A cube of white chalk is painted red and then cut parallel

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Wed May 23, 2018 4:55 am

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A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red.

a. 15%
b. 16.67 %
c. 20%
d. 25%
e. 33.33%

The OA is the option D.

I would love to know how can I solve this PS question. Please, someone could give me an approach. Thanks in advance.

Source: Beat The GMAT — Problem Solving | Wed May 23, 2018 4:55 am

nyc20: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon May 21, 2018 6:04 am

Answer

by nyc20 » Wed May 23, 2018 5:58 am

Answer is D.

Let cube of length = 2a
Now the cube is cut from center to form 2 rectangular cuboids => measurement of cuboid will be 2a , 2a, a ( As only height will be cut short to half of cube =a )

Now all the portions of cuboid is painted red except the cut part which will have measurement equal to area of 1 side of cube = 2a *2a = 4a^2

Total surface area of cuboid = 2(lb+bh+lh) = 2(2a∗2a+2a∗a+2a∗a)=2∗8a2=16a22(2a∗2a+2a∗a+2a∗a)=2∗8a2=16a2

=> % of cuboid not painted red =4a216a2∗1004a216a2∗100= 25%

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by Scott@TargetTestPrep » Thu May 24, 2018 5:04 pm

M7MBA wrote:A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red.

a. 15%
b. 16.67 %
c. 20%
d. 25%
e. 33.33%

We can let the edge of the cube be 1. When all the faces are painted red, the red surface area is 6(1^2) = 6. When it’s cut into half, each new solid will have a red surface area that is half of the original, or 3, while one face the new solid is exposed as white with area 1^2 = 1. So the total surface area (red and white) is 3 + 1 = 4, and since the white surface area is 1, we see that 1/4, or 25%, of the total surface area is not painted red.

Answer: D

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