UPSC Prelims 2013 · CSAT

Question 51: Logical Reasoning and Mental Ability

A cube has six numbers marked 1, 2, 3, 4, 5 and 6 on its faces. Three views of the cube are shown below :

What possible numbers can exist on the two faces marked Ⓐ and Ⓑ, respectively on the cube ?

three views of a cube showing the numbers 1, 6, 4; 3, 1, 2; and 3, 5, 6 on their visible faces, followed by a fourth cube showing 5 on the right face and the faces marked A (front) and B (top) with circled letters

a2 and 3

b6 and 1

c1 and 4

d3 and 1

AnswerUPSC’s answer is (a).

From the three views, face 1 touches 6, 4, 3 and 2, so 5 is opposite 1. Face 6 touches 1, 4, 3 and 5, so 2 is opposite 6, leaving 3 opposite 4. In the last view, both A and B touch face 5, so neither can be 1, which sits opposite 5. That rules out (b), (c) and (d). Option (a), A = 2 and B = 3, fits, and it also matches the way the faces are arranged around a corner.

Why each option is right or wrong

(a) Right. 2 and 3 both touch 5 and touch each other.
(b) Wrong. 1 is opposite 5, so it cannot be beside it.
(c) Wrong. 1 is opposite 5.
(d) Wrong. 1 is opposite 5.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2013, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.