UPSC PYQPrelims 2025

Civil Services Examination · Question 15

A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6. Select the correct answer using the code given below:

  1. I only
  2. II only
  3. Both I and II
  4. Neither I nor II
Show answer & explanation

Answer: (C) Both I and II

Explanation

60 = 3 × 4 × 5 needs 2 + 3 + 4 = 9 cuts. Unpainted inner pieces = 1 × 2 × 3 = 6. (Answer as per the official UPSC answer key.)