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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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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)
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Is |x| > |y|? [#permalink] New post 15 May 2014, 11:29
Is |x| > |y|?
(1) x^2 > y^2
(2) x > y
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Re: Is |x| > |y|? [#permalink] New post 15 May 2014, 12:36
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To find out the sufficiency for the problem statement,

Option 1:
x^2 > y^2

Quick (and dirty) method : to look for the cases where the option would lead to contradictory or insufficient conclusions to the problem statement

Looking at modulus function, one can verify by checking the inequality scenario in positive and negative domains.
Using values
i) x= 5,y=4
ii) x=-5,y=4
iii) x=-5,y=-4
iv) x= 5,y=-4 ,
all such cases would lead to a definitive conclusion on inequality |x|>|y|

Otherwise also, x^2 > y^2
=> |x|*|x|>|y|*|y|
=> |x| > |y| .. taking sq. root of both sides(which are positive)

SO, 1st option is sufficient


Option 2 :
x > y
Quick (and dirty) method

Using values
i) x = 5, y = -6
ii) x = 5 , y = 4 ,
both give different conclusions on inequality |x|>|y|

SO, 2nd option is insufficient

correct option is
[Reveal] Spoiler:
(B)


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Re: Is |x| > |y|? [#permalink] New post 15 May 2014, 14:45
gmatacequants wrote:
To find out the sufficiency for the problem statement,

Option 1:
x^2 > y^2

Quick (and dirty) method : to look for the cases where the option would lead to contradictory or insufficient conclusions to the problem statement

Looking at modulus function, one can verify by checking the inequality scenario in positive and negative domains.
Using values
i) x= 5,y=4
ii) x=-5,y=4
iii) x=-5,y=-4
iv) x= 5,y=-4 ,
all such cases would lead to a definitive conclusion on inequality |x|>|y|

Otherwise also, x^2 > y^2
=> |x|*|x|>|y|*|y|
=> |x| > |y| .. taking sq. root of both sides(which are positive)

SO, 1st option is sufficient


Option 2 :
x > y
Quick (and dirty) method

Using values
i) x = 5, y = -6
ii) x = 5 , y = 4 ,
both give different conclusions on inequality |x|>|y|

SO, 2nd option is insufficient

correct option is
[Reveal] Spoiler:
(B)


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why no consideration is given to decimal values of x and y ?
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Re: Is |x| > |y|? [#permalink] New post 15 May 2014, 21:53
dhirajx wrote:
Is |x| > |y|?
(1) x^2 > y^2
(2) x > y



Sol:

We need to know whether |x|>|y|

St 1 tells us that x^2>y^2 or \sqrt{x^2} > \sqrt{y^2}
Also |x|=\sqrt{x^2}
So we have |x|>|y| St 1 is clearly sufficient

St 2 says x>y if x=5,y=3 then |x|>|y|
but if x=-3 and y=-5 then |y|>|x|

Ans is A
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Re: Is |x| > |y|? [#permalink] New post 16 May 2014, 00:21
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Re: Is |x| > |y|?   [#permalink] 16 May 2014, 00:21
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