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if x^2>y^2

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if x^2>y^2

by clock60 » Wed Jan 05, 2011 10:15 am
hi guys, spend too much time on the problem, it will be great to look at other`s thinking

If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y
oa is A
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Jan 05, 2011 10:25 am
clock60 wrote:If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y
x^2 > y^2 implies |x| > |y|

Statement 1: x > |y|
Implies x is greater than a positive quantity |y|. Hence x is positive. Now if y is negative, x is certainly greater than y. If y is positive, then also x greater than y as x > |y|.

Sufficient.

Statement 2: |x| > y
In this case however there is no such direct relation.
For example,
  • 1. x = -5, y = 2 => |x| > y BUT x < y
    2. x = 5, y = 2 => |x| > y AND x > y
Not sufficient.

The correct answer is A.
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by clock60 » Wed Jan 05, 2011 10:44 am
hi Anurag thank you for quick reply
only one thing to specify. is it possible to prove that 2 st is insufficient without picking numbers, i feel myself nervous when i pick numbers..
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by Anurag@Gurome » Wed Jan 05, 2011 10:52 am
clock60 wrote:hi Anurag thank you for quick reply
only one thing to specify. is it possible to prove that 2 st is insufficient without picking numbers, i feel myself nervous when i pick numbers..
Sure.
But without picking the numbers the concept is somewhat abstract. If you are pretty fluent with the abstractness of the sign of variable, you can always do so.

Statement 2: |x| > y
Implies two possible cases each with two sub-case:

Case 1: y positive
  • 1. x positive => x > y (This follows from the fact that |x| > y and x, y both positive)
    2. x negative => x < y (This follows directly from the fact that x is negative but y is positive)
Case 2: y negative
  • 1. x positive => x > y (This follows directly from the fact that x is positive but y is negative)
    2. x negative => x < y (This follows from the fact that |x| > |y| and x, y both negative)
Hence insufficient.
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by clock60 » Wed Jan 05, 2011 11:54 am
thanks Anurad
exactly what i was looking for
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