Question

Element X is a hard dark-red solid. A cube of it is tapped lightly with a small hammer. One corner of the cube breaks off into N pieces and a collection of small bits.

a) N = 8
b) N = 27
c) N = 6
d) N = 1

Answer 1

Element X, a hard dark-red solid, breaks into N = 6 pieces when tapped lightly. The cube loses one corner, leaving five faces intact. Option c, N = 6, best describes this scenario, matching the described fragmentation.

The information given suggests that tapping the cube results in one corner breaking off into multiple pieces. Let's analyze the options:

a) N = 8: This implies the cube breaks into 8 pieces, which could represent smaller cubes. However, it doesn't match the description of breaking off one corner.

b) N = 27: This implies the cube breaks into 27 pieces, potentially representing even smaller cubes. Again, it doesn't align with the description of breaking off one corner.

c) N = 6: This option suggests that the cube breaks into 6 pieces, which might be more plausible if we consider a corner breaking off and the remaining five faces forming the pieces.

d) N = 1: This option suggests that the cube breaks into one piece, which contradicts the information given about breaking off one corner into multiple pieces.

Based on the description, the most suitable option seems to be N = 6 (option c), as it aligns with breaking off one corner and leaving the other five faces intact.