GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Jul 2020, 16:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If x + y > 0, is x > |y|?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Apr 2010
Posts: 124
If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

07 May 2010, 21:05
4
1
27
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:45) correct 45% (01:45) wrong based on 757 sessions

### HideShow timer Statistics

If x + y > 0, is x > |y|?

(1) x > y
(2) y < 0
Math Expert
Joined: 02 Sep 2009
Posts: 65062
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

08 May 2010, 13:28
5
6
bibha wrote:
If x+y > 0, is x> |y|
i. x>y
ii.y<0

Thanks

If x + y >0, is x > |y|?

$$x>|y|$$ means:
A. $$x>-y$$, if $$y\leq{0}$$;
B. $$x>y$$, if $$y>{0}$$.
So we should check whether above two inequalities are true.

First inequality is given to be true in the stem (x>-y), so we should check whether $$x>y$$ is true.

(1) x > y. Sufficient.
(2) y < 0 --> $$|y|=-y$$. Question becomes is $$x>-y$$. This given to be true in the stem. Sufficient.

_________________
##### General Discussion
Senior Manager
Joined: 03 Mar 2010
Posts: 316
Schools: Simon '16 (M$) Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 04:58 1 If x + y >0, is x > |y|? (1) x > y (2) y < 0 Please help me with approach. I am having tough time with inequality. What is the better way to solve such questions? Picking number or doing algebraically? Here how i attempted this: Given: x+y > 0 , x > -y To prove: x > |y| Stmt1: x > y. Now |y| = +y when y > 0 and |y| = -y when y < 0. As can be seen, x > +y and x > -y. Hence x > |y|. Sufficient. Stmt2: y < 0. |y| = -y . So is x > -y? From what is given, x > -y. Sufficient. Ans: D. _________________ My dad once said to me: Son, nothing succeeds like success. Retired Moderator Joined: 16 Nov 2010 Posts: 1163 Location: United States (IN) Concentration: Strategy, Technology Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 05:43 1 If x+y > 0 then x and y are both +ve ---------------- A or x is -ve and y is +ve with y > |x| ------------- B or x is +ve and y is -ve with x > |y| ------------- C (1) is sufficient as if x > y, then x > -y too in this case (because x + y > 0 it could be case B or case C ) => x > |y| (2) y < 0, so x is +ve and x > |y| Answer - D _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Director Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing. Affiliations: University of Chicago Booth School of Business Joined: 03 Feb 2011 Posts: 611 Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 09:19 2 1 First strategy ------------------ You can throw in the values of x and y to be sure of the behavior of the inequality x > |y| 1. x > y and x + y > 0 x = 4 y = 3 the answer is yes x = 4 y = -3 the answer is yes sufficient 2. y < 0 and x + y > 0 y = -4 x = 4.5 the answer is yes sufficient Answer D. Second strategy : Doing algebra will lead to same inference. ----------------- Is x > |y| ? The question can be rephrased as - Is x > y and x > -y ? Adding the two we have x + x > y - y or 2x > 0 or x > 0 So the question becomes Is x > 0? 1. x > y x + y >0 Adding the above two. 2x +y > y or x > 0 sufficient 2. 0>y x + y > 0 Adding the above two. x + y > y or x > 0 sufficient Hence D. Senior Manager Joined: 01 Feb 2011 Posts: 490 Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 17:42 1 Good solution there buddy. gmat1220 wrote: First strategy ------------------ You can throw in the values of x and y to be sure of the behavior of the inequality x > |y| 1. x > y and x + y > 0 x = 4 y = 3 the answer is yes x = 4 y = -3 the answer is yes sufficient 2. y < 0 and x + y > 0 y = -4 x = 4.5 the answer is yes sufficient Answer D. Second strategy : Doing algebra will lead to same inference. ----------------- Is x > |y| ? The question can be rephrased as - Is x > y and x > -y ? Adding the two we have x + x > y - y or 2x > 0 or x > 0 So the question becomes Is x > 0? 1. x > y x + y >0 Adding the above two. 2x +y > y or x > 0 sufficient 2. 0>y x + y > 0 Adding the above two. x + y > y or x > 0 sufficient Hence D. Manager Joined: 17 Jan 2011 Posts: 200 Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 19:25 Try with 1)x=0, y=0 2)x=1, y=-1 3)x=-1, y=1 a) eliminates 1 and 3 above, so 2 can help find out the ans b) eliminates 1 and 3 above, so 2 can help find out the ans Either i.e. D _________________ Good Luck!!! ***Help and be helped!!!**** SVP Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2448 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 08 Apr 2011, 20:26 x+y> 0 this statement implies that either both are +ve or one is +ve and other negative , but with a condition that the absolute value of +ve number > than that of -ve. --------------------------------------1 1. x>y => x must be +ve. y can be either -ve or +ve. when x,y are +ve is x > |y|? is true. when x +ve and y -ve then also is x > |y|? is true using ----------------------1 2. y<0 => x must be +ve and its absolute value > than that of Y. which is the same thing asked => is x > |y|? thus D _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Senior Manager Joined: 03 Mar 2010 Posts: 316 Schools: Simon '16 (M$)
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

09 Apr 2011, 02:32
Thanks everyone. Different approaches gave me better idea on how to approach such problems. All i need now is some more inequality practice.
_________________
My dad once said to me: Son, nothing succeeds like success.
Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 718
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

20 May 2011, 03:02
for x+y > 0 x has to be > |y|
the statement itself is sufficient.

meaning D is clean.
Intern
Joined: 04 Sep 2010
Posts: 15
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

20 May 2011, 05:41
If x + y >0, is x > |y|?
(1) x > y
(2) y < 0

Please help me with approach. I am having tough time with inequality. What is the better way to solve such questions? Picking number or doing algebraically?

Here how i attempted this:
Given: x+y > 0 , x > -y
To prove: x > |y|

Stmt1: x > y. Now |y| = +y when y > 0 and |y| = -y when y < 0. As can be seen, x > +y and x > -y. Hence x > |y|. Sufficient.

Stmt2: y < 0. |y| = -y . So is x > -y? From what is given, x > -y. Sufficient.

Ans: D.

X+Y > 0 tells (Both are positive or X>Y or vice versa)
For X >|Y|? True when X is positive and > Y, So first two cases

Stmt 1 tells X> Y so x has to be positive to satisfy X+Y > 0 - true
Stmt2 : Y<0 , so x has to be positive to satisfy X+Y > 0 - true

D
Retired Moderator
Joined: 05 Jul 2006
Posts: 1321
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

14 May 2013, 12:39
If x+y > 0, is x> |y|
i. x>y
ii.y<0

given

x>-y or -x<y..... question is -x<y<x ?? stem provides first part of this inequality (-x<y)

from 1

x>y...suff therefore sure -x<y<x .

from 2

y is -ve and question becomes is x>-y i.e. is -x<y ... provided in the stem
Manager
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

28 Nov 2013, 01:18
Bunuel wrote:
bibha wrote:
If x+y > 0, is x> |y|
i. x>y
ii.y<0

Thanks

If x + y >0, is x > |y|?

$$x>|y|$$ means:
A. $$x>-y$$, if $$y\leq{0}$$;
B. $$x>y$$, if $$y>{0}$$.
So we should check whether above two inequalities are true.

First inequality is given to be true in the stem (x>-y), so we should check whether $$x>y$$ is true.

(1) x > y. Sufficient.
(2) y < 0 --> $$|y|=-y$$. Question becomes is $$x>-y$$. This given to be true in the stem. Sufficient.

Hi Bunuel,
(2) y < 0 --> |y|=-y. Question becomes is x>-y. This given to be true in the stem. Sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 65062
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

28 Nov 2013, 05:42
sunita123 wrote:
Bunuel wrote:
bibha wrote:
If x+y > 0, is x> |y|
i. x>y
ii.y<0

Thanks

If x + y >0, is x > |y|?

$$x>|y|$$ means:
A. $$x>-y$$, if $$y\leq{0}$$;
B. $$x>y$$, if $$y>{0}$$.
So we should check whether above two inequalities are true.

