Reasoning

Wrong Number Series: Practice Questions with Answers

11 practice questions on Wrong Number Series, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Find the wrong number in the series: 1, 4, 9, 16, 24, 36, 49

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   Answer: 24 (should be 25)

   Solution:

   1. These are perfect squares: 1², 2², 3², 4², 5², 6², 7² = 1, 4, 9, 16, 25, 36, 49.
   2. The 5th term should be 5² = 25, but 24 is given instead.

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2. Q.2

   Find the wrong number in the series: 2, 6, 18, 54, 160, 486

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   Answer: 160 (should be 162)

   Solution:

   1. Each term should be the previous term × 3: 2, 6, 18, 54, 162, 486.
   2. The 5th term should be 54 × 3 = 162, but 160 is given instead.

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3. Q.3

   Find the wrong number in the series: 7, 13, 25, 49, 97, 191

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   Answer: 191 (should be 193)

   Solution:

   1. The differences are 6, 12, 24, 48, 94 — each difference should double the previous one (6, 12, 24, 48, 96).
   2. The 6th term should be 97 + 96 = 193, but 191 is given instead.

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4. Q.4

   Find the wrong number in the series: 2, 5, 10, 17, 26, 37, 50, 64

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   Answer: 64 (should be 65)

   Solution:

   1. The differences between consecutive terms are 3, 5, 7, 9, 11, 13, … — each 2 more than the last (this is the n² + 1 series: 1²+1, 2²+1, 3²+1, …).
   2. Following the pattern, the 8th term should be 8² + 1 = 65, but 64 is given instead.

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5. Q.5

   Find the wrong number in the series: 3, 6, 12, 24, 48, 90, 192

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   Answer: 90 (should be 96)

   Solution:

   1. Each term should be double the previous one: 3, 6, 12, 24, 48, 96, 192.
   2. The 6th term should be 48 × 2 = 96, but 90 is given instead.

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6. Q.6

   Find the wrong number in the series: 5, 10, 17, 26, 37, 51, 65

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   Answer: 51 (should be 50)

   Solution:

   1. The differences are 5, 7, 9, 11, 13, 15 — each 2 more than the last.
   2. Following the pattern, the 6th term should be 37 + 13 = 50, but 51 is given instead.

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7. Q.7

   Find the wrong number in the series: 2, 6, 12, 20, 32, 42, 56

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   Answer: 32 (should be 30)

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8. Q.8

   Find the wrong number in the series: 1, 2, 6, 24, 120, 620, 5040

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   Answer: 620 (should be 720 — the series is n!, and 6! = 720)

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9. Q.9

   Find the wrong number in the series: 7, 14, 28, 55, 112, 224

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   Answer: 55 (should be 56)

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10. Q.10

    Find the wrong number in the series: 4, 9, 16, 25, 35, 49, 64

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    Answer: 35 (should be 36)

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11. Q.11

    Find the wrong number in the series: 3, 9, 27, 81, 242, 729

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    Answer: 242 (should be 243 — the series is 3ⁿ, and 3⁵ = 243)

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