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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   55% (hard)

Question Stats: 47% (01:42) correct 53% (01:32) wrong based on 17 sessions

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If $$x > y > 0$$, is $$y < 2?$$

1) $$1/x = 1/2$$

2) $$(1/x)+(1/y) =1$$

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82

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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.

Since we have 2 variables ($$x$$ and $$y$$) and 1 equation $$( x > y$$), D is most likely to be the answer.

Condition 1)

$$1/x = 1/2$$ implies that $$x = 2$$. Since $$x > y$$, we must have $$y < 2$$.

Condition 1) is sufficient.

Condition 2)

The original condition $$x > y > 0$$ implies that $$1/x < 1/y$$.

Using $$1/x + 1/y = 1$$ and $$1/x < 1/y$$ together, we can see that $$1/y > 1/2$$.

Thus, $$0 < y < 2$$.

Condition 2) is sufficient.

Therefore, the answer is D.

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Intern  Joined: 18 Nov 2014
Posts: 12

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I think this is a high-quality question and I agree with explanation. good explanation
Intern  Joined: 24 Nov 2017
Posts: 2

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1
MathRevolution wrote:
Official Solution:

Using $$1/x + 1/y = 1$$ and $$1/x < 1/y$$ together, we can see that $$1/y > 1/2$$.

Thus, $$0 < y < 2$$.

Condition 2) is sufficient.

Therefore, the answer is D.

Hi, could you please expand on how the two equations result in the inequality 1/y>1/2?

Thank you
Intern  B
Joined: 03 Feb 2019
Posts: 2

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awjpca wrote:
MathRevolution wrote:
Official Solution:

Using $$1/x + 1/y = 1$$ and $$1/x < 1/y$$ together, we can see that $$1/y > 1/2$$.

Thus, $$0 < y < 2$$.

Condition 2) is sufficient.

Therefore, the answer is D.

Hi, could you please expand on how the two equations result in the inequality 1/y>1/2?

Thank you

I would also be grateful if you could expand on this!
Intern  B
Joined: 08 Jul 2018
Posts: 2
GMAT 1: 580 Q44 V26 GMAT 2: 640 Q45 V33 Show Tags

2
Caroline1606 wrote:
awjpca wrote:
MathRevolution wrote:
Official Solution:

Using $$1/x + 1/y = 1$$ and $$1/x < 1/y$$ together, we can see that $$1/y > 1/2$$.

Thus, $$0 < y < 2$$.

Condition 2) is sufficient.

Therefore, the answer is D.

Hi, could you please expand on how the two equations result in the inequality 1/y>1/2?

Thank you

I would also be grateful if you could expand on this!

1/X +1/Y =1. And 1/X<1/Y. One of the 2 numbers has got to be greater than 1/2 right for both the equations to be possible? Now since 1/X<1/Y, 1/Y is the number that is greater than 1/2. That's how you get 1/Y>1/2. So the second equation is also SUFFICIENT
Intern  Joined: 23 Apr 2019
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I think this is a poor-quality question and I don't agree with the explanation. I believe that this question is flawed as both statements can be true at the same time in order to get the same solution. As I understand, statements can not contradict in GMAT, please check.
Intern  Joined: 23 May 2019
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please elaborate on how statement 2 is sufficient by itself.
Intern  B
Joined: 25 Sep 2018
Posts: 2

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the statement 1 is sufficient.

But for Statement 2 i dont agree with the solution.
If we solve the statement 2 we get (x+y)/xy=1 ---> (x+y)-xy=0 this tells us that x=y=2 or x=y=0 and neither of it holds true as in the question it is given as x>y>0 and not x≥y. So the 2nd statement contradicts the info given in the question fact itself.

please correct me if I am wrong  Re: M60-07   [#permalink] 31 Jul 2019, 00:34
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