Is q > t ?

(1) qp2 < tp2

(2) qp3 > tp3

The answer to the above Question is A) ...But if i rephase Question
Is q > t ?

(1) qp2 <= tp2

(2) qp3 > tp3

What should be the answer...I think it should be E )......Bcoz in that case P can be zero and the first statement has two possibilities
1) q<t
2) 0=0

Please let me know your comments.

is q>t?
st.1) qp2<tp2
= q<t
sufficient

s.2 ) qp3>tp3
= q>t
sufficient

so the answer will be D - please correct me where i m wrong.

likewise i get B when you are rephrasing.
which imp property am i missing?

Here's the thing: statements are always true. You can count on them as fact. Because of that, you should determine what additional information you can draw from them.

Statement 1 tells you that qp^2 < tp^2. If p were zero, then qp^2 and tp^2 would also be zero and they would be equal to each other. However, they are not equal. Thus, p cannot be zero. If p is not zero, then p^2 MUST be positive, since squaring either a negative or positive number results in a positive number. So now let's look at what we have:

q * (some positive number) < t * (some positive number)

I can divide an identical positive number out of both sides of an inequality without disrupting the inequality. Thus, I divide that positive out and statement 1 tells me that q < t. Sufficient.

_________________
Jamie Nelson
ManhattanGMAT Instructor