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## If x < 0, is y > 0 ?

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 1 member reply
melguy Master | Next Rank: 500 Posts
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#### If x < 0, is y > 0 ?

Sat Oct 29, 2016 3:51 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Hello

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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Brent@GMATPrepNow GMAT Instructor
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Sat Oct 29, 2016 5:49 am
Quote:
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

RELATED VIDEOS
- Inequalities - Part I: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/video/979
- Inequalities - Part II: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/video/982

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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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melguy Master | Next Rank: 500 Posts
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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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Brent@GMATPrepNow GMAT Instructor
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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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ceilidh.erickson GMAT Instructor
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Mon Oct 31, 2016 7:27 am
Quote:
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.

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