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S95-17

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S95-17 [#permalink]

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New post 16 Sep 2014, 00:49
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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New post 16 Sep 2014, 00:49
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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.


Answer: C
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New post 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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New post 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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Re S95-17 [#permalink]

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New post 03 Aug 2016, 02:33
I think this is a high-quality question and I agree with explanation.

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New post 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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New post 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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