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|

Question stem, rephrased:
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.

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|


OAC

Question : is (x)(y+z)>0

To answer the question we only need to know the signs of x, y and z

Statement 1) |x+y|=|x|+|y|

It only suggests that x and y have same sign i.e. signs are are both positive or both negative
sign of z is unknown therefore NOT SUFFICIENT


Statement 2) |z+y|=|y|+|z|

It only suggests that z and y have same sign i.e. signs are are both positive or both negative
sign of x is unknown therefore NOT SUFFICIENT

Combining the two statements
Sign of x and y and z are all same therefore

Either, (x)(y+z)>0 will be (+ve)(+ve + +ve) which will be Greater than 0
Or, (x)(y+z)>0 will be (-ve)(-ve + -ve) which will be eventually be Greater than 0

SUFFICIENT

Answer: Option C