- What number should come next in this series? 3, 6, 12, 24, 48, …
Correct answer: 96
The next number is 96. Each term is found by doubling the previous term: 3 becomes 6, 6 becomes 12, 12 becomes 24, and 24 becomes 48. Doubling 48 gives 96.
- What number should come next in this series? 5, 9, 13, 17, 21, …
Correct answer: 25
The next number is 25. The series increases by a constant 4 each step (5, 9, 13, 17, 21), so adding 4 to 21 produces 25.
- What number is missing in this series? 81, 27, 9, ?, 1
Correct answer: 3
The missing number is 3. Each term is divided by 3 to get the next (81 to 27 to 9), so 9 divided by 3 is 3, and 3 divided by 3 is 1.
- What number should come next in this series? 2, 3, 5, 8, 12, 17, …
Correct answer: 23
The next number is 23. The amount added grows by one each step: +1, +2, +3, +4, +5, so the next step adds 6 to 17, giving 23.
- What number should come next in this series? 1, 4, 9, 16, 25, …
Correct answer: 36
The next number is 36. These are perfect squares: 1, 4, 9, 16, 25 are the squares of 1 through 5, so the square of 6 is 36.
- What number should come next in this alternating series? 7, 14, 9, 18, 11, …
Correct answer: 22
The next number is 22. The series alternates between two rules: the first set (7, 9, 11) rises by 2, and the second set doubles each preceding odd number (7 to 14, 9 to 18), so 11 doubles to 22.
- What number should come next in this series? 100, 90, 80, 70, 60, …
Correct answer: 50
The next number is 50. The series decreases by a constant 10 each step, so subtracting 10 from 60 gives 50.
- What number should come next in this series? 1, 2, 4, 7, 11, 16, …
Correct answer: 22
The next number is 22. The gaps between terms grow by 1 each time: +1, +2, +3, +4, +5, so the next gap of +6 added to 16 yields 22.
- Which letter should come next in this series? A, C, E, G, I, ...
Correct answer: K
The next letter is K. The series skips one letter each time (A, C, E, G, I represent positions 1, 3, 5, 7, 9), so the next position is 11, which is K.
- Which letter should come next in this series? B, D, G, K, P, ...
Correct answer: V
The next letter is V. The gaps between letters increase: +2, +3, +4, +5, so the next gap of +6 from P lands on V.
- Which pair of letters should come next? AZ, BY, CX, DW, ...
Correct answer: EV
The next pair is EV. The first letter moves forward through the alphabet (A, B, C, D, then E) while the second moves backward (Z, Y, X, W, then V), giving EV.
- Which letter should replace the question mark? Z, X, V, T, ?
Correct answer: R
The missing letter is R. The series moves backward through the alphabet skipping one letter each time (Z, X, V, T), so the next letter back from T is R.
- Which group of letters should come next? AB, CD, EF, GH, ...
Correct answer: IJ
The next group is IJ. Each pair takes the next two consecutive letters of the alphabet (AB, CD, EF, GH), so the pair after GH is IJ.
- A store buys a jacket for $40 and sells it for $52. What is the percentage markup based on the cost?
- 12%
- 20%
- 30%
- 25%
Correct answer: 30%
The markup is 30%. The profit is $52 minus $40, which is $12, and $12 divided by the $40 cost equals 0.30, or 30%.
- A train travels 240 miles in 4 hours. At the same speed, how far will it travel in 7 hours?
- 360 miles
- 420 miles
- 480 miles
- 410 miles
Correct answer: 420 miles
The train will travel 420 miles. Its speed is 240 miles divided by 4 hours, which is 60 miles per hour, and 60 multiplied by 7 hours equals 420 miles.
- Three workers can paint a fence in 6 hours. How long would it take if 6 workers worked at the same rate?
- 3 hours
- 12 hours
- 4 hours
- 2 hours
Correct answer: 3 hours
It would take 3 hours. The total work equals 3 workers times 6 hours, which is 18 worker-hours, and dividing 18 by 6 workers gives 3 hours.
- A recipe that serves 4 people requires 3 cups of flour. How many cups are needed to serve 10 people?
- 6 cups
- 7 cups
- 7.5 cups
- 8 cups
Correct answer: 7.5 cups
You need 7.5 cups. Each person requires 3 cups divided by 4, which is 0.75 cups, and 0.75 multiplied by 10 people equals 7.5 cups.
- Sara is 3 times as old as her brother. In 6 years, she will be twice as old as he is then. How old is Sara now?
Correct answer: 18
Sara is 18. If her brother is 6, then Sara is 18 now; in 6 years he is 12 and she is 24, and 24 is twice 12, satisfying the condition.
- A phone originally priced at $300 is discounted by 20%, then an additional 10% is taken off the sale price. What is the final price?
Correct answer: $216
The final price is $216. The first 20% off brings $300 to $240, and taking 10% off $240 removes $24, leaving $216.
- What is 35% of 80?
Correct answer: 28
The answer is 28. Converting 35% to 0.35 and multiplying by 80 gives 28.
- The ratio of cats to dogs at a shelter is 3:5. If there are 24 cats, how many dogs are there?
Correct answer: 40
There are 40 dogs. Each ratio unit equals 24 cats divided by 3, which is 8, and multiplying 8 by the 5 dog units gives 40.
- What is the sum of 41 and 32?
- 73
- 127
- 125
- 1211
Correct answer: 1211
The sum is 1211. Using a common denominator of 12, 41 becomes 123 and 32 becomes 128, and adding them gives 1211.
- A number increased by 25% equals 90. What is the original number?
Correct answer: 72
The original number is 72. Since 90 represents 125% of the original, dividing 90 by 1.25 returns the starting value of 72.
