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

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

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New post 02 Dec 2013, 19:06
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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
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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New post 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: \((abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2\) --> \(abc=3*7*13=273\).

Answer: C.
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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New post 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

Answer is C
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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New post 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: \((abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2\) --> \(abc=3*7*13=272\).

Answer: C.


Hi Bunuel,
I think there is a typo, the answer would be 273, not 272 :) :)
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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New post 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..
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Re: Sides of box have areas of 91, 39, 21. What is the volume?  [#permalink]

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New post 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: \((abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2\) --> \(abc=3*7*13=272\).

Answer: C.


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


Typo edited. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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