape with 4 dots
The answer is a shape with 4 dots, because the first pair adds exactly two dots, going from 1 to 3, so the matching pair must add two dots to the 2-dot shape to make 4. A shape with 3 dots adds only one, while 5 or 6 dots add too many.
- Look at this figure analogy: a triangle with a flat top edge is to a triangle flipped to have a flat bottom edge as a trapezoid with a wide top is to ______. Which figure completes the analogy?
- A wider trapezoid with a wide top
- A triangle with a flat bottom
- A trapezoid flipped to have a wide bottom
- The same trapezoid with a wide top
Correct answer: A trapezoid flipped to have a wide bottom
The answer is a trapezoid flipped to have a wide bottom, because the first pair turns the figure upside down so its wide and narrow edges trade places, so the matching pair must flip the trapezoid so its wide edge is now on the bottom. Keeping it unchanged, widening it, or switching to a triangle all fail to apply the upside-down flip.
- Look at this figure analogy: a single shape is to that shape with its mirror image drawn beside it as a single comma-shape is to ______. Which figure completes the analogy?
- A single comma-shape unchanged
- A comma-shape beside its mirror image
- A comma-shape turned upside down
- Two identical comma-shapes facing the same way
Correct answer: A comma-shape beside its mirror image
The answer is a comma-shape beside its mirror image, because the first pair adds a mirrored copy next to the original, so the matching pair must place the comma-shape next to its flipped reflection. Leaving it unchanged adds nothing, two same-facing copies are not mirrored, and an upside-down comma turns it rather than reflecting it.
- On the OLSAT, a Pattern Matrix item shows a 3-by-3 grid with one empty cell. How do you find the figure that belongs in the empty cell?
- Choose the figure that matches the very first cell
- Pick any figure that has not appeared yet
- Use the patterns running across the rows and down the columns to predict the missing figure
- Select the figure with the brightest color
Correct answer: Use the patterns running across the rows and down the columns to predict the missing figure
The correct answer is to use the patterns running across the rows and down the columns to predict the missing figure, because a pattern matrix hides rules in both directions that the empty cell must satisfy. Picking an unused figure, copying the first cell, or choosing by brightness ignores the row and column logic that defines the grid.
- A 3-by-3 grid is shown. In each row, a shape is shaded one-quarter on the left in the first cell, half on the left in the second cell, and three-quarters on the left in the third cell. The bottom row shows a quarter-shaded oval, a half-shaded oval, and an empty cell. Which figure belongs in the empty cell?
- A fully shaded oval
- A half-shaded oval
- A quarter-shaded oval
- A three-quarters-shaded oval
Correct answer: A three-quarters-shaded oval
The answer is a three-quarters-shaded oval, because each row adds another quarter of shading, going from a quarter to a half to three-quarters, so the bottom row after a quarter and a half oval must show a three-quarters-shaded oval. A fully shaded oval adds too much, while a half or quarter oval repeats an earlier cell.
- A 3-by-3 grid is shown. Reading down each column, the number of small triangles decreases by one, starting with three at the top. The left column shows three triangles, two triangles, and an empty bottom cell. How many triangles belong in the empty cell?
- Three triangles
- Four triangles
- One triangle
- Two triangles
Correct answer: One triangle
The answer is one triangle, because each column drops one triangle as it moves down, going three, two, and then one, so the empty bottom cell after three and two triangles must hold one. Two or three triangles repeats a cell above, and four triangles goes the wrong way by adding triangles.
- A 3-by-3 grid is shown. In each row, a circle moves from the left side of the cell to the center and then to the right side. The middle row shows a circle on the left, a circle in the center, and an empty cell. Where should the circle be in the empty cell?
- Outside the cell
- On the right side
- In the center
- On the left side
Correct answer: On the right side
The answer is on the right side, because the circle slides across each row from left to center to right, so the empty cell after the left and center positions must show the circle on the right. Placing it on the left or center repeats an earlier cell, and putting it outside the cell is not part of the pattern.
- A 3-by-3 grid is shown. Across each row, an outline shape gains one more loop of an inner spiral, so the first cell has one loop, the second has two, and the third has three. The bottom row shows one loop, two loops, and an empty cell. How many loops belong in the empty cell?
