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# Sides of box have areas of 91, 39, 21. What is the volume?

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Intern
Joined: 21 Nov 2013
Posts: 11
Concentration: Strategy, Technology
Schools: Ross '18 (M)
Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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02 Dec 2013, 19:06
1
5
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Difficulty:

25% (medium)

Question Stats:

78% (02:01) correct 22% (01:39) wrong based on 158 sessions

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Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?

A) 252
B) 269
C) 273
D) 920
E) 1911
Math Expert
Joined: 02 Sep 2009
Posts: 52392
Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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03 Dec 2013, 01:28
5
jamesphw wrote:
Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?

A) 252
B) 269
C) 273
D) 920
E) 1911

Say the dimensions of the rectangular solid are a, b and c. It's volume is abc.

ab = 91;
ac = 39,
bc = 21.

Multiply these three: $$(abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2$$ --> $$abc=3*7*13=273$$.

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Posts: 1169
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
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WE: Engineering (Energy and Utilities)
Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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02 Dec 2013, 21:47
The sides are

$$\sqrt{\frac{91*21}{39}}$$ = $$\sqrt{\frac{13*7*3*7}{13*3}}$$ = 7

$$\sqrt{\frac{91*39}{21}}$$ = $$\sqrt{\frac{13*7*13*3}{3*7}}$$ = 13

$$\sqrt{\frac{21*39}{91}}$$ = $$\sqrt{\frac{3*7*13*3}{13*7}}$$ = 3

Volume = 13*3*7 = 273

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Status: Miles to go....before i sleep
Joined: 26 May 2013
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Location: India
Concentration: Finance, Marketing
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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04 Dec 2013, 06:54
1
Bunuel wrote:
jamesphw wrote:
Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?

Multiply these three: $$(abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2$$ --> $$abc=3*7*13=272$$.

Hi Bunuel,
I think there is a typo, the answer would be 273, not 272
Intern
Status: Miles to go....before i sleep
Joined: 26 May 2013
Posts: 14
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q47 V25
Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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04 Dec 2013, 07:06
1
jamesphw wrote:
Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?

A) 252
B) 269
C) 273
D) 920
E) 1911

One easy way to get the answer for this question is just multiply the unit's digits of these three numbers, i.e (1*9*1 = 9) (Why the multiplication is needed?, you can see the solution suggested by Bunuel in the above post)
Now look out for the answer whose square gives us a 9 in the unit place.
So, it is easy to pic (C) 273 whose square will give us a 9 in the unit place( 3*3), and hence this is the answer.

Hope that helps..
Math Expert
Joined: 02 Sep 2009
Posts: 52392
Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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04 Dec 2013, 07:38
Caesar wrote:
Bunuel wrote:
jamesphw wrote:
Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?

Multiply these three: $$(abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2$$ --> $$abc=3*7*13=272$$.

Hi Bunuel,
I think there is a typo, the answer would be 273, not 272

Typo edited. Thank you.
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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07 May 2017, 15:07
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Re: Sides of box have areas of 91, 39, 21. What is the volume? &nbs [#permalink] 07 May 2017, 15:07
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