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a is the product of 3 and the square root of 2, b is the

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a is the product of 3 and the square root of 2, b is the [#permalink] New post 09 Nov 2016, 15:30
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Question Stats:

85% (03:09) correct 14% (00:00) wrong based on 7 sessions
a is the product of 3 and the square root of 2, b is the product of 2 and the square root of 3, and c is the product of 2 and the square root of 6. If x is the square of the sum of a and b, y is the product of 6 and the difference of 5 and c, and z is the product of 2 squared and 3 squared, what is \(\frac{xy}{z}\)?


A. \(1\)
B. \(30 - 12\sqrt{6}\)
C. \(36\)
D. \(30 + 12\sqrt{6}\)
E. \(64\)

Drill 3
Question: 11
Page: 292
[Reveal] Spoiler: OA

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GMAT Club Legend
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Joined: 07 Jun 2014
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Re: a is the product of 3 and the square root of 2, b is the [#permalink] New post 09 Nov 2016, 15:37
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Explanation


Let’s translate this question, one step at a time.

a= \(3\sqrt{2}\), b = \(2\sqrt{3}\) and c= \(2\sqrt{6}\)

x = \((3\sqrt{2}+ 2\sqrt{3})^2\)
= \((3\sqrt{2}+ 2\sqrt{3})(3\sqrt{2}+ 2\sqrt{3})\)

= \(30+12\sqrt{6}\)

y = \(6(5 - 2\sqrt{6})\)=\(30-12\sqrt{6}\)

z = \(2^2*3^2\) =\(36\).

\(\frac{xy}{z}\)=\((30-12\sqrt{6})(30+12\sqrt{6})\frac{1}{36}\) = 1

Hence option A is correct.

Did you recognize the common quadratics? The product of x and y in the last chunk of the question contains one that could save you that intermediary step: \((x + y)(x - y) = x^2 - y^2\). Of course, it doesn’t take too much longer to write out the math.
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Re: a is the product of 3 and the square root of 2, b is the [#permalink] New post 23 Jun 2017, 13:36
You said x = 3 + 12*sqrt(6). This is not correct.

x = (3*sqrt(2)+2*sqrt(3))^2 = 30 + 12*sqrt(6).
GMAT Club Legend
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Joined: 07 Jun 2014
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Re: a is the product of 3 and the square root of 2, b is the [#permalink] New post 24 Jun 2017, 00:12
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asdfasdfasdf wrote:
You said x = 3 + 12*sqrt(6). This is not correct.

x = (3*sqrt(2)+2*sqrt(3))^2 = 30 + 12*sqrt(6).


Thanks for pointing out!
It was a typo
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Re: a is the product of 3 and the square root of 2, b is the   [#permalink] 24 Jun 2017, 00:12
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a is the product of 3 and the square root of 2, b is the

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