Two different positions of the same dice with faces 3, 7, 8, 2, 9 and 4 are shown below. Select the number that will be on the face opposite to the one having 4.
- (a)9
- (b)3
- (c)8
- (d)2
Answer
Why
Correct — C. Faces drawn in the same view are adjacent, so find 4's opposite by elimination.
View 1 shows 7, 3 and 8 on one cube — all three mutually adjacent.
View 2 shows 9, 2 and 8 — again all mutually adjacent.
Rule: a face seen beside four different faces is opposite the fifth.
8 appears with 7 and 3 in view 1, and with 9 and 2 in view 2. That is four distinct neighbours: 7, 3, 9 and 2.
The six faces are 3, 7, 8, 2, 9 and 4, so the only face left for 8 is 4. The face opposite 4 is therefore 8 — option (c).
Why the others are wrong
- (a)9 — Option (a) names 9, which shares view 2 with 8. Because 8 is opposite 4, all four of 7, 3, 9 and 2 are 4's side faces, and 9 is one of them.
- (b)3 — Option (b) names 3, drawn beside 7 and 8 in view 1. It is one of 8's four neighbours, and the face opposite 4 has to be the one 8 never meets.
- (d)2 — Option (d) names 2, drawn beside 9 and 8 in view 2. Like 3 and 9 it is a neighbour of 8, which makes it a side face of 4, not the one facing it.
Concept
Two views are enough here because one face repeats. 8 appears in both views, and each view hands it two fresh neighbours.
A face with four distinct neighbours has run out of side faces, so the one remaining number must be its opposite. That is the fastest route in any dice question — find the face drawn most often and count its company.
Nothing has to be rotated mentally, and the common-face matching method that two-view problems usually demand is not needed.
The question asks for the face opposite 4, and 4 is never drawn at all. That is deliberate: you reach it only by elimination, through the face that appears twice.
Key facts
- The six faces of this dice are 3, 7, 8, 2, 9 and 4.
- 8 is the only face shown in both views, which gives it four distinct neighbours: 7, 3, 9 and 2.
- With 8 adjacent to four faces, the remaining face 4 must be the one opposite it.
Study next
Common traps
- Searching the pictures for 4 and giving up when it is not drawn
- Assuming the two views show different dice rather than the same one
- Picking a face that shares a view with 8, which makes it a neighbour and not an opposite
Two-view dice items are settled by whichever face repeats across the views, so start by finding it.
A three-view lettered version sits in the same paper — also asked 10 Sep 2024, 16:00, Reasoning Q.16.
Related PYQs
No directly related past PYQ was found.