- One loop
- Four loops
- Two loops
- Three loops
Correct answer: Three loops
The answer is three loops, because each row adds one loop at a time, going one, two, and then three, so the empty cell after one and two loops must contain three. Two or one loop repeats an earlier cell, and four loops adds one beyond the pattern for that row.
- A 3-by-3 grid is shown. Down each column the shape changes color in a repeating cycle of black, then gray, then white. The middle column shows black on top, gray in the middle, and an empty bottom cell. Which shading belongs in the empty cell?
Correct answer: White
The answer is white, because each column cycles through black, gray, and white from top to bottom, so the bottom cell after black and gray must be white. Black or gray repeats a cell above, and a striped fill is not one of the three shades in the cycle.
- A 3-by-3 grid is shown. In each cell a single shape is rotated so that, reading across each row, it turns a half-turn between the first and second cells and another half-turn between the second and third cells. The bottom row shows an upright key, an upside-down key, and an empty cell. Which figure belongs in the empty cell?
- Two keys
- A sideways key
- An upright key
- An upside-down key
Correct answer: An upright key
The answer is an upright key, because each row flips the shape a half-turn each step, so an upright key becomes upside down and then a second half-turn returns it to upright. An upside-down key repeats the middle cell, a sideways key uses the wrong amount of turn, and two keys changes the count.
- A 3-by-3 grid is shown. In each row, a shape is plain in the first cell, has a circle drawn around it in the second cell, and has both a circle and a square drawn around it in the third cell. The top row shows a plain leaf, a leaf circled once, and an empty cell. Which figure belongs in the empty cell?
- A leaf inside both a circle and a square
- A plain leaf
- A leaf inside two circles
- A leaf inside only a square
Correct answer: A leaf inside both a circle and a square
The answer is a leaf inside both a circle and a square, because each row adds an enclosing shape step by step, ending with the leaf inside both a circle and a square, so the top row must finish the same way. A plain leaf removes the enclosures, a leaf in only a square skips the circle, and a leaf in two circles adds the wrong shape.
- A 3-by-3 grid is shown. Reading across each row, a clock hand turns one-quarter clockwise from cell to cell. The bottom row shows the hand pointing left, the hand pointing up, and an empty cell. Where should the hand point in the empty cell?
- To the right
- Down
- Up
- To the left
Correct answer: To the right
The answer is to the right, because the hand turns a quarter clockwise each step, going from left to up to right, so the empty cell after left and up must point to the right. Pointing left or up repeats an earlier cell, and pointing down skips past the correct quarter turn.
- On the OLSAT, a Figural Series shows a row of pictures that change step by step and asks for the next one. How do you decide which figure comes next?
- Choose the figure that is not shown in the row
- Pick the figure that takes up the most space
- Find the rule that changes each figure into the next, then continue it one more step
- Repeat the very first figure in the row
Correct answer: Find the rule that changes each figure into the next, then continue it one more step
The correct answer is to find the rule that changes each figure into the next, then continue it one more step, because a figural series moves by a steady rule that you extend to predict the next picture. Repeating the first figure, choosing an unseen figure, or picking by size ignores the step-by-step rule the series follows.
- A row of figures is shown: a shape with 1 hole, a shape with 3 holes, a shape with 5 holes, then a shape with 7 holes. Which figure comes next in the series?
- A shape with 9 holes
- A shape with 8 holes
- A shape with 6 holes
- A shape with 7 holes
Correct answer: A shape with 9 holes
The answer is a shape with 9 holes, because each figure adds two holes to the one before, going 1, 3, 5, 7, so the next figure has 9 holes. A shape with 8 holes adds only one, 6 holes goes backward, and 7 holes repeats the previous figure.
- A row of figures is shown: a shape standing upright, the same shape tipped a quarter-turn, the shape tipped a half-turn upside down, then the shape tipped three-quarters of a turn. Which figure comes next in the series?
- The shape back standing upright
- The shape tipped a quarter-turn
- The shape upside down
- A completely different shape
Correct answer: The shape back standing upright
The answer is the shape back standing upright, because the figure turns a quarter at a time all the way around, and after three-quarters of a turn the next quarter brings it full circle back to upright. Repeating a quarter-turn or the upside-down position skips the final step, and a new shape breaks the rotation pattern.
- A row of figures is shown: a triangle, a circle, a triangle, then a circle. Which figure comes next in the series?