- What is 53 expressed as a percentage?
- 35%
- 53%
- 60%
- 65%
Correct answer: 60%
The answer is 60%. Dividing 3 by 5 gives 0.6, which equals 60%.
- If 8 pens cost $6, what is the cost of 20 pens at the same rate?
Correct answer: $15
The cost is $15. Each pen costs $6 divided by 8, which is $0.75, and 0.75 multiplied by 20 pens equals $15.
- A shirt's price rose from $20 to $25. What was the percentage increase?
- 20%
- 30%
- 25%
- 15%
Correct answer: 25%
The increase was 25%. The price rose by $5, and $5 divided by the original $20 equals 0.25, or 25%.
- Solve for x: 4x−7=21
Correct answer: 7
The value of x is 7. Adding 7 to both sides gives 4x equals 28, and dividing both sides by 4 yields x equals 7.
- Solve for x: 3(x+2)=18
Correct answer: 4
The value of x is 4. Dividing both sides by 3 gives x plus 2 equals 6, and subtracting 2 leaves x equals 4.
- If 2x+3y=12 and x=3, what is the value of y?
Correct answer: 2
The value of y is 2. Substituting x equals 3 gives 6 plus 3y equals 12, so 3y equals 6 and y equals 2.
- Solve for x: 5x+4=9
Correct answer: 25
The value of x is 25. Subtracting 4 from both sides gives x divided by 5 equals 5, and multiplying both sides by 5 yields x equals 25.
- If 5x=3x+14, what is x?
Correct answer: 7
The value of x is 7. Subtracting 3x from both sides gives 2x equals 14, so dividing by 2 produces x equals 7.
- A table shows sales of $200 in January, $350 in February, and $450 in March. What were the average monthly sales for the quarter?
Correct answer: $333
The average was about $333. Adding $200, $350, and $450 gives $1,000, and dividing by the 3 months yields roughly $333.
- A bar graph shows a company sold 120 units in 2024 and 150 units in 2025. What was the percentage increase in units sold?
- 20%
- 30%
- 25%
- 15%
Correct answer: 25%
The increase was 25%. Sales rose by 30 units, and 30 divided by the 2024 total of 120 equals 0.25, or 25%.
- A pie chart shows a $4,000 budget split as 40% rent, 30% food, 20% transport, and 10% savings. How much is allocated to food?
Correct answer: $1,200
Food receives $1,200. Multiplying the 30% food share by the $4,000 budget gives $1,200.
- A table lists test scores: Ann 80, Ben 90, Carl 70, Dana 100. What is the range of the scores?
Correct answer: 30
The range is 30. The range is the highest score minus the lowest, which is Dana's 100 minus Carl's 70, equaling 30.
- A graph shows revenue of $50K in Q1, $60K in Q2, $45K in Q3, and $65K in Q4. Which quarter had the highest revenue?
Correct answer: Q4
The highest revenue was in Q4. Comparing the four figures, $65K in Q4 exceeds the $50K, $60K, and $45K of the other quarters.
- A table shows a factory produced 300 items on Monday and 360 on Tuesday. If Tuesday's level continues, how many items are produced over 5 days like Tuesday?
Correct answer: 1,800
The total is 1,800. Multiplying Tuesday's output of 360 items by 5 days gives 1,800.
- All managers attended the meeting. No interns attended the meeting. Which statement must be true?
- All interns are managers
- No manager is an intern
- Some interns attended
- All attendees are interns
Correct answer: No manager is an intern
It must be true that no manager is an intern. Since every manager attended but no intern attended, no person can be both a manager and an intern.
- If it rains, the game is canceled. The game was not canceled. What can be concluded?
- It rained
- It did not rain
- The game was postponed
- It might have rained
Correct answer: It did not rain
The conclusion is that it did not rain. Because rain always causes cancellation and the game was not canceled, rain could not have occurred.
- Four people finish a race. Maria beat Tom. Tom beat Lee. Lee beat Joe. Who finished last?
Correct answer: Joe
Joe finished last. The order from the clues is Maria ahead of Tom, Tom ahead of Lee, and Lee ahead of Joe, placing Joe at the end.
- Every book on the shelf is blue. The item in my hand is not blue. What must be true about the item?
- It is a book on the shelf
- It is not a book on the shelf
- It is blue
- It belongs on the shelf
Correct answer: It is not a book on the shelf
It must be true that the item is not a book on the shelf. Since all shelf books are blue and this item is not blue, it cannot be one of those books.
- Three boxes are labeled A, B, and C. Box A is heavier than Box C. Box B is lighter than Box C. Which box is the heaviest?
- Box A
- Box B
- Box C
- Cannot be determined
Correct answer: Box A
Box A is the heaviest. Box A outweighs Box C, and Box C outweighs Box B, so Box A is heavier than both of the others.
- In a code, MOVE is written as NPWF (each letter shifted forward by one). How is CALM written in the same code?
Correct answer: DBMN
CALM is written as DBMN. Shifting each letter forward by one turns C into D, A into B, L into M, and M into N.
- If all squares are rectangles and all rectangles are shapes, which statement must be true?
- All shapes are squares
- All squares are shapes
- All rectangles are squares
- Some shapes are not rectangles
Correct answer: All squares are shapes
It must be true that all squares are shapes. Since every square is a rectangle and every rectangle is a shape, every square is therefore a shape.
- A clerk processes 15 forms per hour. How many forms will the clerk process in a 7-hour shift?
Correct answer: 105
The clerk processes 105 forms. Multiplying the rate of 15 forms per hour by the 7-hour shift gives 105.
