A cube has six numbers marked 1, 2, 3, 4, 5 and 6 on its faces. Three views of the cube are shown below: What possible number can exist on the two faces marked A and B, respectively on the cube?
- A.2 and 3
- B.6 and 1
- C.1 and 4
- D.3 and 1
▶ Answer & Explanation
Correct answer: D. 3 and 1
In a standard die, opposite faces sum to 7. Analyzing the given views, we can deduce the positions of numbers relative to each other. For instance, from view 1 and view 2, we see that 1 is adjacent to 5 and 6, and 2 is adjacent to 5 and 6. This implies 1 and 2 are opposite to each other. From view 2 and view 3, we see 5 is adjacent to 2 and 4, and 6 is adjacent to 2 and 4. This indicates 5 and 6 are opposite. Therefore, the remaining pair, 1 and 3, must also be opposite. In the question's diagram, A is shown adjacent to 3 and 1, and B is shown adjacent to 4 and 5. Since 3 and 1 are opposite, A cannot be adjacent to both simultaneously, indicating A must be the face opposite to the one showing 3 and 1, which is 2. Similarly, B is adjacent to 4 and 5; since 4 and 5 are adjacent to 6, B must be opposite to 6, making B=1.
Source: UPSC csat 2013