- A triangle
- A circle
- A square
- A star
Correct answer: A triangle
The answer is a triangle, because the figures alternate steadily between a triangle and a circle, so after the last circle the pattern returns to a triangle. A circle would repeat the shape just shown, and a square or star never appears in the alternating pattern.
- A row of figures is shown: a square split into 2 equal parts, a square split into 3 equal parts, a square split into 4 equal parts, then a square split into 5 equal parts. Which figure comes next in the series?
- A whole square with no split
- A square split into 6 equal parts
- A square split into 4 equal parts
- A square split into 7 equal parts
Correct answer: A square split into 6 equal parts
The answer is a square split into 6 equal parts, because each square gains one more equal part than the one before, going 2, 3, 4, 5, so the next square is split into 6 parts. A square in 4 parts goes backward, 7 parts skips ahead by two, and a whole square removes the splits.
- A row of figures is shown: one circle, then a circle stacked on a circle, then three circles stacked, then four circles stacked. Which figure comes next in the series?
- One circle
- Five circles stacked
- Two circles stacked
- Three circles stacked
Correct answer: Five circles stacked
The answer is five circles stacked, because each figure adds one more circle to the stack, counting one, two, three, four, so the next figure has five circles stacked. Three, two, or one circle all go backward instead of adding one more to the stack.
- A row of figures is shown: a small black square at the top of a tall box, the same square a little lower, the square lower still, then the square near the bottom. Which figure comes next in the series?
- The square in the middle
- The square at the very bottom of the box
- Two squares in the box
- The square back at the top
Correct answer: The square at the very bottom of the box
The answer is the square at the very bottom of the box, because the square slides steadily downward each step, so the next position is the very bottom. Returning to the top or jumping to the middle reverses the motion, and adding a second square changes the figure instead of moving the single square.
- A row of figures is shown: a hexagon, a pentagon, a square, then a triangle. Which figure comes next in the series?
- A circle
- A square
- A pentagon
- A single straight line segment
Correct answer: A circle
The answer is a circle, because each shape loses one side as the series moves along, going from six sides to five to four to three, and after three sides the next figure has no straight sides at all, which is a circle. A square or pentagon goes backward, and a single straight line segment is not a closed shape, so the smooth circle continues the shrinking-sides idea.
- A row of figures is shown: an empty grid of four cells, the same grid with one cell shaded, the grid with two cells shaded, then the grid with three cells shaded. Which figure comes next in the series?
- The grid with all four cells shaded
- The empty grid again
- The grid with two cells shaded
- The grid with one cell shaded
Correct answer: The grid with all four cells shaded
The answer is the grid with all four cells shaded, because each figure shades one more cell than the one before, going from zero to one to two to three, so the next figure shades the fourth and final cell. Shading two cells or one cell goes backward, and the empty grid removes all the shading.
- A row of figures is shown: a shape with a tiny tail, a shape with a slightly longer tail, a shape with an even longer tail, then a shape with a very long tail. Which figure comes next in the series?
- A shape with a tiny tail again
- A shape with no tail
- A shape with a slightly longer tail
- A shape with an even longer tail than before
Correct answer: A shape with an even longer tail than before
The answer is a shape with an even longer tail than before, because each figure stretches the tail a bit longer, so the next figure continues lengthening the tail. Returning to a tiny tail, removing the tail, or repeating a slightly longer tail all break the steady lengthening pattern.
- Look at this number series: 4,8,12,16, ____. What number comes next?
Correct answer: 20
The next number is 20, because each term grows by adding 4 to the one before it, so 16 plus 4 gives 20. The choices 18, 22, and 24 do not result from adding the steady step of 4 to 16.
- Look at this number series: 2,4,8,16, ____. What number comes next?
Correct answer: 32
The next number is 32, because each term is double the term before it, so 16 doubled is 32. Adding instead of doubling would give 24 or 20, and 18 ignores the pattern entirely, so none of those follow the rule.
- Look at this number series: 30,27,24,21, ____. What number comes next?
Correct answer: 18
The next number is 18, because the series counts down by subtracting 3 each step, so 21 minus 3 gives 18. The values 19, 20, and 17 do not match a steady drop of 3 from 21.
- Look at this number series: 1,3,6,10, ____. What number comes next?
Correct answer: 15
The next number is 15, because the amount added grows by one each time, adding 2, then 3, then 4, then 5, so 10 plus 5 gives 15. Simply adding a fixed number would give 13 or 14, and 16 overshoots the growing step.
- Look at this number series: 100,50,25, ____. What number comes next?
Correct answer: 12.5
The next number is 12.5, because each term is half of the one before it, so half of 25 is 12.5. Subtracting a fixed amount would give 10 or 15, and 20 does not result from halving 25.
- Look at this number series: 5,10,20,40, ____. What number comes next?
Correct answer: 80
The next number is 80, because each term doubles the previous one, so 40 doubled is 80. Adding a fixed amount would give 60 or 50, and 45 ignores the doubling rule.
- Look at this number series: 81,27,9, ____. What number comes next?
Correct answer: 3
The next number is 3, because each term is one-third of the term before it, so 9 divided by 3 is 3. The values 6 and 4 do not come from dividing by 3, and 1 skips a step in the pattern.
- Look at this number series: 7,14,21,28, ____. What number comes next?
Correct answer: 35
The next number is 35, because the series counts up by 7 each step, so 28 plus 7 gives 35. The numbers 33, 34, and 36 do not result from adding the steady step of 7 to 28.
- Look at this number series: 2,5,11,23, ____. What number comes next?
Correct answer: 47
The next number is 47, because each term is doubled and then 1 is added, so 23 doubled is 46 and adding 1 gives 47. Choices like 46 stop before adding 1, while 35 and 44 do not fit the double-then-add-one rule.
- Look at this number series: 1,4,9,16, ____. What number comes next?
Correct answer: 25
The next number is 25, because the series lists the squares of 1, 2, 3, and 4, so the next is 5 times 5, which is 25. The values 20, 24, and 21 are not perfect squares and do not continue the pattern.
- Look at this number series: 64,32,16,8, ____. What number comes next?
Correct answer: 4
The next number is 4, because each term is half of the one before it, so half of 8 is 4. Subtracting a fixed amount would give 6 or 5, and 2 skips a step by halving twice.
- Look at this number series: 3,6,12,24, ____. What number comes next?
Correct answer: 48
The next number is 48, because each term doubles the previous one, so 24 doubled is 48. Adding a fixed amount would give 36 or 30, and 40 does not result from doubling 24.
- Look at this number series: 11,22,33,44, ____. What number comes next?
Correct answer: 55
The next number is 55, because the series increases by 11 each step, so 44 plus 11 gives 55. The values 66, 54, and 50 do not match a steady increase of 11 from 44.
- Look at this number series: 90,80,70,60, ____. What number comes next?
Correct answer: 50
The next number is 50, because the series decreases by 10 each step, so 60 minus 10 gives 50. The values 55, 45, and 40 do not match a steady drop of 10 from 60.
- Look at this number series: 1,2,4,7,11, ____. What number comes next?
Correct answer: 16
The next number is 16, because the amount added grows by one each time, adding 1, then 2, then 3, then 4, then 5, so 11 plus 5 gives 16. Adding a fixed number would give 14 or 15, and 17 overshoots the growing step.
- In this letter series, each letter stands for its place in the alphabet: B, D, F, H, ____. Which letter comes next?
Correct answer: J
The next letter is J, because the series skips one letter each step, moving from B to D to F to H, and the letter two places after H is J. The letters I and K break the every-other-letter spacing, and L jumps too far ahead.
- Study these three number groups and find the missing value: (3,12), (5,20), (7, ____). What number completes the last pair?
Correct answer: 28
The missing number is 28, because in each pair the second number is the first multiplied by 4, so 7 times 4 is 28. The value 21 would be times 3, 35 would be times 5, and 14 would be times 2, so none uses the consistent rule of multiplying by 4.
- Study these number pairs and find the missing value: (10,7), (15,12), (20, ____). What number completes the last pair?
Correct answer: 17
The missing number is 17, because in each pair the second number is 3 less than the first, so 20 minus 3 is 17. The values 16, 18, and 15 do not follow the consistent rule of subtracting 3 from the first number.
- Each group follows the same rule: (2,3,5), (4,6,10), (5, 7, ____). What number completes the last group?
Correct answer: 12
The missing number is 12, because in each group the third number is the sum of the first two, so 5 plus 7 is 12. The values 11, 13, and 14 do not equal the sum of the first two numbers in the group.
- Each group follows the same rule: (8,2,4), (12,3,4), (20, 5, ____). What number completes the last group?
Correct answer: 4
The missing number is 4, because in each group the first number divided by the second gives the third, so 20 divided by 5 is 4. The values 3, 5, and 15 do not result from dividing the first number by the second.
- Study these number pairs and find the missing value: (4,9), (6,13), (8, ____). What number completes the last pair?
Correct answer: 17
The missing number is 17, because in each pair the second number is the first doubled and then increased by 1, so 8 doubled is 16 and adding 1 gives 17. The values 16, 15, and 18 do not follow the double-then-add-one rule.
- Each group follows the same rule: (6,1,7), (4,5,9), (3, 8, ____). What number completes the last group?
Correct answer: 11
The missing number is 11, because in each group the third number is the sum of the first two, so 3 plus 8 is 11. The values 10 and 12 are off by one, and 24 multiplies instead of adds, so none follows the addition rule.
- Study these number pairs and find the missing value: (1,1), (2,4), (3,9), (4, ____). What number completes the last pair?
Correct answer: 16
The missing number is 16, because in each pair the second number is the first multiplied by itself, so 4 times 4 is 16. The value 12 would be times 3 and 8 would be times 2, while 20 is too large, so none matches multiplying the number by itself.
- Each group follows the same rule: (5,10,2), (9,18,2), (6, 24, ____). What number completes the last group?
Correct answer: 4
The missing number is 4, because in each group the second number divided by the first gives the third, so 24 divided by 6 is 4. The values 2, 3, and 6 do not result from dividing the second number by the first.
- Study these number pairs and find the missing value: (12,6), (18,9), (24, ____). What number completes the last pair?
Correct answer: 12
The missing number is 12, because in each pair the second number is half of the first, so half of 24 is 12. The values 10, 14, and 16 do not equal half of 24, so none follows the consistent halving rule.
- Each group follows the same rule: (3,4,12), (2,5,10), (6, 3, ____). What number completes the last group?
Correct answer: 18
The missing number is 18, because in each group the third number is the product of the first two, so 6 times 3 is 18. The value 9 adds instead of multiplies, while 15 and 12 do not equal 6 times 3, so none follows the multiplication rule.
- Study these number pairs and find the missing value: (20,16), (30,26), (50, ____). What number completes the last pair?
Correct answer: 46
The missing number is 46, because in each pair the second number is 4 less than the first, so 50 minus 4 is 46. The values 45, 44, and 48 do not follow the consistent rule of subtracting 4 from the first number.
- Each group follows the same rule: (7,2,14), (5,4,20), (8, 3, ____). What number completes the last group?
Correct answer: 24
The missing number is 24, because in each group the third number is the first multiplied by the second, so 8 times 3 is 24. The value 11 adds instead of multiplies, while 21 and 16 do not equal 8 times 3, so none follows the multiplication rule.
- Study these number pairs and find the missing value: (2,6), (3,9), (4,12), (5, ____). What number completes the last pair?
Correct answer: 15
The missing number is 15, because in each pair the second number is the first multiplied by 3, so 5 times 3 is 15. The values 14, 16, and 18 do not equal 5 times 3, so none follows the consistent rule of multiplying by 3.
- Each group follows the same rule: (10,3,7), (9,2,7), (14, 6, ____). What number completes the last group?
Correct answer: 8
The missing number is 8, because in each group the third number is the first minus the second, so 14 minus 6 is 8. The value 20 adds instead of subtracts, while 6 and 9 do not equal 14 minus 6, so none follows the subtraction rule.
- In a number grid, the top row reads 1, 2, 3 and the middle row reads 2, 4, 6. Each number in the middle row is double the number directly above it. The bottom row begins 3, 6 and follows the rule that each number is triple the top number above it. What number completes the bottom row under the 3?
Correct answer: 9
The missing number is 9, because the bottom row triples each top number, and the top number above the blank is 3, so 3 times 3 is 9. The values 7, 12, and 6 do not equal the top number tripled, so none fits the column rule.
- In a 3-by-3 number grid, each row increases by the same step. The top row reads 1, 2, 3 and the middle row reads 4, 5, 6. The bottom row reads 7, 8, ____. What number belongs in the empty box?
Correct answer: 9
The missing number is 9, because each row counts up by 1 across its boxes, so after 7 and 8 the next number is 9. The values 10, 11, and 12 skip past the steady step of 1 in the bottom row.
- In a number grid, each row adds the first two boxes to get the third. The top row reads 2, 3, 5 and the middle row reads 4, 1, 5. The bottom row reads 6, 2, ____. What number belongs in the empty box?
Correct answer: 8
The missing number is 8, because in each row the third box equals the sum of the first two, so 6 plus 2 is 8. The value 4 subtracts the boxes, 12 multiplies them, and 10 does not match the sum, so none follows the add-the-first-two rule.
- In a 3-by-3 number grid, each column counts down by the same step. The top row reads 9, 8, 7 and the middle row reads 6, 5, 4. The bottom row reads 3, 2, ____. What number belongs in the empty box?
Correct answer: 1
The missing number is 1, because each row counts down by 1 across its boxes, so after 3 and 2 the next number is 1. The values 0, 2, and 3 do not match the steady drop of 1 in the bottom row.
- In a number grid, the third box in each row is the first box times the second. The top row reads 2, 4, 8 and the middle row reads 3, 3, 9. The bottom row reads 5, 2, ____. What number belongs in the empty box?
Correct answer: 10
The missing number is 10, because in each row the third box equals the first multiplied by the second, so 5 times 2 is 10. The value 7 adds the boxes, 12 does not match, and 25 multiplies 5 by itself, so none follows the multiply-the-first-two rule.
- In a 3-by-3 number grid, every row reads the same three numbers. The top row reads 5, 10, 15 and the middle row reads 5, 10, 15. The bottom row reads 5, 10, ____. What number belongs in the empty box?
Correct answer: 15
The missing number is 15, because every row in the grid repeats the same numbers 5, 10, 15, so the bottom row must end with 15 to match. The values 20, 25, and 5 do not keep the rows identical.
- In a number grid, each box doubles as you read down a column. The left column reads 1, 2, 4 from top to bottom. The middle column reads 3, 6, 12. The right column reads 5, 10, ____. What number belongs at the bottom of the right column?
Correct answer: 20
The missing number is 20, because each box is double the one above it in the column, so 10 doubled is 20. The values 15 and 25 do not result from doubling 10, and 30 triples it instead, so none fits the doubling rule.
- In a 3-by-3 number grid, each row increases by 2. The top row reads 1, 3, 5 and the middle row reads 2, 4, 6. The bottom row reads 3, 5, ____. What number belongs in the empty box?
Correct answer: 7
The missing number is 7, because each row counts up by 2 across its boxes, so after 3 and 5 the next number is 7. The values 6, 8, and 9 do not match the steady step of 2 in the bottom row.
- In a number grid, the bottom box of each column is the top box minus the middle box. The left column reads 9, 4, 5 from top to bottom. The middle column reads 8, 3, 5. The right column reads 10, 6, ____. What number belongs at the bottom of the right column?
Correct answer: 4
The missing number is 4, because in each column the bottom box equals the top box minus the middle box, so 10 minus 6 is 4. The value 16 adds the boxes, while 5 and 3 do not equal 10 minus 6, so none follows the subtraction rule.
- In a 3-by-3 number grid, each column adds the same amount. The top row reads 2, 5, 8 and the middle row reads 4, 7, 10, so each column grows by 2 going down. The bottom row reads 6, 9, ____. What number belongs in the empty box?
Correct answer: 12
The missing number is 12, because each column increases by 2 from the middle box to the bottom box, and the box above the blank is 10, so 10 plus 2 is 12. The values 11, 13, and 10 do not match the column step of 2.
- In a number grid, the third number in each row is the first divided by the second. The top row reads 12, 4, 3 and the middle row reads 20, 5, 4. The bottom row reads 18, 6, ____. What number belongs in the empty box?
Correct answer: 3
The missing number is 3, because in each row the third box equals the first divided by the second, so 18 divided by 6 is 3. The values 4, 12, and 6 do not result from dividing 18 by 6, so none follows the division rule.
- In a 3-by-3 number grid, every row sums to 15. The top row reads 4, 5, 6 and the middle row reads 7, 5, 3. The bottom row reads 8, 2, ____. What number belongs in the empty box?
Correct answer: 5
The missing number is 5, because each row must add up to 15, and 8 plus 2 is 10, so the blank needs 5 more to reach 15. The values 4, 6, and 3 would make the row total something other than 15.
