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CogAT Quantitative study materials
CogAT Quantitative study resources

CogAT Quantitative practice questions

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Question 1Numerical analogies, series, puzzles and justified comparisons

Number analogy: 2 -> 5, 4 -> 7, 6 -> ?

  1. 8
  2. 9 Correct answer.
  3. 10
  4. 12

Explanation

Each starting number increases by 3. Since 6 + 3 = 9, the missing number is 9.

Question 2Numerical analogies, series, puzzles and justified comparisons

Number analogy: 10 -> 8, 7 -> 5, 12 -> ?

  1. 10 Correct answer.
  2. 11
  3. 14
  4. 6

Explanation

Each ending number is 2 less than the starting number. Since 12 - 2 = 10, the answer is 10.

Question 3Numerical analogies, series, puzzles and justified comparisons

Number analogy: 4 -> 16, 6 -> 24, 8 -> ?

  1. 28
  2. 30
  3. 36
  4. 32 Correct answer.

Explanation

Each starting number is multiplied by 4. Since 8 x 4 = 32, the missing number is 32.

Question 4Numerical analogies, series, puzzles and justified comparisons

Number analogy: 9 -> 3, 12 -> 4, 15 -> ?

  1. 5 Correct answer.
  2. 6
  3. 7
  4. 3

Explanation

Each starting number is divided by 3. Since 15 divided by 3 is 5, the missing number is 5.

Question 5Numerical analogies, series, puzzles and justified comparisons

Number analogy: 2 -> 7, 5 -> 10, 8 -> ?

  1. 11
  2. 12
  3. 13 Correct answer.
  4. 16

Explanation

Each pair follows the rule add 5. Since 8 + 5 = 13, the answer is 13.

Question 6Numerical analogies, series, puzzles and justified comparisons

Number analogy: 3 -> 10, 5 -> 16, 7 -> ?

  1. 20
  2. 22 Correct answer.
  3. 24
  4. 28

Explanation

The rule is multiply by 3 and then add 1. For 7, 7 x 3 + 1 = 22.

Question 7Numerical analogies, series, puzzles and justified comparisons

Number analogy: 6 -> 4, 9 -> 7, 13 -> ?

  1. 9
  2. 10
  3. 11 Correct answer.
  4. 12

Explanation

Each ending number is 2 less than the starting number. Since 13 - 2 = 11, the answer is 11.

Question 8Numerical analogies, series, puzzles and justified comparisons

Number analogy: 2 -> 6, 4 -> 20, 6 -> ?

  1. 30
  2. 36
  3. 40
  4. 42 Correct answer.

Explanation

Each number is multiplied by the next whole number: 2 x 3 = 6 and 4 x 5 = 20. So 6 x 7 = 42.

Question 9Numerical analogies, series, puzzles and justified comparisons

Number analogy: 5 -> 12, 8 -> 18, 11 -> ?

  1. 24 Correct answer.
  2. 25
  3. 26
  4. 28

Explanation

The rule is double the number, then add 2. For 11, 11 x 2 + 2 = 24.

Question 10Numerical analogies, series, puzzles and justified comparisons

Number analogy: 4 -> 9, 6 -> 13, 10 -> ?

  1. 18
  2. 20
  3. 21 Correct answer.
  4. 24

Explanation

Each pair follows 2 times the starting number plus 1. For 10, 2 x 10 + 1 = 21.

Question 11Numerical analogies, series, puzzles and justified comparisons

Number analogy: 18 -> 6, 27 -> 9, 36 -> ?

  1. 10
  2. 12 Correct answer.
  3. 14
  4. 18

Explanation

Each starting number is divided by 3. Since 36 divided by 3 is 12, the missing number is 12.

Question 12Numerical analogies, series, puzzles and justified comparisons

Number analogy: 7 -> 15, 10 -> 21, 13 -> ?

  1. 25
  2. 26
  3. 28
  4. 27 Correct answer.

Explanation

The rule is double the starting number and add 1. Since 13 x 2 + 1 = 27, the answer is 27.

Question 13Numerical analogies, series, puzzles and justified comparisons

Number analogy: 3 -> 8, 6 -> 17, 9 -> ?

  1. 24
  2. 25
  3. 26 Correct answer.
  4. 27

Explanation

Each result is 3 times the starting number minus 1. Since 9 x 3 - 1 = 26, the missing number is 26.

Question 14Numerical analogies, series, puzzles and justified comparisons

Number analogy: 16 -> 4, 25 -> 5, 49 -> ?

  1. 7 Correct answer.
  2. 8
  3. 9
  4. 6

Explanation

Each ending number is the square root of the starting number. The square root of 49 is 7.

Question 15Numerical analogies, series, puzzles and justified comparisons

Number analogy: 2 -> 9, 4 -> 17, 6 -> ?

  1. 23
  2. 25 Correct answer.
  3. 27
  4. 29

Explanation

The rule is multiply by 4 and add 1. Since 6 x 4 + 1 = 25, the answer is 25.

Question 16Numerical analogies, series, puzzles and justified comparisons

Number analogy: 3 -> 12, 5 -> 30, 7 -> ?

