prachi18oct wrote:If a, b are nonzero integers, what is the value of ab?

(1) a = ab - 1
(2) a + b = 3

Ian Stewart wrote:Statement 2 is not sufficient, because a and b might be, among other possibilities, 2 and 1, or 4 and -1, and ab can have different values.

For Statement 1, we have:

a = ab - 1
1 = ab - a
1 = a(b-1)

So we know that a and b-1 are integers which multiply together to give 1. That can only happen if they're both equal to 1, or both equal to -1. But b-1 cannot equal -1, because that would mean b=0, and we know b is nonzero. So the only way the equation can be true is if a=1 and b-1 = 1, so b=2, and ab must be 2.

So Statement 1 is sufficient and the answer is A.