UPSC Prelims 2019 · CSAT
Question 72: Basic Numeracy
Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted ?
AnswerUPSC’s answer is (b).
Count by the number of black faces, treating rotations of the cube as the same. 0 black: 1. 1 black: 1. 2 black: 2 (adjacent faces or opposite faces). 3 black: 2 (three meeting at a corner, or two opposite faces plus one more). 4 black: 2, mirroring 2 black. 5 black: 1. 6 black: 1. Total = 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10.
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: undercounts; 10 distinct paintings exist.
- (b) Right: 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10.
- (c) Wrong: overcounts by one.
- (d) Wrong: overcounts by two.
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.