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x ≥ 0 y ≥ 0

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1654 [0], given: 396

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x ≥ 0 y ≥ 0 [#permalink] New post 15 Apr 2018, 04:39
Expert's post
00:00

Question Stats:

73% (00:32) correct 26% (01:32) wrong based on 26 sessions
x ≥ 0
y ≥ 0


Quantity A
Quantity B
\(\sqrt{x^{12}}-y\)
\((x^3-\sqrt{y})(x^3+\sqrt{y})\)


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 8
Page: 511
[Reveal] Spoiler: OA

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Director
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Joined: 07 Jan 2018
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Kudos [?]: 477 [0], given: 84

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Re: x ≥ 0 y ≥ 0 [#permalink] New post 18 Apr 2018, 01:21
qty B is in the form \((x -y) (x + y)\) hence it can be transformed into \(x^2 -y^2\)
qty B will become \((x^3)^2 - y = x^6 - y\)
qty A becomes \(x^6-y\) when square root is removed hence both quantities are equal
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1654 [0], given: 396

CAT Tests
Re: x ≥ 0 y ≥ 0 [#permalink] New post 22 Apr 2018, 12:20
Expert's post
Explanation

In Quantity A, \(\sqrt{x^{12}}-y=\sqrt{(x^{6})^{2}}-y\).

In Quantity B, you may recognize one of the common quadratics: \((a + b)(a - b) = a^2 - b^2\).

If not, FOIL; either way, Quantity B is \(x^6 - y\). Thus, the two quantities are equal.
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Sandy
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Re: x ≥ 0 y ≥ 0   [#permalink] 22 Apr 2018, 12:20
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