Two different positions of the same dice are given below. Which is the number on the face opposite the face containing 5?

- (a)6
- (b)3
- (c)1
- (d)2
Answer
Why
Correct — B. Work from the face the two views share.
3 is on top in both positions, so the second picture is the first turned about the vertical axis.
Such a turn keeps 3 on top and swings the side faces past you. Across the two views the sides shown are 1, 6, 4 and 2 — four different numbers, every one of them touching the 3 above.
A face that touches 3 cannot lie opposite it, so the face opposite 3 is the number that never appears: 5.
The pair is 3 and 5, so the face opposite 5 is 3, option (b).
Why the others are wrong
- (a)6 — 6 is a side face in the first view, sitting beside the top 3. Side faces touch both the top and the bottom, so 6 is adjacent to 5 rather than opposite it.
- (c)1 — 1 is the front face of the first view, which makes it another side face — adjacent to the 3 above and to the 5 below, and opposite neither.
- (d)2 — 2 is the right-hand face of the second view, a side face again. Every number shown beside a top-facing 3 is adjacent to it, so 1, 6, 4 and 2 are all ruled out together.
Concept
Two-view dice questions are settled by elimination, not by rotating the cube in your head.
Find the face common to both views and make it the anchor. Every other face appearing in either view stands beside that anchor, and a cube has six faces in all — so the number that never appears is the anchor's opposite.
Here 3 is common and 1, 6, 4 and 2 all appear beside it, which leaves 5 unseen and therefore opposite 3.
The question asks for the face opposite 5, not the face opposite 3. Both name the same pair, so the answer is 3 — but the reversal is where careless marks go.
Key facts
- The two views share the top face 3, so they differ by a rotation about the vertical axis.
- The side faces shown across the two views are 1, 6, 4 and 2, all of them adjacent to 3.
- 5 appears in neither view, so 5 and 3 are the opposite pair.
Study next
Common traps
- Rotating the cube mentally instead of listing which faces stand beside the shared one.
- Working out the 3 and 5 pair correctly and then answering the wrong half of it.
The net version of the same idea is at 12 Sep 2024, 16:00, Reasoning Q.17, where a folded sheet replaces the two views and the strip rule replaces elimination.
Related PYQs
No directly related past PYQ was found.