If x < 0, is y > 0 ?

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

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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Source: Beat The GMAT — Data Sufficiency | Sat Oct 29, 2016 3:51 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

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!

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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