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# If x and y are integers with y > 0, is x positive ?

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Director
Joined: 02 Oct 2017
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If x and y are integers with y > 0, is x positive ?  [#permalink]

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Updated on: 03 Aug 2018, 10:11
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Difficulty:

25% (medium)

Question Stats:

73% (01:14) correct 27% (01:30) wrong based on 45 sessions

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If x and y are integers with y > 0, is x positive ?

(1) |x| - y = 0

(2) |x - y| > |x + y|

Originally posted by push12345 on 21 Jul 2018, 01:13.
Last edited by Bunuel on 03 Aug 2018, 10:11, edited 2 times in total.
Edited the question.
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Re: If x and y are integers with y > 0, is x positive ?  [#permalink]

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21 Jul 2018, 01:35
1
To find whether x is positive

Statement 1

|x| - y = 0

=> |x| = y

=> x can be either y or -y

=> x can be either positive or negative

Statement 1 is insufficient

Statement 2

|x-y|>|x+y|

=> $$(x-y)^2 > (x+y)^2$$

=> $$x^2 + y^2 - 2xy > x^2 + y^2 + 2xy$$

=> $$-2xy > 2xy$$

=> $$-2x > 2x$$ (since y>0)

=> -x > x

=> x is negative

Statement 2 is sufficient

Hence option B
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Re: If x and y are integers with y > 0, is x positive ?  [#permalink]

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21 Jul 2018, 02:45
push12345 wrote:
If x & y are integers with y>0, is x positive ?

i) |x|-y=0

ii)|x-y|>|x+y|

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1) |X|-y=0...
|X|=y....
Since y>0, X can be y or -y hence either positive or negative but not 0
Insufficient

2) |x-y|>|x+y|
Now the equation should tell us that ..
subtraction will result in a higher value only if both the variables are opposite in SIGN
So x and y are opposite in sign ....
But y>0, so X<0...... sufficient

OR

Square both sides as both sides are positive..
$$x^2+y^2-2xy>x^2+y^2+2xy...........-2xy>2xy$$
2y>0, so -x>x....only possible if x <0
Sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x and y are integers with y > 0, is x positive ?  [#permalink]

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21 Jul 2018, 03:51
push12345 wrote:
If x and y are integers with y > 0, is x positive ?

(1) |x| - y = 0

(2) |x - y| > |x + y|
For statement 1: y>0, |X|=y and since y>0, X also should be greater than 0. Wouldn't that be sufficient?

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Joined: 11 Jul 2018
Posts: 13
Re: If x and y are integers with y > 0, is x positive ?  [#permalink]

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21 Jul 2018, 03:55
PamulaV wrote:
push12345 wrote:
If x and y are integers with y > 0, is x positive ?

(1) |x| - y = 0

(2) |x - y| > |x + y|
For statement 1: y>0, |X|=y and since y>0, X also should be greater than 0. Wouldn't that be sufficient?

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app
No, all it really tells you is that the modulus of x is a positive number. So you know the distance of the number from 0 on the number life, but no clue is given about the direction.

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Re: If x and y are integers with y > 0, is x positive ? &nbs [#permalink] 21 Jul 2018, 03:55
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