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

Question

Competition Mode Question

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

(1) |x| - y = 0

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

shameekv1989 · Answer

i) y = |x| => y is positive - same as what is given in the question stem - Insufficient

ii) |x - y| > |x + y| => Squaring both sides

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

4xy < 0

Given y > 0 -> x has to be less than 0 i.e. negative

Sufficient

Answer - B

Kinshook · Answer

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

(1) |x| - y = 0
|x| = y > 0
x may be +ve or -ve
NOT SUFFICIENT

(2) |x - y| > |x + y|
Since y>0
|y-x| > |y+x|; x must be -ve
SUFFICIENT

IMO B

freedom128 · Answer

(1) |x| = y = positive, so x can be positive or negative
NOT SUFFICIENT

(2) Squaring both sides, 
(x-y)^2 > (x+y)^2 
x^2 + y^2 -2xy > x^2 + y^2 +2xy
-4xy>0
Since y is positive, x must be negative
SUFFICIENT

FINAL ANSWER IS (B)

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exc4libur · Answer

(1) insufic |x|-y=0…(y>0)…|x|=y |x|>0: x>0 or x<0 (2) sufic |x - y| > |x + y| if x=0 then y = y (invalid) if x>0 then x-y < x+y (invalid) if x<0 then -x-y > -x+y (valid) Ans (B)

Archit3110 · Answer

given y>0
#1
|x| - y = 0
possible when x >y and since value os x is lxl so x can be either + or -ve so insufficient
#2

|x - y| > |x + y|

only possible when value of x is -ve integer
IMO B ; sufficient

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

(1) |x| - y = 0

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

chaitralirr · Answer

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

(1) |x| - y = 0

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

Statement 1:

(1) |x| - y = 0

If we consider X as positive X= 6, y=6

6-6=0 or if X is negative X=-6 the modulus will make it 6. So X can be positive or negative

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

Lets consider X as positive X=6

|6-2|>|6+2| Therefore X cannot be positive

|-6-2|>|-6+2| 8>4 Therefore X is not positive

And X is not positive hence statement B is sufficient

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

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GMAT Data Sufficiency (DS) Questions

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

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