Hi [email protected],

What do you mean when you ask, "Can we use non integer value here to get the solution?"
If you're referring to plugging in values for a and b, it's perfectly fine to plug in ANY kind of number (integer and non-integer), since there's nothing in the question that restricts what kind of numbers a and b are.
Having said that, the question does tell us that ab ≠ 0, so we can't plug in 0 for a or b.

Cheers,
Brent

HI shibsriz,

This question is perfect for TESTing Values (and there are some useful Number Properties that are worth noting).

We're told and A and B cannot = 0. We're asked if AB > A/B? This is a YES/NO question.

Fact 1: |B| > 1

This tells us that B can be greater than 1 OR less than -1.

B = 2
A = 0
Is 0 > 0? NO.

B = 2
A = 1
Is 2 > 1/2? YES
Fact 1 is INSUFFICIENT

Fact 2: AB + A/B > 0

Here, we know that A and B must have the SAME SIGN (either both positive OR both negative)

B = 2
A = 1
Is 2 > 1/2? YES

B = 1
A = 1
Is 1 > 1/1? NO
Fact 2 is INSUFFICIENT

Combined, we know
B is greater than 1 OR less than -1
A and B have the same sign

Here we have some interesting Number Property:
First, since A and B have the same sign, both AB and A/B will be positive.
Second, since B is either greater than 1 or less than -1, multiplying by B makes AB "bigger" and dividing by B makes A/B "smaller"

This means that in all possibilities, AB will be greater than A/B. You can plug in as many cases as you need to, but the answer will always be YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich