Is X > Y ?

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shrey2287: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Thu Apr 15, 2010 9:36 pm; Thanked: 1 times

by shrey2287 » Mon Sep 24, 2012 8:29 am

If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y

OA A

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Source: Beat The GMAT — Data Sufficiency | Mon Sep 24, 2012 8:29 am

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Mon Sep 24, 2012 9:16 am

The answer is A

The whole relation between x^2 and y^2 is a bit misleading.

Question - Is x>y

Statement 1 - x >|y| which means that x is positive and greater than y, irrespective of y being negative or positive. Sufficient

Statement 2 - |x|>y. Just shows that mod x is greater than y. x can be either negative and less than y or positive and greater than y. Insufficient

I don't actually see the relation between x^2 and y^2 playing a role in solving this question.

Regards
Anup

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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 » Tue Sep 25, 2012 6:38 am

shrey2287 wrote:If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y

Let's begin by exploring what conclusions we can make about x and y if x^2 > y^2.
This tells us that the magnitude of x is greater than the magnitude of y.
In other words, if we examine x and y on the number line, the distance from x to 0 will be greater than the distance from y to 0.

So, if x^2 > y^2, there are 6 possible cases to consider (all shown on the number line).
case a: ......x...y...0.............
case b: ......x.......0...y..........
case c: ......x.......0............. (and y=0)
case d: ..........y...0...........x..
case e: ..............0..y...x.......
case f: ...............0.......x...... (and y=0)

Now let's tackle the question.

Target question: Is x > y?

Statement 1: x > |y|
Since |y| is greater than or equal to 0, statement 1 tells us that x must be positive.
When we check our 6 possible cases, we can see that this eliminates cases a, b and c (where x is negative), leaving us with cases d, e and f.
In cases d, e and f, x is definitely greater that y.
As such, statement 1 is SUFFICIENT

Statement 2: |x| > y
If |x| > y, which of our 6 possible cases can we eliminate?
We cannot eliminate any of the cases.
In one case, (case a) x is not greater that y.
In one case, (case c) x is greater that y.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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