Is y positive

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Is y positive

by phanikpk » Sat Jul 19, 2014 10:56 pm
If x+y is Z, Is y positive?
1) x+z=y
2) y+z=x

Please help

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by [email protected] » Sat Jul 19, 2014 11:17 pm
Hi phanikpk,

This DS question can be solved with a combination of TESTing VALUES and Algebra:

We're told that X + Y = Z. We're asked if Y is positive. This is a YES/NO question.

Fact 1: X + Z = Y

Combining the two equations that we have, we end up with....

X + (X+ Y) = Y
2X + Y = Y
2X = 0

This tells us that X = 0 and Y = Z

If....
X = 0, Y = 0, Z = 0, then the answer to the question is NO.
X = 0, Y = 1, Z = 1, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: Y + Z = X

Combining this equation with the equation given in the prompt, we have...

Y + (X + Y) = X
2Y + X = X
2Y = 0

This tells us that Y = 0 and X = Z

Since the question asks if Y is positive, we now know that the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT

Final Answer: B

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by GMATinsight » Sun Jul 20, 2014 2:49 am
phanikpk wrote:If x+y is Z, Is y positive?
1) x+z=y
2) y+z=x

Please help
Given, X+Y = Z

Question : Is Y > 0 ?

Statement 1) X+Z = Y
i.e. X+(X+Y) = Y
i.e. 2X =0
i.e. X = 0
But Y is unknown whether it's greater than or less than zero therefore
INSUFFICIENT

Statement 2) Y+Z = X
i.e. Y+(X+Y) = X
i.e. 2Y =0
i.e. Y = 0

SUFFICIENT

Answer: Option B
Last edited by GMATinsight on Mon Jul 21, 2014 8:35 am, edited 1 time in total.
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by GMATGuruNY » Mon Jul 21, 2014 4:40 am
phanikpk wrote:If x+y is Z, Is y positive?
1) x+z=y
2) y+z=x
When given two equations, one approach is to ADD the two equations.

Statement 1: x+z = y
Adding together x+z = y and x+y = z, we get:
(x+z) + (x+y) = y+z
2x + y + z = y + z
2x = 0
x = 0.
If x=0 and z=1, then x+z=y implies that y=1.
In this case, y is positive.
If x=0 and z=0, then x+z=y implies that y=0.
In this case, y is NOT positive.
INSUFFICIENT.

Statement 2: y+z = x
Adding together y+z = x and x+y = z, we get:
(y+z) + (x+y) = x+z
x + 2y + z = x+z
2y = 0
y = 0.
SUFFICIENT.

The correct answer is B.
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