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

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Manager
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If x + y > 0, is x > |y|? [#permalink]

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07 May 2010, 22:05
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If x + y > 0, is x > |y|?

(1) x > y
(2) y < 0
[Reveal] Spoiler: OA
Math Expert
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Re: If x + y > 0, is x > |y|? [#permalink]

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08 May 2010, 14:28
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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.

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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 10:19
2
KUDOS
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

Second strategy : Doing algebra will lead to same inference.
-----------------
Is x > |y| ?
The question can be rephrased as - Is x > y and x > -y ?
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.
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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 18:42
1
KUDOS
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

Second strategy : Doing algebra will lead to same inference.
-----------------
Is x > |y| ?
The question can be rephrased as - Is x > y and x > -y ?
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.
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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 05:58
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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.
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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 06:43
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|

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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 20:25
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
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Re: If x + y > 0, is x > |y|? [#permalink]

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08 Apr 2011, 21:26
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
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Re: If x + y > 0, is x > |y|? [#permalink]

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09 Apr 2011, 03:32
Thanks everyone. Different approaches gave me better idea on how to approach such problems. All i need now is some more inequality practice.
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Re: If x + y > 0, is x > |y|? [#permalink]

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20 May 2011, 04:02
for x+y > 0 x has to be > |y|
the statement itself is sufficient.

meaning D is clean.
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Re: If x + y > 0, is x > |y|? [#permalink]

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20 May 2011, 06:41
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
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Re: If x + y > 0, is x > |y|? [#permalink]

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14 May 2013, 13:39
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
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Re: If x + y > 0, is x > |y|? [#permalink]

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28 Nov 2013, 02:18
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.

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Re: If x + y > 0, is x > |y|? [#permalink]

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28 Nov 2013, 06:42
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.
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Re: If x + y > 0, is x > |y|? [#permalink]

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24 Jan 2014, 15:34
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|.

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Re: If x + y > 0, is x > |y|? [#permalink]

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Re: If x + y > 0, is x > |y|? [#permalink]

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03 Feb 2015, 22:33
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.
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Re: If x + y > 0, is x > |y|?   [#permalink] 03 Feb 2015, 22:33
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