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Is y - x > 1/x - y ?

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by vinni.k » Mon Jan 23, 2012 3:45 am
Is y - x > 1/x - y ?

(1). |x - y| > 1
(2). y > x

Answer is B

Thanks & Regards
Vinni
Last edited by vinni.k on Mon Jan 23, 2012 8:50 am, edited 1 time in total.
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Jan 23, 2012 5:06 am
vinni.k wrote:Is y-x > 1/(x-y)?

(1). |x - y| > 1
(2). y > x

Answer is B

Thanks & Regards
Vinni
I've amended the problem, which had been posted incorrectly.
Question stem, corrected: Is y-x > 1/(x-y)?
Statement 1, corrected: |x-y| > 1.

Statement 1: |x-y| > 1.
If x-y = 2, then y-x = -2.
Plugging these values into the question stem:
-2 > 1/2?
NO.

If x-y = -2, then y-x = 2.
Plugging these values into the question stem:
2 > 1/-2?
YES.
Since in the first case the answer is NO and in the second case the answer is YES, INSUFFICIENT.

Statement 2: y>x.
Thus, y-x > 0 and x-y < 0.
Plugging these relationships into the question stem:
positive > 1/(negative)?
Since the answer will always be YES, SUFFICIENT.

The correct answer is B.
Last edited by GMATGuruNY on Mon Jan 23, 2012 8:43 am, edited 1 time in total.
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by MBACenter » Mon Jan 23, 2012 8:36 am
vinni.k wrote:Is y - x > 1/(x - y) ?

(1). |x - y| > 1
(2). y > x

Answer is B

Thanks & Regards
Vinni
Another approach to this problem is to invent our own little third unknown called "z." If we say that z = y - x, then -z = x - y. So then the question becomes, "Is z > 1/-z?"

*THAT* question is much, much easier to answer. The answer will be YES if z is positive and NO if z is negative.

So the question becomes, "Is z positive?" and therefore, "Is y - x positive?" or, in other words, "Is y - x > 0?"

Or, more ominously, "Is y > x?"

STATEMENT 1 needs to be reduced. How to reduce it depends on whether x is greater than y.

If x is greater than or equal to y, the statement becomes x - y > 1 or x > y + 1. This would clearly make the answer to our question NO.

If y is greater than x, the statement becomes y - x > 1 or y > x + 1. This would clearly make the answer to our question YES.

So statement 1 is not sufficient to give a definitive yes or a definitive no.

STATEMENT 2, on the other hand, gives us nothing less than the reductive condition of the goal statement we wanted to verify. So, it is sufficient to say definitely YES.
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by vinni.k » Mon Jan 23, 2012 8:49 am
Mitch, thanks for correcting my mistake. I was solving this question incorrectly because of this reason. I should not have missed the signs of absolute values.
I have also edited the first post so that others don't get confuse if they want to solve this question.
GMATGuruNY wrote:
I've amended the problem, which had been posted incorrectly.
Question stem, corrected: Is y-x > 1(x-y)?
Statement 1, corrected: |x-y| > 1.

Statement 1: |x-y| > 1.
If x-y = 2, then y-x = -2.
Plugging these values into the question stem:
-2 > 1/2?
NO.

If x-y = -2, then y-x = 2.
Plugging these values into the question stem:
2 > 1/-2?
YES.
Since in the first case the answer is NO and in the second case the answer is YES, INSUFFICIENT.

Statement 2: y>x.
Thus, y-x > 0 and x-y < 0.
Plugging these relationships into the question stem:
positive > 1/(negative)?
Since the answer will always be YES, SUFFICIENT.

The correct answer is B.
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