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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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Difficulty:   15% (low)

Question Stats: 76% (01:02) correct 24% (01:46) wrong based on 57 sessions

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[GMAT math practice question]

Attachment: 20180104_173047.png [ 1.22 KiB | Viewed 614 times ]

The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72

_________________
Director  V
Joined: 06 Jan 2015
Posts: 641
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

Attachment:
20180104_173047.png

The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72

As it is rectangular solid areas of faces A, B, and C = l*b,b*h,l*h

Volume of the solid is l*b*h

So l*b*b*h*l*h = $$l^2*b^2*h^2$$

Volume of the solid =\sqrt{$$l^2*b^2*h^2$$}

=\sqrt{12*15*20}=60
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Director  V
Joined: 06 Jan 2015
Posts: 641
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

Attachment:
20180104_173047.png

The areas of faces A, B, and C of the rectangular solid shown in the above figure are 12, 15, and 20, respectively. What is the volume of the solid?

A. 36
B. 48
C. 60
D. 64
E. 72

As it is rectangular solid areas of faces A, B, and C = l*b,b*h,l*h

Volume of the solid is l*b*h

So l*b*b*h*l*h = $$l^2*b^2*h^2$$

Volume of the solid =\sqrt{$$l^2*b^2*h^2$$}

=\sqrt{12*15*20}=60

Hence C
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The areas of faces A, B, and C of the rectangular solid shown in the a  [#permalink]

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=>

Let $$a$$ and $$b$$ be the edges of face $$A$$, and let $$b$$ and $$c$$ be the edges of face $$B$$. Then the edges of face $$C$$ are $$a$$ and $$c$$. Moreover, the volume of the solid is $$abc$$. Now,
$$ab = 12$$, $$bc = 15$$ and $$ca = 20$$.
Multiplying these together yields
$$(ab)(bc)(ca) = a^2b^2c^2 = (abc)^2 = 12*15*20 = 3600 = 60^2$$
So $$abc = 60$$.
Therefore, the answer is C.

Answer: C
_________________ Re: The areas of faces A, B, and C of the rectangular solid shown in the a   [#permalink] 07 Jan 2018, 18:16
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# The areas of faces A, B, and C of the rectangular solid shown in the a

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