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j_shreyans
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Question stem, rephrased:j_shreyans wrote:Guys ,
x,y&z are nonzero numbers is (x)(y+z)>0
1) |x+y|=|x|+|y|
2) |z+y|=|y|+|z|
Are x and y+z the SAME SIGN?
Statement 1 offers no information about z and thus is INSUFFICIENT.
Statement 2 offers no information about x and thus is INSUFFICIENT.
To determine whether the two statements combined are sufficient, test the following combinations in each statement:
1, 1
-1, 1
1, -1
-1, -1
Statement 1: |x+y|=|x|+|y|
|1+1|=|1|+|1| --> 2=2
|-1+1|=|-1|+|1| --> 0=2
|1+(-1)|=|1|+|-1| --> 0=2
|-1+(-1)|=|-1|+|-1| --> 2=2
The cases in red indicate that x and y must be the same sign.
By extension, statement 2 -- |z+y|=|y|+|z| -- implies that y and z must be the same sign.
Thus:
The two statements combined imply that x, y and z are all the same sign.
SUFFICIENT.
The correct answer is C.
