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

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Difficulty:   65% (hard)

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

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

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

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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 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 B Joined: 16 Nov 2010 Posts: 1163 Location: United States (IN) Concentration: Strategy, Technology Re: If x + y > 0, is x > |y|? [#permalink] ### Show Tags 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 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 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 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 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]

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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]

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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]

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

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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  G
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: If x + y > 0, is x > |y|?  [#permalink]

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

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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]

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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

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

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If the statement mentioned, Integers

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

### Show Tags

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 V
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
Re: If x + y > 0, is x > |y|?  [#permalink]

### Show Tags

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

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