Is x greater than y ? (1) x - y x and |y| = y

Question

Competition Mode Question

Is x greater than y?

(1) x−y<|x|−|y|
(2) |x|>x and |y|=y

GMATBusters · Accepted Answer

Is x greater than y ?

( St1) x−y < |x|−|y|
Case 1) If x is +ve,
x-y < x−|y|
or, -y < −|y|
or y > |y|
NOT Possible, hence x is NOT +ve

Case 2) if x is –ve
x-y < -x−|y|
2x < y−|y|
Now, y−|y| can be 0, when y > or = 0 : x<y
y−|y| = 2y when y<0
so, 2x<2y : x<y
So, sufficient to say that x<y sufficient
SUFFICIENT

( St2) |x|>x and |y|=y

x is negative and y is positive or zero
So, sufficient to say that x<y

SUFFICIENT

Answer D

ArunSharma12 · Answer

Is x greater than y ?

(1) x−y>|x|−|y|
(2) |x|>x and |y|=y

statement 1:
x - y > |x| - |y|
this tells us that x,y have opposite signs and x,y are not equal to zero.
 (x,y): (-,+) this is not allowed as left side will always be negative and right side will be positive or lower negative value
(x,y): (+,-) this is allowed as left side will result in higher positive value than right side 
x > y. sufficient

statement 2:
|x|>x: this means x is negative. x can not be 0 or positive
|y|=y: this means y is either 0 or positive.
x< y
sufficient

Ans: D

madgmat2019 · Answer

Is x greater than y ?

(1) x−y>|x|−|y|......from this we can get 2-3 cases(x= -ve, y= +ve & x= +ve, y= -ve)......using which we cannot say if x>y.......INSUFFICIENT
(2) |x|>x and |y|=y....................from this we can say that x is -ve and y is greater than or equal to zero

so x<y.....SUFFICIENT

OA:B

exc4libur · Answer

x>y? (1) sufic pos case: x-y0 neg case: x-y<-x+y, 2x<2y, x0: x-y<-x-y, 2x<0, x<0 valid nothing about y x>0,y<0: x-yx, so must be x<0; and |y|=y, |y|≥0, so y≥0 Ans (D)

minustark · Answer

1) x - y < |x | -|y|
x -|x| < y - |y|.
|x| and |y| is both positive integer. So, when x is positive x-|x| will be 0. When x is negative, x -|x| will be -2x. From this statement, we can say x is negative and y is positive. so, x is always less than y. Suffucient

2) This statement also says x is negative and y is positive. sufficient
D is the answer

freedom128 · Answer

Q. Is x>y? (1) x−|x| x couldn't be 0 or +ve to satisfy both. --> x must be -ve and: when y<0, ie. x=-1, y=-0.5 when y>=0, ie. x=-1, y=0,1.5,.. In any solution selected, xx and |y|=y In other words, x<0 and y>=0. Thus, x

anniaustin · Answer

Statement (1) x-y<|x| - |y| If both x,y positive, then it is not possible If both x,y negative, then xy is always NO Sufficient Statement (2) |x|>x means x is negative |y| =y means y is positive So xy is always NO Sufficient Answer: D

Staphyk · Answer

Is x greater than y? Is x> y? Or Is x xx and |y|=y For |x| > x ,then x must be negative x<0 For |y| = y ,then y must be non-negative (y>=0) .: x< y (Sufficient) D for diagnosis Posted from my mobile device

unraveled · Answer

Is x greater than y?

(1) x−y<|x|−|y|
x = -2, y = 4; x - y = -6, |x|−|y| = -2 NO
For x = 0 and x > 0 no values of x satisfies the condition.

SUFFICIENT.

(2) |x|>x and |y|=y
Thus, x < 0 and y > 0 Hence y > x NO.

SUFFICIENT.

Answer D.

lacktutor · Answer

Is x > y ?

(Statement1): x —y < |x| —|y|
x and y cannot be non-negative at the same time.

x < 0 and y > 0
—2–1 < |—2| —|1|
—3 < 1 (No)

x< 0 and y < 0
—3 —(—2) < |—3| —| —2|
—1 < 1 (No)
Sufficient

(Statement2): | x| > x and | y| = y
—> x should be less than zero (x< 0)
—> y should be greater or equal to zero ( y >=0)
(Always No)
Sufficient

Answer (D)

Posted from my mobile device

unraveled · Answer

GMATBusters · Answer

there was a typo in question. it was corrected later.

Thanks

unraveled · Answer

Ohh..!! i didn't notice that. Sorry

Normally he solves the questions so seeing the error i thought may be he missed something. Hence pointed out. I take back my words.

Thekingmaker · Answer

This was a tough call wherein even though B was a cake walk but tread carefully and chose D

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Is x greater than y ? (1) x - y < |x| - |y| (2) |x| > x and |y| = y

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