  1. 42
  2. 49
  3. 54
  4. 56 Correct answer.

Explanation

Each number is multiplied by the next whole number. Since 7 x 8 = 56, the missing value is 56.

Question 17Numerical analogies, series, puzzles and justified comparisons

Number analogy: 2 -> 5, 4 -> 17, 6 -> 37, 8 -> ?

  1. 63
  2. 64
  3. 65 Correct answer.
  4. 66

Explanation

Each result is the starting number squared plus 1. Since 8 squared is 64, 8 -> 65.

Question 18Numerical analogies, series, puzzles and justified comparisons

Number analogy: 12 -> 7, 20 -> 11, 32 -> ?

  1. 15
  2. 16
  3. 17 Correct answer.
  4. 18

Explanation

Each result is half of the starting number plus 1. Half of 32 is 16, and 16 + 1 = 17.

Question 19Numerical analogies, series, puzzles and justified comparisons

Number analogy: 3 -> 11, 6 -> 38, 9 -> ?

  1. 81
  2. 83 Correct answer.
  3. 85
  4. 92

Explanation

Each result is the starting number squared plus 2. Since 9 squared is 81, 81 + 2 = 83.

Question 20Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 7 + ? = 12. What number is missing?

  1. 4
  2. 5 Correct answer.
  3. 6
  4. 7

Explanation

The missing number must make 7 total 12. Since 12 - 7 = 5, the missing number is 5.

Question 21Numerical analogies, series, puzzles and justified comparisons

Number puzzle: ? - 4 = 9. What number is missing?

  1. 11
  2. 12
  3. 13 Correct answer.
  4. 14

Explanation

The missing number must be 4 more than 9. Since 9 + 4 = 13, the missing number is 13.

Question 22Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 3 x ? = 18. What number is missing?

  1. 4
  2. 5
  3. 6 Correct answer.
  4. 7

Explanation

To make 18 from 3 equal groups, each group must have 6. So 3 x 6 = 18.

Question 23Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 20 / ? = 5. What number is missing?

  1. 2
  2. 3
  3. 4 Correct answer.
  4. 5

Explanation

The divisor must make 20 split into groups of 5. Since 20 divided by 4 is 5, the missing number is 4.

Question 24Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 8 + 6 = ? + 5. What number is missing?

  1. 8
  2. 9 Correct answer.
  3. 10
  4. 11

Explanation

The left side is 8 + 6 = 14. To make the right side 14, the missing number must be 9 because 9 + 5 = 14.

Question 25Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 4 x ? = 2 x 10. What number is missing?

  1. 4
  2. 5 Correct answer.
  3. 6
  4. 8

Explanation

The right side equals 20. Since 4 x 5 = 20, the missing number is 5.

Question 26Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 15 - ? = 7. What number is missing?

  1. 6
  2. 7
  3. 8 Correct answer.
  4. 9

Explanation

The number removed from 15 must leave 7. Since 15 - 8 = 7, the missing number is 8.

Question 27Numerical analogies, series, puzzles and justified comparisons

Number puzzle: A box has 6 red counters and some blue counters. There are 10 counters in all. How many blue counters are there?

  1. 3
  2. 4 Correct answer.
  3. 5
  4. 6

Explanation

The total is 10 and 6 are red. The missing blue counters are 10 - 6 = 4.

Question 28Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 3 + 2 x ? = 15. What number is missing?

  1. 5
  2. 6 Correct answer.
  3. 7
  4. 9

Explanation

Subtract 3 from 15 to get 12. Then 2 x ? = 12, so the missing number is 6.

Question 29Numerical analogies, series, puzzles and justified comparisons

Number puzzle: (? + 4) x 2 = 18. What number is missing?

  1. 4
  2. 5 Correct answer.
  3. 6
  4. 7

Explanation

First divide 18 by 2 to get 9. Then ? + 4 = 9, so the missing number is 5.

Question 30Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 24 / ? + 3 = 9. What number is missing?

  1. 3
  2. 4 Correct answer.
  3. 6
  4. 8

Explanation

The division part must equal 6 because 6 + 3 = 9. Since 24 / 4 = 6, the missing number is 4.

Question 31Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 5 x ? - 7 = 18. What number is missing?

  1. 4
  2. 5 Correct answer.
  3. 6
  4. 7

Explanation

Add 7 to 18 to get 25. Since 5 x 5 = 25, the missing number is 5.

Question 32Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 2 x (? + 3) = 22. What number is missing?

  1. 7
  2. 8 Correct answer.
  3. 9
  4. 11

Explanation

Divide 22 by 2 to get 11. Then ? + 3 = 11, so the missing number is 8.

Question 33Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 36 - 4 x ? = 12. What number is missing?

  1. 4
  2. 5
  3. 6 Correct answer.
  4. 8

Explanation

The subtracted part must be 24 because 36 - 24 = 12. Since 4 x 6 = 24, the missing number is 6.

Question 34Numerical analogies, series, puzzles and justified comparisons

Number puzzle: ? / 3 + 8 = 14. What number is missing?

