Is x y ? (1) |x – y| |y|

Question

Is x > y ?

(1) |x – y| < |x|

(2) |x| > |y|

yashikaaggarwal · Answer

Is x > y ? (1) |x – y| < |x| Case 1: x – y < x 0 |y| Case 1: X > Y Case 2: X > -Y or -X < Y (Insufficient) Combining both: X can be more than Y or X can be less than Y (insufficient) Answer is E

Archit3110 · Answer

target is x>y #1 |x – y| < |x| |x – y| - |x|<0 possible when x>y and also when x |y| insufficient from 1 &2 value of x & y can be x>y or y>x option E

NCC · Answer

Target Question ---> x > y ?

Stmt1]
| x - y | < | x |
| x - y | - | x | < 0

case1: x < 0
- x + y + x < 0
y < 0

case2: x > 0
x - y - x < 0
y > 0

different results so not sufficient

Stmt2]
| x | - | y | > 0

case1: x < 0
- x - y > 0
x < - y
cant say much

case2: x > 0
x - y > 0
sufficient

different answers so not sufficient

Together]

case1: x < 0
substitute y < 0 in x < - y
x < y

Ans to Target Q: No

case2: x > 0
substitute y > 0 in x - y > 0
x > y

Ans to Target Q: Yes

Different answers so cannot conclude.

ANS: E

Aeyvei · Answer

Is x > y ?

(1) |x – y| < |x|

This is only telling us that either x and y are both positive or both negative because otherwise, LHS won't be less than |x|

Since there are no restrictions we can easily choose cases to prove both yes and no are possible.
then,
Yes case: x=10 and y= 5 and |10 – 5| < |10|
No case: x=-10 and y=-5 and |-10 – (-5)| < |-10|

(2) |x| > |y|

Not sufficient as well since
Yes case: x=10 and y= 5
No case: x=-10 and y=-5

c) Because the same examples can be used for both the statements, So, E!

Is x > y ? (1) |x – y| < |x| (2) |x| > |y|

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions