If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what

[Vincen]

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%

[spoiler]OA=D[/spoiler]

Source: GMAT Club Tests

[Scott@TargetTestPrep]

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%

[spoiler]OA=D[/spoiler]

Solution:

The surface area of the 4-cm cube before it’s cut is 6 x 4^2 = 96 cm^2.

The total surface area of the 4-cm cube after it’s cut into 64 1-cm cubes is (6 x 1^2) x 64 = 384 cm^2.

Thus, the increase in surface area is 384 - 96 = 288 cm^2. Since 288 is exactly 3 times 96, the percent increase is 300%.

Answer: D