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M60-08

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
GPA: 3.82
M60-08  [#permalink]

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New post 11 Jun 2018, 03:07
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

30% (02:00) correct 70% (00:45) wrong based on 10 sessions

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If \(x>y\), is \(x^2>xy\)?



1) \(x>0\)

2) \(y>0\)

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Math Revolution GMAT Instructor
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V
Joined: 16 Aug 2015
Posts: 8014
GMAT 1: 760 Q51 V42
GPA: 3.82
Re M60-08  [#permalink]

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New post 11 Jun 2018, 03:07
Official Solution:



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.



Modifying the question:

\(x^2>xy\)

⇔ \(x^2-xy > 0\)

⇔ \(x(x-y) > 0\)

⇔ \(x > 0\) since \(x > y\) (which implies that \(x - y > 0\)).

So, the question is equivalent to asking 'is \(x > 0?\)'.



Since condition 1) is same as the modified question, it is sufficient.



Condition 2):

Since \(x > y\), condition 2) \((y > 0)\) implies that \(x > 0\).

Condition 2) is also sufficient.

Therefore, the answer is D.

Answer: D

Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.

Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can't figure out condition 2), you should choose D as the answer.



Answer: D
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Re M60-08  [#permalink]

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New post 18 Jan 2019, 03:06
I think this is a high-quality question and I agree with explanation.
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Re M60-08   [#permalink] 18 Jan 2019, 03:06
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