Six letters U, V, W, X, Y and Z are written on different faces of a dice. Two positions of this dice are shown in the figure. Find the letter on the face opposite to V.

- (a)Z
- (b)W
- (c)X
- (d)Y
Answer
Why
Correct — A. View 1 shows U on top with V and X on the two visible side faces; view 2 shows U on top with X and Z.
Rule: U stays on top, so the die has only been spun about the vertical axis and the four side faces keep their fixed ring order.
Two side faces drawn together in one picture are next to each other. View 1 makes X a neighbour of V; view 2 makes X a neighbour of Z.
A face in a ring of four has exactly two neighbours, so V and Z are X's two neighbours — and in a ring of four, the two neighbours of a face sit opposite each other.
So V is opposite Z — option (a).
Why the others are wrong
- (b)W — W appears in neither view, so it is either the fourth side face or the face under U. Either way it is not V's partner, because the ring already settles that.
- (c)X — X shares an edge with V in view 1. Two faces you can see in the same picture meet at an edge, so they can never be opposite.
- (d)Y — Y is absent from both views exactly as W is, and the ring rules it out the same way: X's two neighbours are V and Z, and those are the opposite pair.
Concept
The same two-view method as the previous question, but the shared face is on top, so the turn is a spin about the vertical axis.
That spin never disturbs the order of the four side faces. They sit in a ring, and each has two neighbours and one face opposite. The pictures hand you adjacency, one pair at a time.
X appears in both views next to a different letter each time, which is the whole point of the pair of pictures: it identifies both of X's neighbours, and two neighbours of the same face in a four-ring are opposite each other.
You cannot tell from these two views whether W or Y is the fourth side face and which one lies under U, and you do not need to. The question asks only about V, and the ring settles V without touching that ambiguity.
Key facts
- View 1 shows U on top, V on the left face and X on the right face.
- View 2 shows U on top, X on the left face and Z on the right face.
- V, X and Z all touch U, so all three are side faces of the ring around U.
- In a ring of four faces, the two neighbours of any face are opposite one another, which puts V opposite Z.
Study next
Common traps
- Reading V and X as opposite because they are drawn on the two visible faces.
- Trying to place W and Y, which these two views cannot decide.
- Losing track of which side face is left and which is right between the two drawings.
SSC pairs this with the same format at Reasoning Q.24 of this 12 Sep 2024, 12:30 paper, where the common face is on the right rather than on top. Naming the fixed face first is what turns both into one-line questions.
Related PYQs
No directly related past PYQ was found.