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Math Expert V
Joined: 02 Sep 2009
Posts: 55173
S95-17  [#permalink]

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1 00:00

Difficulty:   45% (medium)

Question Stats: 54% (01:00) correct 46% (00:51) wrong based on 90 sessions

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Is $$x \gt y$$?

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

(2) $$xy \lt 0$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re S95-17  [#permalink]

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1
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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Intern  Joined: 09 Apr 2015
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Re: S95-17  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re: S95-17  [#permalink]

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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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Manager  B
Joined: 27 May 2016
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Location: India
Concentration: Finance, Strategy
GMAT 1: 690 Q49 V34 GPA: 3.2
WE: Engineering (Consulting)
Re S95-17  [#permalink]

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I think this is a high-quality question and I agree with explanation.
Manager  B
Joined: 27 May 2016
Posts: 65
Location: India
Concentration: Finance, Strategy
GMAT 1: 690 Q49 V34 GPA: 3.2
WE: Engineering (Consulting)
Re: S95-17  [#permalink]

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Another tricky one!
I now realise that lesser the information given in a DS question, the harder it becomes.
Intern  B
Joined: 08 Sep 2017
Posts: 5
Re: S95-17  [#permalink]

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if x=0.5 & y=0.5 ..... ANS = E
Manager  G
Joined: 30 May 2017
Posts: 135
Location: United States
Schools: HBS '21
GMAT 1: 690 Q50 V32 GRE 1: Q168 V164 GPA: 3.57
Re: S95-17  [#permalink]

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Patrick999

The answer is NOT "E"

if x=0.5 & y=0.5 ..... Then xy>0 which contradicts Statement 2
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Kindly press the +1Kudos if you like the explanation. Thanks a lot!!! Re: S95-17   [#permalink] 08 Jan 2018, 19:48
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# S95-17

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