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PS: Kaplan Practice Question 12

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PS: Kaplan Practice Question 12 [#permalink]

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New post 13 Dec 2008, 13:17
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Question 12

A cube of white chalk is painted red, and then cut parallel to a pair of parallel 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 2/3%
c. 20%
d. 25%
e. 33 1/3%

I had picked answer option e. since as per my calculations, that answer was coming out to be right.

I checked with the answer key and explanations, and their answer option, d. 25% made absolute sense. can somebody tell me how to calculate 25%

My logic was,
Since both cuboids are equal volume, obviously they mus've been cut on one side, which halved it. that means the sides of the cuboid are a, a, and a/ assuming the cube sides were a each

The part not painted red would be area a^2, and the total area available would be 2*a^2 + 4*((a^2)/4).
The ratio of the above would come out to be 33 1/2 %
Is my calculation flawed?

Please help.

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Re: PS: Kaplan Practice Question 12 [#permalink]

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New post 13 Dec 2008, 15:26
hbs2012 wrote:
Question 12

A cube of white chalk is painted red, and then cut parallel to a pair of parallel 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 2/3%
c. 20%
d. 25%
e. 33 1/3%

I had picked answer option e. since as per my calculations, that answer was coming out to be right.

I checked with the answer key and explanations, and their answer option, d. 25% made absolute sense. can somebody tell me how to calculate 25%

My logic was,
Since both cuboids are equal volume, obviously they mus've been cut on one side, which halved it. that means the sides of the cuboid are a, a, and a/ assuming the cube sides were a each

The part not painted red would be area a^2, and the total area available would be 2*a^2 + 4*((a^2)/4).
The ratio of the above would come out to be 33 1/2 %
Is my calculation flawed?

Please help.


One side is a/2 in half-cut cube.

Total area = 2*a^2 + 4*(a * a/2) = 4a^2
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Re: PS: Kaplan Practice Question 12 [#permalink]

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New post 15 Dec 2008, 13:42
D

Lets say that x is the area of each face of the original cube.

after the split, the only face that is not red has an area of x.

The total surface area of each of the new solids is - x+x+x/2+x/2+x/2+x/2 = 4x

thus, the ratio of the non red face to the whole surface area is x/4x= 0.25%

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Schools: HBS(08) - Ding. HBS, Stanford, Kellogg, Tuck, Stern, all dings. Yale - Withdrew App. Emory Executive -- Accepted, Matriculated, Withdrewed (yes, I spelled it wrong on purpose). ROSS -- GO BLUE 2011.
Re: PS: Kaplan Practice Question 12 [#permalink]

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New post 15 Dec 2008, 14:39
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Non Math Geek method.

6 of 6 sides are red. 6/6 == 100%

Split in two adds two more sides. so 8 side. 6 are red. 6/8 -- .75%

or

2 of 8 sides white. 2/8 = 25%

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Re: PS: Kaplan Practice Question 12 [#permalink]

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New post 20 Dec 2008, 03:28
yes RahlowJenkins,

your ans looks absolutetly correct.

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Re: PS: Kaplan Practice Question 12   [#permalink] 20 Dec 2008, 03:28
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