If a and b are distinct integers and their product is not equal to zero, is a '>' b?

(1) (a(^3)b – b(^3)a)/(a(^3)b + b(^3)a – 2a(^2)b(^2)) '<' 0

(2) b '<' 0







statement (1):

(a + b)/(a - b) '<' 0
therefore, a + b and a - b have opposite signs. we can divide this statement into 2 cases.

CASE 1: a + b is positive and a - b is negative
a - b is negative --'>' immediately know a '<' b
also, in this case, a + b '>' a - b, so therefore b '>' -b, so therefore b is positive.
that's all we know, though; we know nothing about the sign of a. (note that this case works for (a, b) = (2, 4) but also (-2, 4))

CASE 2: a + b is negative and a - b is positive
a - b is positive --'>' immediately know a '>' b
in this case, a + b '<' a - b, so therefore b '<' -b, so therefore b is negative.
again, that's all we know. (this case works for (a, b) = (2, -4) but also (-2, -4))

this is insufficient, because there's a case in which a '<' b and a case in which a '>' b.

statement 2:
obviously insufficient

together:
this has to be CASE 2 above, so therefore a '>' b.
sufficient.