If x + y 0, is x |y|? (1) x y (2) y

Question

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

(1) x > y
(2) y < 0

Bunuel · Accepted Answer

If x + y > 0, is x > |y|? If y \geq 0 , then the question becomes is x > y? If y < 0 , then the question becomes is x > - y? This is given to be true in the stem! So, we need to determine whether x > y is true. (1) x > y. Directly answers our rephrased question. Sufficient. (2) y < 0. This mean that |y| = -y. So, the question becomes: Is x > -y? Is x + y > 0? This is given to be true in the stem. Sufficient. Answer: D.

gmat1220 · Answer

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.

jamifahad · Answer

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.

yezz · Answer

If x+y > 0, is x> |y| i. x>y ii.y<0 given x>-y or -xy...suff therefore sure -x-y i.e. is -x

GDT · Answer

VeritasKarishma

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

KarishmaB · Answer

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

bumpbot · Answer

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If x + y > 0, is x > |y|? (1) x > y (2) y < 0

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