UPSC Prelims 2016 · CSAT
Question 59: Logical Reasoning and Mental Ability
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is :
AnswerUPSC’s answer is (b).
A cube cut into pieces of one-fourth the side gives 4 x 4 x 4 = 64 small cubes. Pieces with exactly one painted face lie in the middle of each big face, a (4 - 2) x (4 - 2) = 4 block per face. With 6 faces: 6 x 4 = 24. Formula: one face = 6(n - 2)^2; two faces = 12(n - 2); three faces = 8; no face = (n - 2)^3.
Why each option is right or wrong
- (a) 32 does not match 6 x 4.
- (b) Right: 6 faces x 4 = 24.
- (c) 16 is not the count; each face has 4 such cubes.
- (d) 8 is the number of corner cubes, with three painted faces.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.