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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

by Vincen » Tue Jun 30, 2020 6:31 am

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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

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Source: Beat The GMAT — Problem Solving | Tue Jun 30, 2020 6:31 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: 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 wh

by Scott@TargetTestPrep » Thu Apr 22, 2021 10:35 am

Vincen wrote: ↑
Tue Jun 30, 2020 6:31 am
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

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