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# The areas of three faces of a rectangular solid are 12, 15 and 20. Wha

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The areas of three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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19 Apr 2019, 02:34
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Difficulty:

35% (medium)

Question Stats:

67% (01:23) correct 33% (00:51) wrong based on 27 sessions

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[GMAT math practice question]

The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600

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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: 18 Jul 2018 Posts: 902 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] ### Show Tags 19 Apr 2019, 02:46 12 = 4*3 15 = 5*3 20 = 4*5. The sides of the rectangle are 3,4 and 5. Volume = 3*4*5 = 60. B is the answer Posted from my mobile device _________________ Press +1 Kudo If my post helps! CEO Joined: 18 Aug 2017 Posts: 3493 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] ### Show Tags 19 Apr 2019, 04:49 1 MathRevolution wrote: [GMAT math practice question] The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid? A. 30 B. 60 C. 180 D. 900 E. 3600 l*b= 12 b*h=15 l*h=20 l=3,b=4,h=5 l*b*h=2*4*5 = 60 IMO b _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. CEO Joined: 12 Sep 2015 Posts: 3720 Location: Canada Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] ### Show Tags 19 Apr 2019, 05:29 4 Top Contributor MathRevolution wrote: [GMAT math practice question] The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid? A. 30 B. 60 C. 180 D. 900 E. 3600 Let x = the width Let y = the length Let z = the height So, the volume = xyz Area of one face = 12 We can write: xy = 12 Area of one face = 15 We can write: xz = 15 Area of one face = 20 We can write: yz = 20 Combine to get: (xy)(xz)(yz) = (12)(15)(20) Simplify: x²y²z² = 3600 Rewrite as: (xyz)² = 60² So, xyz = 60 In other words, the volume = 60 Answer: B Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7354 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha [#permalink] ### Show Tags 21 Apr 2019, 18:19 => Attachment: 4.19....png [ 6.19 KiB | Viewed 235 times ] The volume of the above rectangular solid is $$xyz$$ and the areas of three of its faces are $$xy, yz, zx$$. We may assume $$xy = 12, yz = 15$$ and $$zx = 20$$ without loss of generality. Therefore, $$(xy)(yz)(zx) = (xyz)^2 = 12*15*20 = 3600 = 60^2$$ Thus, the volume is $$xyz = 60$$. Therefore, the answer is B. Answer: B _________________ 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 three faces of a rectangular solid are 12, 15 and 20. Wha  [#permalink]

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23 Apr 2019, 20:10
MathRevolution wrote:
[GMAT math practice question]

The areas of three faces of a rectangular solid are 12, 15 and 20. What is the volume of the rectangular solid?

A. 30
B. 60
C. 180
D. 900
E. 3600

The dimensions of the rectangular solid must be 3, 4, 5 so that the areas of its three faces could be 3 x 4 = 12, 3 x 5 = 15 and 4 x 5 = 20. So the volume of the solid is 3 x 4 x 5 = 60.

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Re: The areas of three faces of a rectangular solid are 12, 15 and 20. Wha   [#permalink] 23 Apr 2019, 20:10
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