- Solve for x: 2x+9=5x−6
Correct answer: 5
The value of x is 5. Subtracting 2x from both sides gives 9 equals 3x minus 6, then adding 6 gives 15 equals 3x, so x equals 5.
- PAINTER is to BRUSH as WRITER is to which of the following?
Correct answer: Pen
The answer is Pen. A painter uses a brush as the tool to create work, and a writer uses a pen as the tool to create work, so the relationship is worker to primary tool.
- THERMOMETER is to TEMPERATURE as SCALE is to which of the following?
- Kitchen
- Balance
- Number
- Weight
Correct answer: Weight
The answer is Weight. A thermometer measures temperature, and a scale measures weight, so the relationship is instrument to the quantity it measures.
- PUPPY is to DOG as KITTEN is to which of the following?
Correct answer: Cat
The answer is Cat. A puppy is the young form of a dog, and a kitten is the young form of a cat, so the relationship is offspring to adult animal.
- LIBRARY is to BOOKS as ARMORY is to which of the following?
- Soldiers
- Walls
- Battles
- Weapons
Correct answer: Weapons
The answer is Weapons. A library is a place that stores books, and an armory is a place that stores weapons, so the relationship is storehouse to what it holds.
- In the verbal reasoning section, you must complete the analogy: BEE is to HIVE as BIRD is to which of the following?
Correct answer: Nest
The answer is Nest. A bee lives in a hive, and a bird lives in a nest, so the relationship is animal to the dwelling it builds and inhabits.
- DOCTOR is to PATIENT as TEACHER is to which of the following?
Correct answer: Student
The answer is Student. A doctor provides care to a patient, and a teacher provides instruction to a student, so the relationship is professional to the person served.
- WHISPER is to SHOUT as TRICKLE is to which of the following?
Correct answer: Flood
The answer is Flood. A whisper is a quiet version of a shout, and a trickle is a small flow while a flood is a massive flow, so the relationship is small intensity to large intensity.
- CHAPTER is to BOOK as act is to which of the following?
Correct answer: Play
The answer is Play. A chapter is a major division of a book, and an act is a major division of a play, so the relationship is part to the whole work it belongs to.
- ARID is to DESERT as HUMID is to which of the following?
- Mountain
- Jungle
- Tundra
- Plateau
Correct answer: Jungle
The answer is Jungle. Arid describes the dry climate of a desert, and humid describes the damp climate of a jungle, so the relationship is climate trait to the region it characterizes.
- CONDUCTOR is to ORCHESTRA as CAPTAIN is to which of the following?
Correct answer: Ship
The answer is Ship. A conductor leads an orchestra, and a captain leads a ship's crew, so the relationship is leader to the group or vessel directed.
- FRAGILE is to SHATTER as FLAMMABLE is to which of the following?
Correct answer: Burn
The answer is Burn. Something fragile is prone to shatter, and something flammable is prone to burn, so the relationship is property to the outcome it makes likely.
- Choose the word that is most nearly OPPOSITE in meaning to ABUNDANT.
- Plentiful
- Wealthy
- Frequent
- Scarce
Correct answer: Scarce
The answer is Scarce. Abundant means existing in large quantities, and scarce means existing in very small quantities, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to PRAISE.
- Applaud
- Honor
- Admire
- Criticize
Correct answer: Criticize
The answer is Criticize. Praise means to express approval, and criticize means to express disapproval, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to TRANSPARENT.
Correct answer: Opaque
The answer is Opaque. Transparent means allowing light to pass through so things are visible, and opaque means blocking light so things cannot be seen, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to GENEROUS.
Correct answer: Stingy
The answer is Stingy. Generous means willing to give freely, and stingy means unwilling to give or spend, making it the direct opposite.
- In the verbal section, choose the word most nearly OPPOSITE in meaning to TEMPORARY.
- Brief
- Fleeting
- Permanent
- Passing
Correct answer: Permanent
The answer is Permanent. Temporary means lasting only a short time, and permanent means lasting indefinitely, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to ASCEND.
Correct answer: Descend
The answer is Descend. Ascend means to move upward, and descend means to move downward, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to CONCEAL.
Correct answer: Reveal
The answer is Reveal. Conceal means to hide something from view, and reveal means to make it visible or known, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to RIGID.
Correct answer: Flexible
The answer is Flexible. Rigid means stiff and unable to bend, and flexible means able to bend easily, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to ENCOURAGE.
- Support
- Inspire
- Discourage
- Motivate
Correct answer: Discourage
The answer is Discourage. Encourage means to give someone confidence or support to act, and discourage means to take away that confidence or deter action, making it the direct opposite.
- Choose the word that is most nearly OPPOSITE in meaning to DELAY.
- Hasten
- Postpone
- Stall
- Linger
Correct answer: Hasten
The answer is Hasten. Delay means to slow down or put off, and hasten means to speed up or hurry, making it the direct opposite.
- Choose the word that best completes the sentence: Despite the storm warning, the captain remained ___, refusing to alter the ship's course.
- Resolute
- Anxious
- Confused
- Exhausted
Correct answer: Resolute
The answer is resolute. The captain refused to change course despite a warning, which shows firm determination, and resolute means firmly determined.
- Choose the word that best completes the sentence: The new policy was so ___ that even longtime employees struggled to understand its many rules.
- Simple
- Convenient
- Convoluted
- Popular
Correct answer: Convoluted
The answer is convoluted. Employees struggled to understand its many rules, which signals excessive complexity, and convoluted means extremely complicated and hard to follow.
- Choose the word that best completes the sentence: Although she was clearly talented, her ___ kept her from boasting about her achievements.
- Arrogance
- Modesty
- Ambition
- Wealth
Correct answer: Modesty
The answer is modesty. The sentence contrasts talent with not boasting, and modesty is the quality of not drawing attention to one's own abilities.
- Choose the word that best completes the sentence: The witness gave a ___ account of the accident, leaving out no detail the investigators needed.
Correct answer: Thorough
The answer is thorough. The account left out no detail the investigators needed, which describes completeness, and thorough means complete and detailed.
- Choose the word that best completes the sentence: Because the evidence was ___, the jury could not reach a confident verdict.
- Conclusive
- Overwhelming
- Inconclusive
- Detailed
Correct answer: Inconclusive
The answer is inconclusive. The jury could not reach a confident verdict, meaning the evidence failed to settle the matter, and inconclusive means not leading to a firm conclusion.
- In the verbal reasoning section, choose the word that best completes the sentence: The manager praised the report for being ___, presenting its findings clearly and without unnecessary words.
- Concise
- Lengthy
- Repetitive
- Cluttered
Correct answer: Concise
The answer is concise. The report presented findings clearly and without unnecessary words, which describes brevity with clarity, and concise means expressing much in few words.
- Choose the word that best completes the sentence: The volunteers worked ___, finishing the entire cleanup hours ahead of schedule.
- Reluctantly
- Diligently
- Carelessly
- Slowly
Correct answer: Diligently
The answer is diligently. The volunteers finished hours ahead of schedule, which reflects steady hard work, and diligently means in a careful and persistent manner.
- Choose the word that best completes the sentence: His ___ remarks during the meeting offended several colleagues who felt he was being disrespectful.
- Tactful
- Gracious
- Abrasive
- Gentle
Correct answer: Abrasive
The answer is abrasive. The remarks offended colleagues who felt disrespected, which points to a harsh manner, and abrasive means harsh or unpleasant in tone.
- Choose the word that best completes the sentence: The drought left the once-fertile fields ___, unable to support any crops.
Correct answer: Barren
The answer is barren. A drought left fields unable to support crops, which describes lifeless land, and barren means incapable of producing growth.
- Choose the word that best completes the sentence: Rather than accept the criticism, he became ___ and dismissed every suggestion offered.
- Receptive
- Defensive
- Grateful
- Attentive
Correct answer: Defensive
The answer is defensive. He refused criticism and dismissed every suggestion, which describes resisting input to protect himself, and defensive means anxious to justify oneself against perceived attack.
- Choose the word that best completes the sentence: The instructions were so ___ that the team completed the assembly without a single question.
- Ambiguous
- Lucid
- Tangled
- Misleading
Correct answer: Lucid
The answer is lucid. The team completed the assembly with no questions, meaning the instructions were perfectly clear, and lucid means easily understood.
- All registered members received a voucher. Maria is a registered member. Which conclusion must be true?
- Only Maria received a voucher
- Maria did not receive a voucher
- Some members received no voucher
- Maria received a voucher
Correct answer: Maria received a voucher
The answer is that Maria received a voucher. Every registered member received a voucher, and because Maria is a registered member, she necessarily received one.
- No reptiles are warm-blooded. All snakes are reptiles. Which conclusion must be true?
- Some snakes are warm-blooded
- All warm-blooded animals are snakes
- No snakes are warm-blooded
- All reptiles are snakes
Correct answer: No snakes are warm-blooded
The answer is that no snakes are warm-blooded. Snakes belong to the reptile group, and since no reptile is warm-blooded, no snake can be warm-blooded.
- All members of the choir can read music. James cannot read music. Which conclusion must be true?
- James is in the choir
- James is the conductor
- James is not in the choir
- Some choir members cannot read music
Correct answer: James is not in the choir
The answer is that James is not in the choir. Every choir member can read music, and because James cannot read music, he cannot be a member of the choir.
- Some employees in the office are bilingual. All bilingual employees received a bonus. Which conclusion must be true?
- All employees received a bonus
- Some employees received a bonus
- No employees received a bonus
- Only bilingual people work in the office
Correct answer: Some employees received a bonus
The answer is that some employees received a bonus. At least some employees are bilingual, and since every bilingual employee received a bonus, those particular employees must have received one.
- All citrus fruits contain vitamin C. A lemon is a citrus fruit. Which conclusion must be true?
- Only lemons contain vitamin C
- A lemon contains no vitamin C
- All fruits are citrus
- A lemon contains vitamin C
Correct answer: A lemon contains vitamin C
The answer is that a lemon contains vitamin C. Every citrus fruit contains vitamin C, and because a lemon is a citrus fruit, it must contain vitamin C.
- No item on the clearance rack is full price. The jacket is on the clearance rack. Which conclusion must be true?
- The jacket is full price
- The jacket is not full price
- The jacket is the cheapest item
- All jackets are on clearance
Correct answer: The jacket is not full price
The answer is that the jacket is not full price. No clearance-rack item is full price, and since the jacket is on the clearance rack, it cannot be full price.
- Examine the two account numbers and decide whether they are exactly the same or different: 48217-XQ and 48217-XO
- Exactly the same
- Different
- Same except spacing
- Cannot tell
Correct answer: Different
The answer is Different. The first entry ends in the letter Q while the second ends in the letter O, so the two account numbers do not match exactly.
- Examine the two entries and decide whether they are exactly the same or different: Stephenson, R.J. and Stephenson, R.J.
- Different
- Exactly the same
- Different punctuation
- Cannot tell
Correct answer: Exactly the same
The answer is Exactly the same. Both entries read Stephenson, R.J. with identical spelling, capitalization, and punctuation, so they match exactly.
