Find the smallest number y such that y * 162 is a perfect cube. A. 24 B. 27 C. 32 D. 36

GATE 2017 · General Aptitude · Numerical Computation · medium

Answer: y = 36

1. Prime factorize 162: 162 = 2 * 81 = 2 * 3^4. So the prime factorization is 2^1 * 3^4.
2. Find deficiency for each prime factor: For prime 2: current exponent = 1, next multiple of 3 is 3, need 3 - 1 = 2 more. For prime 3: current exponent = 4, next multiple of 3 is 6, need 6 - 4 = 2 more.
3. Compute y: y = 2^2 * 3^2 = 4 * 9 = 36. Verify: y * 162 = 36 * 162 = 2^3 * 3^6 = 8 * 729 = 5832 = 18^3. Confirmed perfect cube.