  1. 12
  2. 15
  3. 18 Correct answer.
  4. 21

Explanation

The division part must equal 6 because 6 + 8 = 14. Therefore ? / 3 = 6, so ? = 18.

Question 35Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 2a + b = 17. If a = 6, what is b?

  1. 3
  2. 4
  3. 5 Correct answer.
  4. 6

Explanation

Substitute a = 6: 2 x 6 + b = 17, so 12 + b = 17. Therefore b = 5.

Question 36Numerical analogies, series, puzzles and justified comparisons

Number puzzle: square + triangle = 13 and square - triangle = 3. What is square?

  1. 5
  2. 6
  3. 8 Correct answer.
  4. 10

Explanation

The two equations are satisfied by square = 8 and triangle = 5, because 8 + 5 = 13 and 8 - 5 = 3.

Question 37Numerical analogies, series, puzzles and justified comparisons

Number puzzle: The same number goes in both blanks: (? x 3) - (? + 4) = 14. What is the number?

  1. 7
  2. 8
  3. 9 Correct answer.
  4. 10

Explanation

Using 9 gives 9 x 3 = 27 and 9 + 4 = 13. Then 27 - 13 = 14, so the number is 9.

Question 38Numerical analogies, series, puzzles and justified comparisons

Number puzzle: 48 / (? - 2) = 8. What number is missing?

  1. 6
  2. 7
  3. 8 Correct answer.
  4. 10

Explanation

The divisor must be 6 because 48 / 6 = 8. So ? - 2 = 6, and ? = 8.

Question 39Numerical analogies, series, puzzles and justified comparisons

Number series: 18, 16, 14, 12, ?

  1. 8
  2. 9
  3. 10 Correct answer.
  4. 11

Explanation

The series subtracts 2 each time. Since 12 - 2 = 10, the next number is 10.

Question 40Numerical analogies, series, puzzles and justified comparisons

Number series: 30, 25, 20, 15, ?

  1. 5
  2. 10 Correct answer.
  3. 12
  4. 14

Explanation

The pattern subtracts 5 each time. Since 15 - 5 = 10, the next number is 10.

Question 41Numerical analogies, series, puzzles and justified comparisons

Number series: 2, 5, 11, 23, ?

  1. 35
  2. 45
  3. 46
  4. 47 Correct answer.

Explanation

Each term is doubled and then 1 is added: 2 -> 5, 5 -> 11, 11 -> 23. So 23 x 2 + 1 = 47.

Question 42Numerical analogies, series, puzzles and justified comparisons

Number series: 4, 9, 16, 25, ?

  1. 30
  2. 32
  3. 36 Correct answer.
  4. 49

Explanation

These are square numbers: 2 squared, 3 squared, 4 squared, and 5 squared. The next is 6 squared, which is 36.

Question 43Numerical analogies, series, puzzles and justified comparisons

Number series: 1, 2, 4, 7, 11, ?

  1. 14
  2. 15
  3. 16 Correct answer.
  4. 18

Explanation

The differences increase by 1: +1, +2, +3, +4. The next difference is +5, so 11 + 5 = 16.

Question 44Numerical analogies, series, puzzles and justified comparisons

Number series: 3, 8, 15, 24, ?

  1. 33
  2. 34
  3. 35 Correct answer.
  4. 36

Explanation

The differences are +5, +7, and +9. The next odd difference is +11, so 24 + 11 = 35.

Question 45Numerical analogies, series, puzzles and justified comparisons

Number series: 81, 27, 9, 3, ?

  1. 0
  2. 1 Correct answer.
  3. 2
  4. 6

Explanation

Each number is divided by 3. Since 3 divided by 3 is 1, the next number is 1.

Question 46Numerical analogies, series, puzzles and justified comparisons

Number series: 6, 10, 18, 34, ?

  1. 50
  2. 62
  3. 66 Correct answer.
  4. 70

Explanation

Each term is doubled and then 2 is subtracted. So 34 x 2 - 2 = 66.

Question 47Numerical analogies, series, puzzles and justified comparisons

Number series: 2, 3, 5, 8, 13, ?

  1. 18
  2. 20
  3. 21 Correct answer.
  4. 24

Explanation

Each term is the sum of the two previous terms. Since 8 + 13 = 21, the next number is 21.

Question 48Numerical analogies, series, puzzles and justified comparisons

Number series: 7, 14, 12, 24, 22, ?

  1. 33
  2. 42
  3. 44 Correct answer.
  4. 46

Explanation

The pattern alternates multiply by 2, then subtract 2. After 22, multiply by 2 to get 44.

Question 49Numerical analogies, series, puzzles and justified comparisons

Number series: 1, 4, 9, 16, ?

  1. 20
  2. 24
  3. 25 Correct answer.
  4. 36

Explanation

The terms are square numbers: 1 squared, 2 squared, 3 squared, and 4 squared. The next is 5 squared, or 25.

Question 50Numerical analogies, series, puzzles and justified comparisons

Number series: 100, 90, 81, 73, ?

  1. 64
  2. 65
  3. 66 Correct answer.
  4. 67

Explanation

The differences are -10, -9, and -8. The next difference is -7, so 73 - 7 = 66.