- Examine the two product codes and decide whether they are exactly the same or different: 7B-90041-CC and 7B-90041-CG
- Same except a digit
- Cannot tell
- Exactly the same
- Different
Correct answer: Different
The answer is Different. The first code ends in the pair C-C while the second ends in C-G, so the final character differs and the codes do not match.
- Examine the two strings and decide whether they are exactly the same or different: 0.005720 and 0.005270
- Exactly the same
- Different ordering of digits
- Different
- Same value
Correct answer: Different
The answer is Different. Reading left to right, one string has 720 at the end while the other has 270, so the digit order differs and the strings are not identical.
- A spatial 'next in series' question shows four figures: a square with 1 dot, a square with 2 dots, a square with 3 dots, and a square with 4 dots. Each figure adds one dot in a fixed reading order. How many dots should the next square in the series contain?
Correct answer: 5
The next square should contain 5 dots. The series increases by exactly one dot each step (1, 2, 3, 4), so the figure that comes next continues the pattern by adding one more, giving 5 dots.
- In a CCAT shape series, an arrow rotates a quarter turn clockwise at each step. The first arrow points up, the second points right, and the third points down. Which direction should the fourth arrow in the series point?
Correct answer: Left
The fourth arrow should point left. Each step rotates the arrow a quarter turn (90 degrees) clockwise: up, then right, then down, and the next quarter turn from down is left.
- A series of shapes alternates in this order: circle, triangle, circle, triangle, circle. Following the established alternating pattern, what shape comes next in the series?
Correct answer: Triangle
The next shape is a triangle. The series strictly alternates between circle and triangle, and because the most recent shape shown is a circle, the alternating rule places a triangle next.
- A spatial series shows a black square, then a white square, then a black square, then a white square. The shading flips between black and white at every step. What should the fifth figure in this series be?
- A white square
- A black triangle
- A gray square
- A black square
Correct answer: A black square
The fifth figure should be a black square. The shading alternates black, white, black, white, so the step after a white square returns to black while the square shape itself stays the same.
- In a figure series, the number of sides of each shape grows by one: a triangle (3 sides), then a square (4 sides), then a pentagon (5 sides). Which shape correctly continues this series?
- A hexagon (6 sides)
- Another pentagon (5 sides)
- A square (4 sides)
- A circle (0 sides)
Correct answer: A hexagon (6 sides)
A hexagon (6 sides) continues the series. Each shape adds exactly one side to the previous one (3, 4, 5), so the next shape must have 6 sides, which is a hexagon.
- A spatial series shows a shape that shrinks at each step: a large circle, then a medium circle, then a small circle. The size decreases by one level every step. What should the next figure in the series look like?
- A large circle
- An even smaller circle
- A medium square
- A large triangle
Correct answer: An even smaller circle
The next figure should be an even smaller circle. The series keeps the same circle shape while reducing size one level at a time, so the figure following the small circle is a still smaller circle.
- A 3-by-3 figure matrix has a missing bottom-right cell. Across each row, the count of stars increases from 1 to 2 to 3. The bottom row already shows 1 star and 2 stars in its first two cells. How many stars belong in the missing bottom-right cell?
Correct answer: 3
The missing cell should contain 3 stars. Every row of the matrix increases by one star moving left to right (1, 2, 3), so the third cell in the bottom row must hold 3 stars.
- In a matrix pattern, each row contains the same three shapes (circle, square, triangle) but in a rotated order. Row one is circle-square-triangle, row two is square-triangle-circle, and row three begins triangle-circle. Which shape fills the missing final cell of row three?
Correct answer: Square
The missing cell is a square. Each row uses the same three shapes exactly once, and since row three already contains a triangle and a circle, the only remaining shape for the last cell is the square.
- A figure matrix shows shading that follows a diagonal rule: cells on the main diagonal are black and all other cells are white. The missing cell sits on the main diagonal. What shading should the missing cell have?
Correct answer: Black
The missing cell should be black. The rule makes every cell on the main diagonal black, and because the missing cell lies on that diagonal, it follows the same rule and must be black.
- In a matrix, the third column is always the combination of the shapes in the first two columns overlaid together. The first two cells of a row show a vertical line and a horizontal line. What should the missing third cell of that row contain?
- Only a vertical line
- A plus sign (cross)
- Only a horizontal line
- A blank cell
Correct answer: A plus sign (cross)
The missing cell should contain a plus sign. The third column overlays the first two cells, and combining a vertical line with a horizontal line produces a crossing pattern, which is a plus sign.
- A matrix follows the rule that the number of dots doubles across each row. The first two cells in a row contain 1 dot and 2 dots. Which value belongs in the missing third cell of that row?
Correct answer: 4 dots
The missing cell should contain 4 dots. The rule doubles the dot count from one cell to the next (1, then 2), so doubling 2 gives 4 dots in the third cell.
- The letter 'b' is rotated 180 degrees (turned completely upside down). Which letter does the rotated shape most resemble?
Correct answer: Q
The rotated shape resembles the letter 'q'. Turning 'b' a full 180 degrees flips it both top-to-bottom and left-to-right, moving the loop to the lower right of the stem, which matches the shape of 'q'.
- An arrow pointing to the upper-right corner of a page is rotated 90 degrees clockwise. After this rotation, which corner does the arrow point toward?
- Lower-right corner
- Upper-left corner
- Lower-left corner
- Upper-right corner
Correct answer: Lower-right corner
After the rotation the arrow points to the lower-right corner. A 90-degree clockwise turn moves a direction one quarter clockwise, so 'upper-right' becomes 'lower-right'.
- A capital letter 'L' is flipped horizontally (mirror-imaged left to right). What does the resulting shape look like?
