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# S95-17

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:49
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Difficulty:

45% (medium)

Question Stats:

54% (00:58) correct 46% (00:47) wrong based on 78 sessions

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Is $$x \gt y$$?

(1) $$6x \gt 5y$$

(2) $$xy \lt 0$$
[Reveal] Spoiler: OA

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Kudos [?]: 135613 [0], given: 12705

Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [0], given: 12705

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16 Sep 2014, 00:49
Expert's post
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Official Solution:

We must determine if $$x$$ is greater than $$y$$.

Statement 1 tells us that $$6x \gt 5y$$. To isolate $$x$$, we divide both sides by 6, leaving $$x \gt \frac{5}{6} y$$. From this inequality, there is no way to tell if $$x \gt y$$ or if $$\frac{5}{6}y \lt x \lt y$$. For example, if $$x = 13$$ and $$y = 12$$, then statement 1 becomes $$13 \gt \frac{5}{6}(12)$$, or $$13 \gt 10$$, which is true, and $$x \gt y$$. If, however, $$x = 11$$ and $$y = 12$$, then statement 1 becomes $$11 \gt \frac{5}{6}(12)$$, or $$11 \gt 10$$, which is also true, only now $$y \gt x$$. In other words, $$x$$ can be greater than or less than $$y$$. Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.

Statement 2 tells us that the product of $$x$$ and $$y$$ is less than 0. This can only be the case if one, but not both, of $$x$$ and $$y$$ is negative, and one, but not both, of $$x$$ and $$y$$ is positive. Yet without further information, there is no way to tell which one is negative and which one is positive, and thus no way to tell if $$x \gt y$$. Statement 2 is NOT sufficient. Eliminate answer choice B. The correct answer must be either C or E.

Considering the statements together, we know that one of $$x$$ and $$y$$ is positive and one is negative, and that $$x \gt \frac{5}{6}y$$. Since no negative number can be greater than the product of a positive fraction and a positive number, we know that $$x$$ must be positive and that $$y$$ must be negative. Thus, $$x \gt y$$. The statements together are sufficient to answer the question.

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20 Jun 2015, 07:16
hi
just wondering , it doesn't say than x and y are integers, so if x were to be .3 and y .31 then the answer would be E?

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20 Jun 2015, 11:40
guillermocalci wrote:
hi
just wondering , it doesn't say than x and y are integers, so if x were to be .3 and y .31 then the answer would be E?

These values of x and y don't satisfy the second statement, which says that xy < 0 (this means that x and y have opposite signs).

Hope it's clear.
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03 Aug 2016, 02:33
I think this is a high-quality question and I agree with explanation.

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Manager
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03 Aug 2016, 02:36
Another tricky one!
I now realise that lesser the information given in a DS question, the harder it becomes.

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28 Oct 2017, 02:31
if x=0.5 & y=0.5 ..... ANS = E

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Re: S95-17   [#permalink] 28 Oct 2017, 02:31
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# S95-17

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