UPSC Prelims 2015 CSAT Paper II · Q54 of 74 Mental Ability medium

Each of the six different faces of a cube has been coated with a different colour i.e., V, I, B, G, Y and O. Following information is given : 1. Colours Y, O and B are on adjacent faces. 2. Colours I, G and Y are on adjacent faces. 3. Colours B, G and Y are on adjacent faces. 4. Colours O, V and B are on adjacent faces. Which is the colour of the face opposite to the face coloured with O ?

  1. (a) B
  2. (b) V
  3. (c) G ✓ UPSC's answer
  4. (d) I

Why the answer is (c)

• From condition 1, Y, O, and B are mutually adjacent, meaning none of these three colors are opposite to each other.

• From condition 4, O, V, and B are mutually adjacent, confirming that O is not opposite to B or V.

• Since O is adjacent to Y, B, and V, the only remaining colors are I and G, so the face opposite O must be either I or G.

• From condition 2, I, G, and Y are mutually adjacent, which means I and G are adjacent to each other and cannot be opposite.

• From condition 3, B, G, and Y are mutually adjacent, which means G is adjacent to B and Y.

• Since O is adjacent to Y and B, and G is also adjacent to Y and B, G and O share two common adjacent faces (Y and B). In a cube, if two faces share two adjacent faces, they are either the same face or opposite. Since they are different, O must be opposite to G.

Why the other options are wrong

(a) B
B is incorrect because condition 1 states that Y, O, and B are on adjacent faces, so O cannot be opposite to B.
(b) V
V is incorrect because condition 4 states that O, V, and B are on adjacent faces, so O cannot be opposite to V.
(d) I
I is incorrect because if O were opposite to I, then G would have to be opposite to one of the other faces, but condition 2 shows I and G are adjacent, and condition 3 shows G is adjacent to B and Y, leaving no valid configuration for I to be opposite O without violating adjacency rules.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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