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 numb…

Mental Ability & Logical Reasoning ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

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.

  1. A. I only
  2. B. II only
  3. C. Both I and II (Correct answer)
  4. D. Neither I nor II

Correct Answer

Option C — Both I and II

Detailed Solution & Explanation

The correct answer is Both I and II.

Key Points

  • 60 = 3×4×5. Minimum cuts to get 60 pieces = cuts along 3 axes: 2 cuts (3 slices) + 3 cuts (4 slices) + 4 cuts (5 slices) = 9 cuts. Statement I is correct.
  • Inner unpainted pieces = (3−2)×(4−2)×(5−2) = 1×2×3 = 6. Statement II is correct. Answer: Both I and II.