- An unchanged 'L' with the foot pointing right
- A backward 'L' with the foot pointing left
- An upside-down 'L'
- A 'T' shape
Correct answer: A backward 'L' with the foot pointing left
The result is a backward 'L' with its foot pointing left. A horizontal flip reverses left and right, so the foot of the 'L', which normally points right, now points left while the vertical stroke stays upright.
- A right-pointing triangle (a triangle with its point on the right side) is rotated 90 degrees counterclockwise. After the rotation, which direction does the point face?
Correct answer: Up
After the rotation the point faces up. A 90-degree counterclockwise turn moves a rightward direction to an upward direction, so the triangle's point shifts from pointing right to pointing up.
- A flag is drawn on a pole with the flag extending to the right of the pole. The whole image is flipped vertically (mirror-imaged top to bottom). After the flip, where does the flag extend relative to the pole?
- To the left of the pole
- Above the pole
- Below the pole
- Still to the right of the pole
Correct answer: Still to the right of the pole
After a vertical flip the flag still extends to the right of the pole. A vertical (top-to-bottom) flip reverses up and down but leaves left and right unchanged, so the flag's left-right side stays the same.
- Four figures are shown together. Three of them are circles of different sizes, and one is a square. Using the odd-one-out rule, which figure does not belong with the others?
- The square
- The largest circle
- The smallest circle
- The medium circle
Correct answer: The square
The square is the odd one out. Three of the four figures share the same shape category of circle, differing only in size, so the square is the single figure that does not match the group.
- A set of four shapes is shown. Three shapes are shaded black and one shape is left white, while all four shapes are triangles. Which shape is the odd one out?
- Any one of the black triangles
- The white triangle
- The largest triangle
- The smallest triangle
Correct answer: The white triangle
The white triangle is the odd one out. All four figures are the same shape, so shading is the distinguishing feature, and the single white triangle differs from the three black ones.
- Four arrows are displayed. Three arrows point upward and one arrow points downward. Applying the outlier rule, which arrow does not belong?
- An upward arrow on the left
- An upward arrow on the right
- The downward arrow
- The middle upward arrow
Correct answer: The downward arrow
The downward arrow is the odd one out. Three of the four arrows share the same upward orientation, so the single arrow pointing the opposite direction is the one that does not belong.
- Four figures appear in a row. Three of them are shapes drawn with straight edges only (a triangle, a square, and a pentagon), and one is a circle. Which figure is the outlier?
- The triangle
- The square
- The pentagon
- The circle
Correct answer: The circle
The circle is the outlier. The other three figures are all made entirely of straight edges, while the circle is the only shape with a continuously curved boundary, so it does not fit the group.
- A square piece of paper is folded once exactly in half from left to right. After folding, how many layers of paper are stacked together?
Correct answer: 2
There are 2 layers after the fold. Folding the paper once in half brings one side directly on top of the other, stacking exactly two layers of paper together.
- A square sheet of paper is folded in half top to bottom, then folded in half again left to right, making two folds total. When the paper is completely unfolded, how many smaller rectangles do the crease lines divide it into?
Correct answer: 4
The creases divide the paper into 4 rectangles. The first fold creates one crease that splits the sheet into 2 parts, and the second perpendicular fold splits each of those in half again, producing a 2-by-2 grid of 4 rectangles.
- A square paper is folded in half once, and then a single hole is punched through both layers near the folded edge. When the paper is unfolded, how many holes appear in total?
Correct answer: 2
Two holes appear when the paper is unfolded. The single punch passes through both stacked layers, so each layer receives one hole, producing two holes that are mirror images across the fold line.
- A flat cross-shaped net is folded up to form a closed cube. A standard cube has six faces. How many faces must the net contain so that every side of the cube is covered?
Correct answer: 6
The net must contain 6 faces. A cube has exactly six sides (top, bottom, and four around the middle), so the flat net must have six square faces, one to cover each face when it is folded together.
- A shape series shows a single dot, then two dots, then four dots, then eight dots, with the count doubling at each step. Following this doubling pattern, how many dots should appear in the next figure?
Correct answer: 16
The next figure should contain 16 dots. The count doubles at every step (1, 2, 4, 8), so doubling 8 gives 16 dots in the following figure.
- In a figure series, a line segment grows longer at each step by adding one identical tick mark: first 1 tick, then 2 ticks, then 3 ticks, then 4 ticks. How many tick marks should the next segment in the series have?
Correct answer: 5
The next segment should have 5 tick marks. Each step adds exactly one tick (1, 2, 3, 4), so continuing the pattern gives 5.
- A spatial series cycles through shading in this fixed order: empty, half-shaded, fully shaded, empty, half-shaded. Following the repeating three-step cycle, what is the shading of the next figure?
- Quarter-shaded
- Fully shaded
- Half-shaded
- Empty
Correct answer: Fully shaded
The next figure is fully shaded. The cycle repeats every three steps (empty, half, full), and since the last figure shown was half-shaded, the next one returns to fully shaded.
- A series shows a single shape that gains one extra internal line at each step: a square with 0 diagonals, then 1 diagonal, then 2 diagonals. A square can hold at most 2 diagonals. What internal feature should the next figure logically add instead, keeping the 'one more line' pattern?
- The square is removed
- Two more diagonals
- One horizontal line through the middle
- Nothing new is added
Correct answer: One horizontal line through the middle
The next figure adds one horizontal line through the middle. The pattern adds exactly one new internal line per step; since both diagonals are used, the simplest single added line is a horizontal one.
- A figure series rotates a single pointer by 45 degrees clockwise at each step. The pointer starts pointing straight up. After three steps of 45-degree clockwise rotations, in which direction does the pointer point?
