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If paint costs $3.20 per quart, and a quart covers 20...

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by BTGmoderatorLU » Sat Jan 13, 2018 12:38 pm
If paint costs $3.20 per quart, and a quart covers 20 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?

A. $1.60
B. $16.00
C. $96.00
D. $108.00
E. $196.00

The OA is C.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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by EconomistGMATTutor » Sun Jan 14, 2018 4:29 am
Hello LUANDATO.

Let's see your question.

If paint costs $3.20 per quart, and a quart covers 20 square feet, it implies that $$20\ ft^2\ per\ 3.20\ dollars$$. A cube of 10 feet on each edge, has 6 faces with area 10*10=100 feet square. Then we have to paint 6*100=600 feet square.

Therefore, it will cost $$\frac{600}{20}\cdot3.20\ \text{dollars}=96\ \text{dollars}$$ to paint the outside of the cube.

This is why the correct answer is the option [spoiler]C=96.0$[/spoiler]

I hope this answer can help you.

I'm available if you'd like a follow-up.

Regards.
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by Jeff@TargetTestPrep » Mon Jan 29, 2018 11:07 am
LUANDATO wrote:If paint costs $3.20 per quart, and a quart covers 20 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?

A. $1.60
B. $16.00
C. $96.00
D. $108.00
E. $196.00
The surface area of the cube is 6(10^2) = 600 square feet.

So 600/20 = 30 quarts will be needed, and it will cost 30 x 3.2 = 96 dollars.

Answer: C

Jeffrey Miller
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[email protected]

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by [email protected] » Mon Jan 29, 2018 6:49 pm
Hi LUANDATO,

The 'math' behind this question can be done in a variety of ways. Here's another way to perform the necessary calculation that keeps the numbers 'small':

We're told that each face of a cube is 10ft x 10ft = 100 sq. ft.

Since 1 quart of paint costs $3.20 and covers 20 sq. ft., we know that 5($3.20) = 5(20 sq. ft)...

5($3.20) = $16 of paint will cover 100 sq. ft.

Since a cube has 6 faces, we'll need to spend 6($16) = $96 to paint all of its sides.

Final Answer: C

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