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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]  09 Nov 2016, 15:30
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Question Stats:

60% (03:09) correct 40% (03:10) wrong based on 10 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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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 118

Kudos [?]: 1897 [0], given: 397

Re: a is the product of 3 and the square root of 2, b is the [#permalink]  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]  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).
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 118

Kudos [?]: 1897 [0], given: 397

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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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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