Correct Answer: C
Explanation:
Algebra Inequalities
lf x + y/ z > 0, then either one of two cases holds z
true. Either (* +y) >0 and z>0, or (*+y) < 0 and z < 0. In other words, in order for the term to be greater than zero, it must be true that either
1) both the numerator and denominator are greater than 0 or 2) both the numerator and denominator are less than 0.
- (1) Regardless of whether (x +y) is positive or negative, the positive or negative value of z must
be in agreement with the sign of(x + y in order for x + y/ z > 0. However, there is no information about z here; NOT sufficient.
- (2) If z<0, then (x + y) must be less than 0.However, this statement gives no information about (x + y) NOT sufficient.
This can be solved using (1) and (2) together. From (2), it is known that z < 0, and, going back
to the original analysis, for the term to be greater than zero, (x + y) must also be less than 0.
If x + y < 0 then x < — y. But x < y from (1) so
x + x < — y + y
2x < 0
x < 0.
The correct answer is C; both statements together are sufficient.