The GATE Grind

GATE 2017 EE – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Find the smallest number $y$ such that $y \times 162$ is a perfect cube.

  1. 24
  2. 27
  3. 32
  4. 36

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Correct answer: (D) 36

Explanation

Factorise $162 = 2 \times 3^4$. A perfect cube needs every prime to have an exponent that is a multiple of 3. The 2 needs two more factors of 2, and $3^4$ needs two more factors of 3, so $y = 2^2 \times 3^2 = 36$.