UPSC Prelims 2019 · CSAT
Question 10: Logical Reasoning and Mental Ability
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ?
AnswerUPSC’s answer is (c).
A 4×4×4 cube cut into 36 pieces means four big 2×2×2 cubes (32 units of volume) plus 32 unit cubes. Blue is on one pair of opposite faces, say top and bottom, and the big cubes show no blue, so they must fill the middle two layers. The unit cubes then form the top and bottom 4×4 layers. In each layer the four central cubes show only the blue face, while edge and corner cubes show two or three faces. So 4 + 4 = 8.
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) Wrong: counts the central cubes of one layer only.
- (b) Wrong: does not match four central cubes in each of two layers.
- (c) Right: four central cubes on the top layer plus four on the bottom.
- (d) Wrong: overcounts; edge and corner cubes show two or three painted faces.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.