If x, y, and z are nonzero numbers, is (x)(y + z) > 0?
Implies is x>0 if (y+z)>0 ? or Is x<0 if (y+z)<0 ?
(1) |x + y| = |x| + |y|
Implies x > 0 and y > 0 or x < 0 and y < 0 - Insufficient as it doesn't speak of z
(2) |z + y| = |y| + |z|
Implies z > 0 and y > 0 or z < 0 and y < 0 - Insufficient as it doesn't speak of x
From 1 and 2
Take condition x > 0 and y > 0, then the value of z > 0 [spoiler]and (x)(y + z) > 0[/spoiler]
Take condition x < 0 and y < 0, then the value of z < 0 [spoiler]and (x)(y + z) > 0[/spoiler]
Hence option C
Absolution
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Source: Beat The GMAT — Data Sufficiency |
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neelgandham
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tpr-becky
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This is about the concept of positive, negative, zero.
for the question to be always true both x and (y+z) must either both be positive or both be negative.
Statement 1 - tells us that both x and y are the same sign but no info about z so insufficient and BCE.
Statement 2 - tells us that both y and z are the same sign but no info about x so insufficient and CE.
If you put them together you find that all three are the same sign - if they are all positive then the multiplication will be positive. if they are all negative then you will have a neg(neg) which is positive.
Therefore C is enough to solve the problem.
for the question to be always true both x and (y+z) must either both be positive or both be negative.
Statement 1 - tells us that both x and y are the same sign but no info about z so insufficient and BCE.
Statement 2 - tells us that both y and z are the same sign but no info about x so insufficient and CE.
If you put them together you find that all three are the same sign - if they are all positive then the multiplication will be positive. if they are all negative then you will have a neg(neg) which is positive.
Therefore C is enough to solve the problem.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA
