Two positions of the same dice are shown. In the first position the faces showing are 3 on top, 1 on the left and 5 on the front.…

Question

Two positions of the same dice are shown. In the first position the faces showing are 3 on top, 1 on the left and 5 on the front. In the second position they are 6 on top, 3 on the left and 5 on the front. Select the number that will be on the face opposite to the one showing the number 6.

1. A. 5
2. B. 3
3. C. 4
4. D. 1 (Correct answer)

Correct Answer

Option D — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• List what each view shows:
  • View 1: 3 on top, 1 on the left, 5 on the front
  • View 2: 6 on top, 3 on the left, 5 on the front
• 5 is common to both views and stays in the same position, so the die has simply been rotated about the axis through 5 and its opposite face.
• Under that rotation the other four faces cycle among themselves. Faces 3, 1 and 6 all appear adjacent to 5, so none of them is opposite it.
• Tracking the cycle, 6 and 1 never appear together in either view and occupy corresponding positions across the rotation, so 1 is opposite 6.

Additional Information

• The governing rule: two faces seen in the same view are adjacent, never opposite. Every face appearing alongside 6 can therefore be eliminated at once.
• When one face is common to both views and unmoved, the die has been rotated about that face's axis — the quickest way to relate the two positions.
• With a standard die the opposite faces sum to 7, but that convention does not apply here: 6 and 1 would sum to 7, yet the answer must be derived from the views rather than assumed.
• A die has 6 faces in 3 opposite pairs, and any single view shows at most 3 mutually adjacent faces.