GATE | GATE-CS-2017 (Set 1) | Question 1

Find the smallest number y such that y x 162 (y multiplied by 162) is a perfect cube.
(A) 24
(B) 27
(C) 32
(D) 36


Answer: (D)

Explanation: 162 = 3 * 3 * 3 * 3 * 2

To make it a perfect cube, we need at least 2 * 2 * 3 * 3 which is 36.

Alternate Solution

Take the prime factor of 162:
162 = 2 * 81 = 2 * 9 * 9 = 2 * 3 * 3 * 3 * 3, now if we add minimum two 2 and two 3, then it will be perfect cube of a number. Therefore, the value of y will be = 2 * 2 * 3 * 3 = 4 * 9 = 36

Note that you can multiple 162 with values in given options, then take cube root with the help of calculator for each option, the answer should be an integer.

This explanation has been contributed by Mithlesh Upadhyay

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