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If x < 0, is y > 0 ?

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If x < 0, is y > 0 ?

by melguy » Sat Oct 29, 2016 3:51 am
Hello

Please help me with this simple yet confusing question

Statement 1

We know that x is negative so other sign has to be positive.
Sufficient

Statement 2
Please confirm if it is safe to rephrase Statement 2 as Is y > x without knowing the sign of y.

If that's the case then can conclude that y is any number greater than x and can be positive and negative.

Please correct me if I am wrong.

Thanks
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by Brent@GMATPrepNow » Sat Oct 29, 2016 5:49 am
If x < 0, is y > 0?

(1) x/y < 0
(2) y - x > 0

Target question: Is y > 0?

Given: x < 0

Statement 1: x/y < 0
We're told that x < 0. In other words, x is NEGATIVE
So, statement 1 is really telling us that (SOME NEGATIVE #)/y = NEGATIVE
So, y must be POSITIVE
In other words, y > 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y - x > 0
Add x to both sides to get y > x
It is also given that x < 0
To try to COMBINE the inequalities, we must get the inequality symbols facing same way.
So, let's rewrite y > x as x < y
Ahhh, so we know that x < 0 and x < y
From this we cannot determine whether or not y > 0
Consider these two conflicting cases:
Case a: x = -2 and y = 1. In this case, y > 0
Case b: x = -2 and y = -1. In this case, y < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Last edited by Brent@GMATPrepNow on Sat Oct 29, 2016 8:39 pm, edited 1 time in total.
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by melguy » Sat Oct 29, 2016 7:01 pm
Thanks Brent.

I had a quick question. I remember reading somewhere that in DS two statements cannot contradict each other. In our case we have Y is positive (1) and Y is negative (2).

Also in the original question we had y - x > 0. I think there was a typo and we have considered it as (2) x - y > 0.

Please confirm if I am missing something.
Last edited by melguy on Mon Oct 31, 2016 6:25 pm, edited 2 times in total.
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by Brent@GMATPrepNow » Sat Oct 29, 2016 8:29 pm
melguy wrote:Thanks Brent.

I had a quick question. I remember reading somewhere that in DS two statements cannot contradict each other. In our case we have Y is positive (1) and Y is negative (2).

Also in the original question we had y - x > 0. I think there was a type and we have considered it as (2) x - y > 0.

Please confirm if I am missing something.

(P.S. I am learning inequalities all over again after many years so please pardon my silly questions!)
You're right; I accidentally transcribed statement 2 incorrectly. I have edited my response accordingly.,

Cheers,
Brent
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by ceilidh.erickson » Mon Oct 31, 2016 7:27 am
Please confirm if it is safe to rephrase Statement 2 as Is y > x without knowing the sign of y.
Just to answer your question directly: yes, you can certainly rephrase (2) as y > x. It's always allowable to add or subtract a variable across an inequality sign, because adding/subtracting don't change the inequality sign. The only danger is in MULTIPLYING. Whenever we multiply or divide a negative across an inequality, the sign flips. For this reason, we should never multiply or divide a variable across an inequality unless we know the sign.

Make sure you don't mix up your addition v. multiplication rules!
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