Absolute Greater than Square

[praks.g]

Is x*|y| > y^2?

(1) x > y

(2) y > 0

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

The original solution is C.

But the solution does not take into account the case: 0<x<1.
If we take this case, the answer should be E.

[jnelson0612]

Is x*|y| > y^2?

(1) x > y

(2) y > 0

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

The original solution is C.

But the solution does not take into account the case: 0<x<1.
If we take this case, the answer should be E.

Be careful! Let's use an x that is between 0 and 1. Let's use 1/2. If we use the statements together, y is positive but less than x. Thus, let's say y is 1/4. Is 1/2 * 1/4 > (1/4)^2? Yes it is.

Because of this, you get the same answer whether you use an x and y between 0 and 1, an x above 1 and a y between 0 and 1, and an x and y both above above 1, as long as you follow all the constraints. Thus, the answer is C.