If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y
OA A
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Is X > Y ?
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anuprajan5
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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
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
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Let's begin by exploring what conclusions we can make about x and y if x^2 > y^2.shrey2287 wrote:If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y
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
