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# Is x > y? (1) |x| > y. (2) x + y > 0.

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Math Expert
Joined: 02 Sep 2009
Posts: 56319
Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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24 Jul 2017, 23:27
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:50) correct 45% (01:35) wrong based on 136 sessions

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Is x > y?

(1) |x| > y .
(2) x + y > 0.

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Intern
Joined: 27 May 2017
Posts: 12
Re: Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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25 Jul 2017, 01:12
St 1. x >y or x < - y NS

St 2 x > - y NS

Ans E

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Joined: 18 Aug 2016
Posts: 617
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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25 Jul 2017, 01:47
1
Bunuel wrote:
Is x > y?

(1) |x| > y .
(2) x + y > 0.

(1) if x>0 then x>y
if x<0 then x>-y
Insufficient

(2) x>-y insufficient

on combining we get x>-y..insufficient

Hence E
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Joined: 16 Apr 2017
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Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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25 Jul 2017, 09:02
Bunuel wrote:
Is x > y?

(1) |x| > y .
(2) x + y > 0.

1) x>y (when x>0) and x<-y when (x<0).....Insufficient
2) x>-y, Clearly insufficient

Combining we get x > y answer C
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Joined: 06 Feb 2016
Posts: 47
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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25 Jul 2017, 14:16
mynamegoeson wrote:
Bunuel wrote:
Is x > y?

(1) |x| > y .
(2) x + y > 0.

(1) if x>0 then x>y
if x<0 then x>-y
Insufficient

(2) x>-y insufficient

on combining we get x>-y..insufficient

Hence E

Why do we get x>-y not x>y?
SVP
Joined: 26 Mar 2013
Posts: 2284
Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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26 Jul 2017, 15:12
2
1
Is x > y?

(1) |x| > y

Let x = 10 & y = 1...........Answer is Yes

Let x = -10 & y =1...........Answer is No

Insufficient

(2) x + y > 0

Case 1: Let x = 10 & y = 1...........Answer is Yes

Case 2: Let x = 10 & y = -1...........Answer is Yes

Case 3: Let x = 1 & y = 10...........Answer is No

Case 4: Let x = -1 & y = 10...........Answer is No

Insufficient

Combining 1 & 2

|x| - y > 0

x + y > 0
----------------- Sum both inequalities as both are in same direction

x + |x| >0 ........The only way to prove this inequality is that x is POSITIVE. If x is negative then result is zero which is invalid.

x > 0 & |x| > y ...........then x > y

Another Approach:

Combine 1 & 2 together.

We need to match cases from Statement 2 that fit into Statement 1

Case 3 & 4 are NOT valid.

Case 1 & 2 are valid

based on above x > y

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Re: Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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26 Jul 2017, 15:50
Bunuel wrote:
Is x > y?

(1) |x| > y .
(2) x + y > 0.

St 1: Insuff
6,3 - Yes
-6,3 - No

St 2: Insuff
-2,4 - No
4,-2 - Yes

Combining Yes & Yes - Suff
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Joined: 15 Jan 2017
Posts: 348
Re: Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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28 Jul 2017, 10:59
For me its E
is x> y?

1) |x| >y
so two cases: a) x > y b) x< -y Not suff
2) x + y> 0
x> - y
Not suff

1) + 2): we have 3 equations --> x> y; x < -y; x> -y So both not suff. So E
OA and OE awaited!
Intern
Joined: 08 Feb 2015
Posts: 22
Re: Is x > y? (1) |x| >  [#permalink]

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31 Jul 2017, 06:15
For me its E
is x> y?

1) |x| >y
so two cases: a) x > y b) x< -y Not suff
2) x + y> 0
x> - y
Not suff

1) + 2): we have 3 equations --> x> y; x < -y; x> -y So both not suff. So E
OA and OE awaited!

x> y; x < -y; x> -y. x>y is as good as x>-y

So x>y, hence C
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Posts: 473
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
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Is x > y? (1) |x| > y. (2) x + y > 0.  [#permalink]

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13 Dec 2017, 14:16
$$x > y$$ ?

Statement 1: $$|x| > y$$ ?
Insufficient
case 1: x = -16, y = 8
case 2: x = 16, y = 8

Statement 2: $$x + y > 0$$
InSufficient
case 1: x = 3, y = 2
case 2: x = 2, y = 3

(1) + (2)

adding two inequalities, $$x + |x| + y > y$$ => $$x + |x| > 0$$ => x is positive
since x is positive => statement 1 : $$|x| > y$$ => $$x > y$$ => answers our question => (C)
Is x > y? (1) |x| > y. (2) x + y > 0.   [#permalink] 13 Dec 2017, 14:16
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