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Input Output Machine Logic

CMAT 2021 · Logical Reasoning · Hard · Input Output

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A number-arrangement machine, when given an input string of numbers, arranges them following a particular pattern:

Input: 3 | 4 | 9 | 7 | 6 | 11 Step I: 9 | 16 | 81 | 49 | 36 | 121 Step II: 12 | 20 | 90 | 56 | 42 | 132 Step III: 17 | 25 | 95 | 61 | 47 | 137 Step IV: 15 | 23 | 93 | 59 | 45 | 135

If 159 is one of the numbers in Step IV, which of the following can be input number?

  1. A.

    13

  2. B.

    10

  3. C.

    12

  4. D.

    22

Answer

C

Explanation

Analysis of steps for input kk: Step I: k2k^2 Step II: k2+kk^2 + k Step III: k2+k+5k^2 + k + 5 Step IV: k2+k+5−2=k2+k+3k^2 + k + 5 - 2 = k^2 + k + 3 Given Step IV number = 159: k2+k+3=159  ⟹  k2+k−156=0k^2 + k + 3 = 159 \implies k^2 + k - 156 = 0. (k+13)(k−12)=0  ⟹  k=12(k + 13)(k - 12) = 0 \implies k = 12.

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