MathRevolution wrote:

[GMAT math practice question]

Is \(\frac{x}{yz}>0\)？

\(1) yz>x^2\)

\(2) x<y+z\)

x/yz will be > 0 if signs of both 'x' and 'yz' are same, i.e., either both are positive or both are negative.

Statement 1:If yz > x^2 then yz has to be positive (because square of x can not be negative).

But sign of x is not given. So we cannot conclude.

Not sufficient.

Statement 2:x < y+z. This doesnt tell anything about signs of y, z or x.

Not sufficient.

Combining the statements:yz is positive so either both y/z are positive, or both y/z are negative.

Lets take the case of y=3, z=2. Here yz =6 and y+z = 5. Now, as per the two statements:

x^2 < 6 and x < 5. Lets take x=2, it satisfies both. And we can also take x=-1, it also satisfies both. But in first case, x/yz will be positive while in second case x/yz will be negative. So

not sufficient, since we cannot determine the sign of x/yz.

Hence

E answer