UPSC Prelims 2023 · CSAT
Question 18: Logical Reasoning and Mental Ability
125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side ?
AnswerUPSC’s answer is (a).
125 = 5 x 5 x 5, so the block is a 5 x 5 x 5 cube. A cube surrounded by others on every side must not touch any outer face. Remove the outer layer from all six faces and what remains is the inner core, a (5 - 2) x (5 - 2) x (5 - 2) = 3 x 3 x 3 cube. So 27 cubes are surrounded on all sides.
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) Right: the inner 3 x 3 x 3 core gives 27.
- (b) Wrong: 25 is the number of cubes in one 5 x 5 layer.
- (c) Wrong: only the 3 x 3 x 3 inner core is fully enclosed.
- (d) Wrong: only the 3 x 3 x 3 inner core is fully enclosed.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.