- Upper-right (northeast)
- Straight right (east)
- Lower-right (southeast)
- Straight down (south)
Correct answer: Lower-right (southeast)
The pointer points lower-right (southeast). Three 45-degree clockwise turns total 135 degrees from straight up, which lands between straight right and straight down, in the southeast direction.
- A series alternates between two shapes while one of them grows: small circle, square, medium circle, square, large circle. Following both the alternation and the growth rule, what should the next figure be?
- A triangle
- A square
- A small circle
- An extra-large circle
Correct answer: A square
The next figure is a square. The series strictly alternates circle and square, and since the last figure was a circle, a square comes next.
- In a 3-by-3 figure matrix, the number of small squares in each cell increases by two as you move left to right across a row. The first cell in the bottom row has 2 squares and the second has 4 squares. How many squares belong in the missing third cell of that row?
Correct answer: 6
The missing cell holds 6 squares. The count rises by two across the row (2, 4), so the third cell continues with 6.
- A 3-by-3 matrix follows the rule that each cell rotates its single arrow 90 degrees clockwise compared to the cell on its left. In a row, the first arrow points up and the second points right. Where should the missing third arrow point?
- Down
- Diagonally up-right
- Left
- Up
Correct answer: Down
The missing arrow points down. Each step rotates 90 degrees clockwise (up, then right), so the next 90-degree clockwise turn from right is down.
- In a figure matrix, the third cell of each row is formed by overlaying the first cell on top of the second cell. The first cell shows a vertical line and the second shows a horizontal line. What should the missing third cell show?
- A plus sign (cross)
- A single horizontal line
- An empty cell
- A single vertical line
Correct answer: A plus sign (cross)
The missing cell shows a plus sign. Overlaying a vertical line and a horizontal line combines them into a crossing plus shape.
- A 3-by-3 matrix uses a rule where the shading rotates: each cell in a row is shaded one position further clockwise (top, right, bottom corner shaded in successive cells). If the first cell has the top shaded and the second has the right shaded, what should the missing third cell have shaded?
- The bottom
- The top
- The center
- The left
Correct answer: The bottom
The missing cell has the bottom shaded. The shaded region moves one position clockwise per cell (top, then right), so the next clockwise position is the bottom.
- A matrix follows the rule that the number of sides shown in each cell decreases by one across a row. The first cell has a pentagon (5 sides) and the second has a square (4 sides). What shape should fill the missing third cell?
- A triangle (3 sides)
- A circle
- A hexagon (6 sides)
- A square (4 sides)
Correct answer: A triangle (3 sides)
The missing cell is a triangle. The side count drops by one across the row (5, 4), so the next shape has 3 sides, which is a triangle.
- In a figure matrix, each row keeps the same shape but adds one dot inside it per column. The first cell has a circle with 1 dot and the second has a circle with 2 dots. How many dots should the missing third circle contain?
Correct answer: 3
The missing circle contains 3 dots. Each column adds one dot (1, 2), so the third cell continues with 3.
- A capital letter 'N' is rotated 180 degrees (turned completely upside down). Because of the letter's symmetry, what does the rotated 'N' look like?
- A 'Z'
- An 'N' (it looks the same)
- An 'M'
- A 'W'
Correct answer: An 'N' (it looks the same)
The rotated figure still looks like an 'N'. The capital 'N' has 180-degree rotational symmetry, so turning it upside down leaves it unchanged.
- A capital letter 'p' (lowercase) is rotated 180 degrees so it is turned completely upside down. Which letter does the result resemble?
Correct answer: A 'd'
The rotated figure resembles a 'd'. Turning a lowercase 'p' a full 180 degrees moves its bowl to the upper area and its stem so that it reads as a 'd'.
- An arrow pointing straight down is rotated 90 degrees counterclockwise. After this single rotation, in which direction does the arrow point?
- Straight up (north)
- Straight right (east)
- Lower-left (southwest)
- Straight left (west)
Correct answer: Straight right (east)
The arrow points straight right. Rotating a downward arrow 90 degrees counterclockwise turns it to point to the right (east).
- A shape that looks like the digit '6' is rotated 180 degrees (turned completely upside down). Which digit does the rotated shape most resemble?
Correct answer: A '9'
The rotated shape resembles a '9'. Turning a '6' a full 180 degrees flips its loop to the top, producing the appearance of a '9'.
- An L-shaped figure with its long arm pointing up and short foot pointing right is rotated 90 degrees clockwise. After the rotation, which way does the short foot point?
Correct answer: Down
The short foot points down. Rotating the figure 90 degrees clockwise turns the foot that pointed right so that it now points down.
- The capital letter 'E' is flipped horizontally (mirror-imaged left to right). Where do the three horizontal bars of the resulting figure point?
- To the left
- To the right
- They disappear
- Straight up
Correct answer: To the left
The bars point to the left. A normal 'E' has bars pointing right; a left-right mirror flip reverses them so they extend to the left.
- A capital letter 'b' is reflected across a vertical mirror line placed to its right (a left-right flip). Which letter does the mirror image resemble?
Correct answer: A 'd'
The mirror image resembles a 'd'. A left-right reflection of 'b' moves its bowl to the other side of the stem, producing a 'd'.
- A right triangle has its right angle at the bottom-left corner, with the vertical side on the left. The triangle is reflected across a vertical mirror line (flipped left to right). Where is the right angle now located?
- At the center
- At the bottom-right corner
- At the bottom-left corner
- At the top-left corner
Correct answer: At the bottom-right corner
The right angle is now at the bottom-right corner. A left-right reflection swaps left and right, moving the bottom-left right angle to the bottom-right.
