Data Sufficiency

S1. Insufficient as nothing is said of z and y
S2. x+y>0 is the implication, sign of x cannot be ascertained.
S1 and S2 combined also, sign of x cannot be ascertained. Hence (E) is answer.

One Common mistake to avoid don't multiply z to 0 without knowing the nature of 'z'

Statement 1:
x < y

a) x can be +ive,0 or -ive
b) z is unknown
z can be less than 0. In that case (x+y) < 0. or x<-y.This satisfies as x<y and x<-y both takes x to negative direction.
z can be greater than 0. In that case (x+y) < 0 or x<-y.Doesn't satisfy the Given data is Statement1 .

So INSUFFICIENT

Statement 2:
z < 0.

In that case (x+y) < 0. or x<-y.
y is unknown
x= 2, y= -3..x>0
x=-3, y=-2..x<0

INSUFFICIENT

Combining (1) and (2)
we get the intersection
This satisfies as x<y and x<-y both takes x to negative direction.
a)x<y
b)x<-y

ArunangsuSahu wrote:One Common mistake to avoid don't multiply z to 0 without knowing the nature of 'z'

Statement 1:
x < y

b) z is unknown
z can be less than 0. In that case (x+y) < 0. or x<-y.This satisfies as x<y and x<-y both takes x to negative direction.
z can be greater than 0. In that case (x+y) < 0 or x<-y.Doesn't satisfy the Given data is Statement1 .

If z is greater than zero, how is (x+y)_< 0 ? shouldn't it be (x+y) > 0?

The correct answer is E if the sign given is less than 0

The correct answer is C if the sign given is greater than 0

Yes, the inequality was a good one...