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

[NandishSS]

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

[melguy]

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

[DavidG@VeritasPrep]

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.

[Matt@VeritasPrep]

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.