Six letters J, T, E, X, I and O 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 X.

- (a)T
- (b)O
- (c)I
- (d)E
Answer
Why
Correct — A. Both views show J on the top face, so the die has only been spun about its vertical axis and J has not moved.
The side faces on show are T and E in the first view, X and I in the second. All four touch J, so O — the letter that never appears — is the face opposite J.
Read each view the same way round, left face then right face: T → E in view 1, X → I in view 2. Stitching them gives one ring of side faces, T → E → X → I → T.
Rule: in a ring of four side faces, the faces two steps apart are opposite.
That pairs T with X, and E with I. So the face opposite X is T, option (a).
Why the others are wrong
- (b)O — O appears in neither view, so it touches none of T, E, X and I. It is the face opposite J, not the one opposite X.
- (c)I — I sits beside X in the second view and shares an edge with it. Adjacent faces can never be opposite.
- (d)E — E lands next to X in the ring once both views are read left-to-right. Adjacency rules E out, and it becomes the answer only if you read one view backwards.
Concept
Two views that share a face need no spatial imagination at all. Fix the shared face — J on top here — and note that the die can then only have been turned about the vertical axis.
Every face visible in either view is therefore a side face touching J. Collect them: T, E, X, I. The sixth letter, O, is never seen, so O is opposite J.
Now lay the four side faces in a ring. Read both views in the same direction and stitch the readings together. Faces two steps apart in that ring are opposite on the die.
The stitching only works if both views are read the same way round. Read left-to-right in one and right-to-left in the other and the ring reverses, which is exactly how a candidate arrives at E.
Key facts
- J is on top in both views, so J's opposite is the letter that never appears, O.
- T, E, X and I are all adjacent to J.
- In a ring of four side faces, opposite faces stand two steps apart.
Study next
Common traps
- Pairing the unseen faces before identifying the face common to both views
- Reading one view left-to-right and the other right-to-left, which reverses the ring
- Answering O because it is the missing letter, when O is opposite J
Two-view letter dice with this exact wording are set at 13 Sep 2024, 16:00, Reasoning Q.10 (the face opposite D) and at 23 Sep 2024, 16:00, Reasoning Q.13 (the face opposite Z).
Related PYQs
No directly related past PYQ was found.