UPSC Prelims 2017 · CSAT
Question 58: Logical Reasoning and Mental Ability
The outer surface of a 4 cm × 4 cm × 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty four 1 cm × 1 cm × 1 cm small cubes. How many small cubes do not have painted faces?
AnswerUPSC’s answer is (a).
A 4 x 4 x 4 cube cut into 64 unit cubes has painted faces on its outer layer only. The cubes with no paint make up the core left after peeling one layer off each side: (4 - 2) x (4 - 2) x (4 - 2) = 2 x 2 x 2 = 8. For an n-cube, the unpainted cubes number (n - 2) cubed.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: the inner core is 2 x 2 x 2 = 8.
- (b) 16 is the number of small squares on one face, not the interior.
- (c) 24 is the number of cubes with exactly one painted face.
- (d) 36 does not match any category of cubes here.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.