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OG2015 PS In the rectangular solid

tagged by: Brent@GMATPrepNow

OG2015 PS In the rectangular solid

In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

OA: A

Experts, please share an approach in solving this problem. Thank you.

GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
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lionsshare wrote:

In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

OA: A
Let the dimensions (length, width and height) of the box be x, y and z
Volume = (length)(width)(height) = xyz
So, our GOAL is to find the value of xyz

The three sides shown have areas 12, 15, and 20, respectively
If one (rectangular) side has area 12, then we can say that xy = 12
If one (rectangular) side has area 15, then we can say that xz = 15
If one (rectangular) side has area 20, then we can say that yz = 20
[notice that we've accounted for all 3 dimensions]

Now, we'll apply the following property: If a = j, and b = k and c = l , then abc = jkl

So, we can write: (xy)(xz)(yz) = (12)(15)(20)
Simplify: x²y²z² = 3600
Rewrite left side as: (xyz)² = 3600
Take the square root of both sides to get: xyz = 60

So, the volume = 60

Cheers,
Brent

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