If a and b are odd integers such that a - b > 7,

We are starting from 1 as we want the lowest possible value. But the option is red is not possible as we need to have an even number less than B.

The next option after that is A = 11 B = 3
So 11 - 2(an even integer less than B) = 9

Answer is C

NandishSS wrote:If a and b are odd integers such that a - b > 7, what is the smallest possible positive difference between a and an even number less than b?

A) 7

B) 8

C) 9

D) 10

E) 11

OA:C

You can also a little logic and the answer choices. If a is ODD and we subtract an EVEN, we'll get an ODD result. (ODD - EVEN = ODD.) So we know the answer is odd. Eliminate B and D. We know that a - b > 7, so if we were to subtract a number smaller than b, the difference would have to be even bigger than 7. Eliminate A. So we just want the smallest odd remaining, which would be C, 9.

Let's say that c is the nearest even number to b that is less than b.

Then we know c = b - 1.

We want a - c.

Since a - b > 7, the smallest possible value of (a - b) = 8.

Since c = (b - 1), the smallest possible value of a - c = (a - (b - 1)) = (a - b) + 1 = 9.