Question

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?

Accepted Answer

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

Input Output Machine Logic

Explanation

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