Class 6 · Olympiad Prep

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Simple Equations & Missing Numbers

40 Class 6 IMO Mathematics Olympiad practice questions on simple equations & missing numbers, part of the Algebraic Thinking topic area. Every question below includes the correct answer and a full explanation.

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  1. 1. If x + 9 = 15, what is x?

    • A.4
    • B.5
    • C.6
    • D.7
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    Answer: C. 6

    x = 15 − 9 = 6.

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  2. 2. If 3y = 27, what is y?

    • A.7
    • B.8
    • C.9
    • D.10
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    Answer: C. 9

    y = 27 ÷ 3 = 9.

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  3. 3. If p ÷ 4 = 9, what is p?

    • A.13
    • B.32
    • C.36
    • D.40
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    Answer: C. 36

    p = 9 × 4 = 36.

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  4. 4. If 4x + 7 = 31, what is x?

    • A.5
    • B.6
    • C.7
    • D.8
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    Answer: B. 6

    4x = 24, so x = 6.

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  5. 5. A number increased by 18 is 47. What is the number?

    • A.19
    • B.29
    • C.39
    • D.65
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    Answer: B. 29

    47 − 18 = 29.

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  6. 6. A number is 6 more than twice 9. What is the number?

    • A.20
    • B.22
    • C.24
    • D.26
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    Answer: C. 24

    2×9+6 = 24.

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  7. 7. If a=5 and b=3, what is the value of 2a+3b?

    • A.16
    • B.17
    • C.18
    • D.19
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    Answer: D. 19

    2×5 + 3×3 = 10+9 = 19.

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  8. 8. A number decreased by 12 gives 25. Find the number.

    • A.35
    • B.36
    • C.37
    • D.38
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    Answer: C. 37

    The number = 25 + 12 = 37.

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  9. 9. If 5x − 4 = 21, find x.

    • A.4
    • B.5
    • C.6
    • D.7
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    Answer: B. 5

    5x = 25, so x = 5.

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  10. 10. Twice a number plus 7 equals 23. Find the number.

    • A.6
    • B.7
    • C.8
    • D.9
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    Answer: C. 8

    2x + 7 = 23 → 2x = 16 → x = 8.

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  11. 11. If 7 less than a number is 20, what is the number?

    • A.13
    • B.17
    • C.27
    • D.33
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    Answer: C. 27

    x − 7 = 20 → x = 27.

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  12. 12. The nth term of a pattern is 2n + 1. What is the 4th term?

    • A.9
    • B.5
    • C.10
    • D.8
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    Answer: A. 9

    2 × 4 + 1 = 9.

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  13. 13. If x + 2 = 16, what is x?

    • A.16
    • B.14
    • C.12
    • D.15
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    Answer: B. 14

    x = 16 − 2 = 14.

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  14. 14. If x + 4 = 22, what is x?

    • A.22
    • B.18
    • C.14
    • D.19
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    Answer: B. 18

    x = 22 − 4 = 18.

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  15. 15. If x + 6 = 15, what is x?

    • A.10
    • B.9
    • C.3
    • D.15
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    Answer: B. 9

    x = 15 − 6 = 9.

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  16. 16. The nth term of a pattern is 2n + 1. What is the 5th term?

    • A.11
    • B.12
    • C.10
    • D.6
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    Answer: A. 11

    2 × 5 + 1 = 11.

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  17. 17. If x + 2 = 12, what is x?

    • A.8
    • B.10
    • C.12
    • D.11
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    Answer: B. 10

    x = 12 − 2 = 10.

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  18. 18. If x + 7 = 14, what is x?

    • A.7
    • B.0
    • C.14
    • D.8
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    Answer: A. 7

    x = 14 − 7 = 7.

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  19. 19. If x + 4 = 16, what is x?

    • A.8
    • B.13
    • C.16
    • D.12
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    Answer: D. 12

    x = 16 − 4 = 12.

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  20. 20. If x + 9 = 19, what is x?

    • A.1
    • B.10
    • C.19
    • D.11
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    Answer: B. 10

    x = 19 − 9 = 10.

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  21. 21. The sum of a number and its double is 36. Find the number.

    • A.10
    • B.11
    • C.12
    • D.13
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    Answer: C. 12

    x + 2x = 36 → 3x = 36 → x = 12.

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  22. 22. If x + 3 = 2x − 5, find x.

    • A.6
    • B.7
    • C.8
    • D.9
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    Answer: C. 8

    Adding 5 and subtracting x from both sides: 3+5 = 2x−x → x = 8.

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  23. 23. A number multiplied by 3, then increased by 5, gives 41. What is the number?

    • A.10
    • B.11
    • C.12
    • D.13
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    Answer: C. 12

    3x + 5 = 41 → 3x = 36 → x = 12.

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  24. 24. If x + 4 = 9, what is x?

    • A.5
    • B.6
    • C.9
    • D.1
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    Answer: A. 5

    x = 9 − 4 = 5.

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  25. 25. If x + 8 = 25, what is x?

    • A.18
    • B.25
    • C.17
    • D.9
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    Answer: C. 17

    x = 25 − 8 = 17.

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  26. 26. The nth term of a pattern is 2n + 1. What is the 10th term?

    • A.11
    • B.21
    • C.22
    • D.20
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    Answer: B. 21

    2 × 10 + 1 = 21.

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  27. 27. If x + 3 = 20, what is x?

    • A.17
    • B.20
    • C.18
    • D.14
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    Answer: A. 17

    x = 20 − 3 = 17.

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  28. 28. The nth term of a pattern is 2n + 1. What is the 7th term?

    • A.8
    • B.16
    • C.15
    • D.14
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    Answer: C. 15

    2 × 7 + 1 = 15.

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  29. 29. If x + 8 = 15, what is x?

    • A.-1
    • B.8
    • C.15
    • D.7
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    Answer: D. 7

    x = 15 − 8 = 7.

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  30. 30. The nth term of a pattern is 2n + 1. What is the 6th term?

    • A.12
    • B.7
    • C.14
    • D.13
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    Answer: D. 13

    2 × 6 + 1 = 13.

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  31. 31. If 4(x + 2) = 32, find x.

    • A.4
    • B.5
    • C.6
    • D.7
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    Answer: C. 6

    4x + 8 = 32 → 4x = 24 → x = 6.

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  32. 32. If x − 5 = 3x − 21, find x.

    • A.6
    • B.7
    • C.8
    • D.9
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    Answer: C. 8

    −5 + 21 = 3x − x → 16 = 2x → x = 8.

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  33. 33. The nth term of a pattern is 2n + 1. What is the 8th term?

    • A.16
    • B.17
    • C.9
    • D.18
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    Answer: B. 17

    2 × 8 + 1 = 17.

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  34. 34. If x + 9 = 22, what is x?

    • A.13
    • B.4
    • C.22
    • D.14
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    Answer: A. 13

    x = 22 − 9 = 13.

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  35. 35. The nth term of a pattern is 2n + 1. What is the 12th term?

    • A.13
    • B.24
    • C.25
    • D.26
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    Answer: C. 25

    2 × 12 + 1 = 25.

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  36. 36. If x + 8 = 26, what is x?

    • A.10
    • B.18
    • C.26
    • D.19
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    Answer: B. 18

    x = 26 − 8 = 18.

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  37. 37. If x + 9 = 29, what is x?

    • A.21
    • B.20
    • C.29
    • D.11
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    Answer: B. 20

    x = 29 − 9 = 20.

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  38. 38. The nth term of a pattern is 2n + 1. What is the 9th term?

    • A.10
    • B.20
    • C.18
    • D.19
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    Answer: D. 19

    2 × 9 + 1 = 19.

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  39. 39. If x + 8 = 22, what is x?

    • A.22
    • B.15
    • C.14
    • D.6
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    Answer: C. 14

    x = 22 − 8 = 14.

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  40. 40. The nth term of a pattern is 2n + 1. What is the 11th term?

    • A.23
    • B.22
    • C.12
    • D.24
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    Answer: A. 23

    2 × 11 + 1 = 23.

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