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# The areas of faces A, B, and C of the rectangular solid shown in the a

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Math Revolution GMAT Instructor
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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04 Jan 2018, 01:31
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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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director 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 04 Jan 2018, 01:41 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 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 04 Jan 2018, 01:42 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 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] ### Show Tags 07 Jan 2018, 18:16 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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