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# Is |x| > |y|?

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Is |x| > |y|? [#permalink]  10 Feb 2013, 04:37
00:00

Difficulty:

25% (medium)

Question Stats:

64% (01:33) correct 36% (00:32) wrong based on 277 sessions
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.
Edited the question.
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Re: Is |x| > |y|? [#permalink]  10 Feb 2013, 04:50
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Expert's post
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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.

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Re: Is IxI > IyI ? [#permalink]  26 Feb 2013, 02:59
fozzzy wrote:
Is IxI > IyI ?
(1) x^2 > y^2
(2) x > y

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

Consider kudos if my post helps

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Re: Is |x| > |y|? [#permalink]  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]  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]  15 May 2014, 12:36
1
KUDOS
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]  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)

Kudos is the best form of appreciation

why no consideration is given to decimal values of x and y ?
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Re: Is |x| > |y|? [#permalink]  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]  16 May 2014, 00:21
Expert's post
dhirajx wrote:
Is $$|x|$$ > $$|y|$$?
(1) $$x^2$$ > $$y^2$$
(2) $$x$$ > $$y$$

Merging similar topics. Please refer to the discussion above.
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Re: Is |x| > |y|? [#permalink]  14 Aug 2015, 07:24
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Re: Is |x| > |y|?   [#permalink] 14 Aug 2015, 07:24
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