Six letters B, F, D, X, N and A are written on different faces of a dice. Two positions of this dice are shown in the figures below. Find the letter on the face opposite to D.

- (a)A
- (b)F
- (c)N
- (d)B
Answer
Why
Correct — A. The two drawings show:
View 1, with B on top, F on the left and D on the right.
View 2, with X on top, N on the left and D on the right.
Rule: any face you can see in the same view as D touches D, so it cannot be the face opposite D.
D appears in both views. The letters sharing a view with it are B and F from the first, X and N from the second. That is four of the remaining five faces, and every one of them touches D.
Of B, F, D, X, N and A, only A is never drawn beside D, so A is the opposite face. That is option (a).
Why the others are wrong
- (b)F — F sits on the left of View 1 while D sits on its right, so the two faces meet along an edge. Adjacent faces on a cube are never opposite.
- (c)N — N shares View 2 with D, on the left while D is on the right. Anything visible in the same view as D is adjacent to it.
- (d)B — B is the top face of View 1 with D on its right, so B and D touch. Only the letter absent from both drawings can lie opposite D.
Concept
A cube has three opposite pairs, and any single view shows three mutually adjacent faces. The whole method is elimination by co-appearance: two faces you can see at once are adjacent, so they cannot be opposite.
Here D is visible in both views, which is the easy case. Collect every letter drawn with D, cross those off, and see what is left.
Six letters, four struck out, one of them D itself, so A remains. No rotation reasoning is needed at all, which is what separates this from the harder variety.
Both views show D in the same position, on the right, so the die has simply been turned about the D face and the four letters that pass across the top and left are all its neighbours.
Key facts
- Two faces visible in the same view of a cube are adjacent, never opposite.
- A cube's six faces form three opposite pairs.
- B, F, X and N all appear alongside D here, which leaves A as the only candidate.
Study next
Common traps
- Assuming the letter drawn diagonally across the cube from D is the opposite face
- Stopping after one view, which rules out only two letters
- Treating the two drawings as different dice rather than one die turned
SSC prints this stem with letters, numbers or symbols on the faces. A letters version appears at 13 Sep 2024, 09:00, Reasoning Q.13, and a symbols version at 13 Sep 2024, 12:30, Reasoning Q.25.
Related PYQs
No directly related past PYQ was found.