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# Is |x| > |y|? (1) x^2 > y^2 (2) x > y

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Manager
Joined: 19 Oct 2011
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Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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13 May 2012, 05:22
16
1
21
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:56) correct 31% (01:06) wrong based on 817 sessions

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Is |x| > |y|?

(1) x^2 > y^2
(2) x > y
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Joined: 02 Sep 2009
Posts: 59725
Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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10 Feb 2013, 05:50
6
6
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 |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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13 May 2012, 07:00
1
Statement 1: x^2 > y^2 => |x| > |y|. Sufficient.
Statement 2: x>y. If x>0 and y>0 then x>y implies |x|>|y|. If x<0 and y<0 then x>y implies |x|<|y|. Insufficient.

A it is.
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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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27 Jun 2012, 11:19
Is |x| > |y|?
(1) x^2 > y^2
(2) x > y

1) This means |x|>|y|. Sufficient.
2) We do not know signs of x and y. If both were positive, then the statement would be true. If both were negative, then the statement would be false. If they had different signs, we would then need to know the vaue of x and y. INSUFFICIENT.

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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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26 Feb 2013, 03:59
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|? (1) x^2 > y^2 (2) x > y  [#permalink]

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16 May 2013, 09:36
1
dvinoth86 wrote:
Is |x| > |y|?

(1) x^2 > y^2
(2) x > y

Stmt1: is sufficients as taking root can give us mod

stmt 2: can be flawed as below:
1. -4 , -5 and 4, 5 substitute for answer.
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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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30 Jun 2013, 10:51
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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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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15 May 2014, 13:36
1
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
(B)

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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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15 May 2014, 22:53
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|? (1) x^2 > y^2 (2) x > y  [#permalink]

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08 Jul 2017, 09:03
Is |x| > |y|?

(1) x^2 > y^2
(2) x > y

I used this approach:
1) + - x> + - Y ---> case 1) x> y case 2) - x >- y which means x < y. Two answers, so not sufficient
2) x> y --> sufficient
What is wrong in this approach? Would appreciate a reply!
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Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y  [#permalink]

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19 Jun 2019, 10:21
Hi All,
I am a little confused with Mods sometimes.
doesnt mod mean distance of value from lets say x or y ?

So in this question, the 2nd statement is telling us that x>y, so whatever value x has it is greater than y and in that sense distance of any value from x is greater than y .

Re: Is |x| > |y|? (1) x^2 > y^2 (2) x > y   [#permalink] 19 Jun 2019, 10:21
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