- A figure of a hand with the thumb pointing left is reflected in a vertical mirror (flipped left to right). After the reflection, which way does the thumb point?
- To the right
- Straight down
- Straight up
- To the left
Correct answer: To the right
The thumb points to the right. A left-right mirror reflection reverses horizontal direction, so a thumb pointing left now points right.
- A shape is reflected across a horizontal mirror line placed below it (flipped top to bottom). If the original shape is a triangle pointing upward, which way does the reflected triangle point?
- To the left
- To the right
- Downward
- Upward
Correct answer: Downward
The reflected triangle points downward. A top-to-bottom flip inverts vertical orientation, so an upward-pointing triangle becomes downward-pointing.
- Four figures are shown. Three are shapes that have a line of symmetry (a square, an equilateral triangle, and a circle), and one is an irregular blob with no line of symmetry. Which figure is the odd one out?
- The triangle
- The irregular blob
- The square
- The circle
Correct answer: The irregular blob
The odd one out is the irregular blob. The other three each have at least one line of symmetry, while the blob has none, making it the exception.
- Four figures are displayed. Three contain an even number of dots (2 dots, 4 dots, and 6 dots), and one contains an odd number (3 dots). Which figure does not belong?
- The figure with 2 dots
- The figure with 4 dots
- The figure with 3 dots
- The figure with 6 dots
Correct answer: The figure with 3 dots
The figure with 3 dots does not belong. The other three all hold an even number of dots, while 3 is odd, making it the exception.
- Four shapes appear in a row. Three are oriented the same way (all arrows pointing left), and one points the opposite way (right). Which is the odd one out?
- The right-pointing arrow
- The second left-pointing arrow
- The third left-pointing arrow
- The first left-pointing arrow
Correct answer: The right-pointing arrow
The odd one out is the right-pointing arrow. The other three all point left, so the single arrow pointing right is the exception.
- Four figures are shown. Three are three-dimensional solids (a cube, a sphere, and a cylinder), and one is a flat two-dimensional shape (a square). Which figure is the odd one out?
- The cylinder
- The cube
- The square
- The sphere
Correct answer: The square
The odd one out is the square. The other three are 3-D solids, while the square is a flat 2-D shape, making it the exception.
- Four figures are shown. Three have rounded outlines (a circle, an oval, and a crescent), and one has only straight edges (a pentagon). Which figure does not belong?
- The crescent
- The pentagon
- The circle
- The oval
Correct answer: The pentagon
The pentagon does not belong. The other three figures all have curved outlines, while the pentagon is made only of straight edges.
- Four boxes each contain a smaller shape. In three of them the inner shape touches the box border, and in one the inner shape floats in the center without touching any side. Which box is the odd one out?
- The first box with a touching shape
- The box with the centered, non-touching shape
- The third box with a touching shape
- The second box with a touching shape
Correct answer: The box with the centered, non-touching shape
The odd one out is the box with the centered, non-touching shape. The other three have inner shapes that touch the border, so the floating one is the exception.
- A square sheet of paper is folded in half from top to bottom. A single hole is then punched through both layers. When the paper is unfolded, how many holes appear in total?
Correct answer: 2
The unfolded paper shows 2 holes. One fold creates two layers, and punching through both leaves one hole per layer, for 2 holes after unfolding.
- A square paper is folded in half top to bottom and then in half again left to right, making four layers. A single hole is punched through all the layers. How many holes appear when the paper is fully unfolded?
Correct answer: 4
The unfolded paper shows 4 holes. Two folds create four stacked layers, and one punch through all four leaves a hole in each layer, giving 4 holes.
- A square sheet is folded once corner to corner to make a triangle. A small notch is cut from the folded edge. When the paper is unfolded, the cut produces a symmetric shape. How many notches appear after unfolding?
Correct answer: 2
The unfolded paper shows 2 notches. The single diagonal fold makes two layers, so one cut through both layers opens into 2 mirror-image notches.
- A flat L-shaped net is folded along its lines to form a three-dimensional shape. The net is made of four squares forming an open-top box shape. When folded, which solid does it best form?
- A sphere
- An open box (cube without a top)
- A flat sheet
- A pyramid
Correct answer: An open box (cube without a top)
The folded net best forms an open box. Four squares folded along their shared edges create the sides and base of a cube-like box that lacks a top face.
- A square sheet is folded in half left to right. On the folded sheet you draw a small triangle near the fold line. When the paper is unfolded, what do you see?
- Four triangles
- Two triangles mirrored across the fold line
- Three triangles
- One triangle only
Correct answer: Two triangles mirrored across the fold line
Unfolding reveals two triangles mirrored across the fold line. A single fold makes two layers, and the drawn shape appears once on each half as a mirror image.
- Imagine a die (cube) where the side facing you shows 3 dots and the top shows 1 dot. The cube is rotated so the top face turns to face you directly, tipping forward toward you. After this single forward tip, which value now faces you?
Correct answer: 1
The face showing 1 now faces you. Tipping the cube forward brings the former top face (1 dot) into the front-facing position.
- A transparent cube has a single arrow drawn on its front face pointing up. The cube is rotated 90 degrees clockwise around the line of sight (the axis pointing toward you). After the rotation, which way does the arrow on the front face point?
- To the left
- To the right
- Down
- Up
Correct answer: To the right
The arrow now points to the right. Rotating the front face 90 degrees clockwise turns an upward arrow so that it points to the right.
- A figure series shows a single square, then two squares side by side, then three squares in a row, with one more square added each step. How many squares should the next figure in the series contain?
Correct answer: 4
The next figure should contain 4 squares. Each step adds exactly one square (1, 2, 3), so continuing the pattern gives 4 squares.
