stuck on ds question

[westie]

is x<y?
(1) 2x<3y
(2) xy>0

[DavidG@VeritasPrep]

is x<y?
(1) 2x<3y
(2) xy>0

S1: 2x < 3y
Rephrase: x < (3/2)y
Or: x < 1.5y

Now pick numbers to test. x = 1.4, y = 1; x <y? NO
x = .5, y = 1; x <y? YES

So S1 is not sufficient.

S2: xy > 0; This just means that x and y have the same charge. Both are + or both are -
No reason we can't use the same scenarios we used to test S1 (both of these scenarios used two positive numbers)
x = 1.4, y = 1; x <y? NO
x = .5, y = 1; x <y? YES

So S2 is not sufficient.

Together: So now we know that x < 1.5y, and that x and y are either both + or -. Because we used the same numbers to test S1 and S2 individually, we can use them again to test the statements together, as we already know that they'll satisfy both conditions. In each case, x < 1.5y and xy>0.
Again:
x = 1.4, y = 1; x <y? NO
x = .5, y = 1; x <y? YES

So together they are not sufficient.

Answer is E.