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

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Sajjad1994
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Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink] New post   05 Nov 2020, 05:58
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A
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E

Difficulty:

55% (hard)

Question Stats:

61% (02:11) correct 39% (01:57) wrong based on 278 sessions
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Is x > y ?

(1) |x – y| < |x|

(2) |x| > |y|
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E
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Re: Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink] New post   05 Nov 2020, 09:41
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Is x > y ?

(1) |x – y| < |x|
Case 1: x – y < x
0<y (Y is positive)
(X can be more than Y or less than Y)

Case 2: x – y < -x
2x<y
x/y < 1/2
(-ve X is more than -y, and +ve X is less than +ve Y)
(Insufficient)

(2) |x| > |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
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Re: Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink] New post   05 Nov 2020, 09:47
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Sajjad1994 wrote:
Is x > y ?

(1) |x – y| < |x|

(2) |x| > |y|


target is x>y
#1
|x – y| < |x|
|x – y| - |x|<0
possible when x>y and also when x<y
test with 2,3 and 5,3
insufficient
#2
|x| > |y|
insufficient
from 1 &2
value of x & y can be x>y or y>x

option E
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Re: Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink] New post   17 Dec 2021, 04:13
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
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Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink] New post   30 Dec 2021, 01:16
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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!
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Is x > y ? (1) |x – y| < |x| (2) |x| > |y| [#permalink]
30 Dec 2021, 01:16
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