If a+b>m, what is the value of positive integer m?

B according to me.
after simplifying statement 2 we get ab<0 or a+b>1 and since a+b is positive("positive integer m") a+b>1.

The question isn't written in GMAT style. But I will attempt the question as per my understanding of what it is asking.

Given, a+b is greater than a positive integer. So a+b is greater than 1 (the smallest positive integer) at least. We need to find if it must be greater than some other positive integer.

Statement 2:

(1/a +1/b)^(-1) < (1/a . 1/b)^(-1)

\(\frac{ab}{(a+b)} - ab < 0\)

\(ab ( \frac{1}{(a+b)} - 1) < 0\)

Now, we know that (a+b) is a positive integer. So 1/(a+b) is less than 1 for sure. So 1/(a+b) - 1 is negative.
Then, for the entire expression to be negative, ab must anyway be positive. Then a and b both must be positive (to ensure that a+b is positive too)

\(\frac{1}{(a+b)} - 1 < 0\)
\(a+b > 1\)

So m is 1.

Statement 2 alone is sufficient.