First inequality is given to be true in the stem (x>-y), so we should check whether $$x>y$$ is true.

(1) x > y. Sufficient.
(2) y < 0 --> $$|y|=-y$$. Question becomes is $$x>-y$$. This given to be true in the stem. Sufficient.

Hi Bunuel,
(2) y < 0 --> |y|=-y. Question becomes is x>-y. This given to be true in the stem. Sufficient.

From (2) since y<0, then |y|=-y. Thus the question becomes: is x>-y? or is x+y>0? The stem says that this is true. Therefore the second statement is sufficient.

Hope it's clear.
_________________
Intern
Joined: 01 Aug 2006
Posts: 30
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

24 Jan 2014, 14:34
x + y > 0 => x > -y.
Given x > -y, is x > |y|?

1. x >y. solving x > y and x > -y (adding), x > 0 => |y| has to be less than x (for the sum to be greater than zero)
2. y < 0. Since x + y > 0, x has to be larger than y (which is negative) and |y|.

D.
Senior Manager
Joined: 05 Nov 2012
Posts: 372
Concentration: Technology, Other
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

03 Feb 2015, 21:33
This is how i approached it. Can someone please confirm if i m correct in my reasoning.

x+y>0 => x>-y
If Y<0 look at blue & Y>0 look at red
-------(-y)[x>-y]----------0[x>-y]-------------(y)[x>y][x>-y]-----------

Now ,
i. x>y means "blue" marked range
ii. y<0 "blue" marked range

Hence D.
Intern
Joined: 12 Feb 2019
Posts: 16
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

18 Apr 2019, 16:52
If the statement mentioned, Integers

then would statement A be sufficient itself ?
Manager
Joined: 02 Jan 2020
Posts: 244
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

02 Jun 2020, 06:30
Bunuel wrote:
bibha wrote:
If x+y > 0, is x> |y|
i. x>y
ii.y<0

Thanks

If x + y >0, is x > |y|?

$$x>|y|$$ means:
A. $$x>-y$$, if $$y\leq{0}$$;
B. $$x>y$$, if $$y>{0}$$.
So we should check whether above two inequalities are true.

First inequality is given to be true in the stem (x>-y), so we should check whether $$x>y$$ is true.

(1) x > y. Sufficient.
(2) y < 0 --> $$|y|=-y$$. Question becomes is $$x>-y$$. This given to be true in the stem. Sufficient.

Don't we check modulus by saying y>=0 and y<0? why is it y<=0
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

05 Jun 2020, 02:48
2
GDT wrote:
Bunuel wrote:
bibha wrote:
If x+y > 0, is x> |y|
i. x>y
ii.y<0

Thanks

If x + y >0, is x > |y|?

$$x>|y|$$ means:
A. $$x>-y$$, if $$y\leq{0}$$;
B. $$x>y$$, if $$y>{0}$$.
So we should check whether above two inequalities are true.

First inequality is given to be true in the stem (x>-y), so we should check whether $$x>y$$ is true.

(1) x > y. Sufficient.
(2) y < 0 --> $$|y|=-y$$. Question becomes is $$x>-y$$. This given to be true in the stem. Sufficient.

Don't we check modulus by saying y>=0 and y<0? why is it y<=0

We need to account for the entire range of values: negative numbers, 0 and positive numbers.

When y > 0,
|y| = y

When y < 0,
|y| = -y

When y = 0,
|y| = y or -y (both are 0 only so it doesn't matter)

The point is that you need to consider the value 0 somewhere. You can do it in either range.

|y| = y when y >= 0
|y| = -y when y < 0

OR

|y| = y when y > 0
|y| = -y when y <= 0
_________________
Karishma
Veritas Prep GMAT Instructor

Re: If x + y > 0, is x > |y|?   [#permalink] 05 Jun 2020, 02:48