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Is |x| > |y|?

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Is |x| > |y|? [#permalink] New post 10 Feb 2013, 04:37
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Is |x| > |y|?

(1) x^2 > y^2
(2) x > y
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2013, 04:41, edited 1 time in total.
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Re: Is |x| > |y|? [#permalink] New post 10 Feb 2013, 04:50
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Is |x| > |y|?

(1) x^2 > y^2. Since both sides are non-negative, then we can safely take the square root: |x| > |y|. Sufficient.

Or: "is |x| > |y|?" can be rewritten as: is x^2 > y^2? (we can safely square the whole inequality since both sides are non-negative). This statement directly answers the question. Sufficient.

(2) x > y. Clearly insufficient: consider x=1 and y=0 for an YES answer and x=1 and y=-2 for a NO answer. Not sufficient.

Answer: A.
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Is IxI > IyI ? [#permalink] New post 26 Feb 2013, 02:45
Is IxI > IyI ?
(1) x^2 > y^2
(2) x > y

Please provide explanations. Thanks!
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Re: Is IxI > IyI ? [#permalink] New post 26 Feb 2013, 02:48
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Re: Is IxI > IyI ? [#permalink] New post 26 Feb 2013, 02:59
fozzzy wrote:
Is IxI > IyI ?
(1) x^2 > y^2
(2) x > y

Please provide explanations. Thanks!


Hi fozzy

when IxI = IyI that implies x^2 = Y^2
hence clearly statement 1 is sufficient

But for statement 2 substitute -ve values for x and y to satisfy the inequality....for -vel values you will get an answer to the question at hand ....but for +ve value it will be a definite yes......hence statement 2 is insufficient.
Moreover when IxI = I yI ,than either x = -y or y = -x.........

Hope that helps

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Re: Is |x| > |y|? [#permalink] New post 30 Jun 2013, 09:51
Is |x| > |y|?

Is x>y?
OR
Is x>-y?

We can also square both sides as we know that x, y are >=0

|x| > |y|
is |x|^2 > |y|^2?
Is x^2 > y^2?

(1) x^2 > y^2

This tells us directly that x^2 is greater than y^2
SUFFICIENT

(2) x > y

5>4
|5| > |4|
5 > 4 (Valid)
Or
-3>-8
|-3| > |-8|
3 > 8 (Invalid)
INSUFFICIENT

(A)
Re: Is |x| > |y|?   [#permalink] 30 Jun 2013, 09:51
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