josemarioamaya wrote:

If a and b are positive integers, is a!/b! an integer?

(1) (b - a)(b + a) = 7! + 1

(2) b + a = 11

I rephrased the question to:

is a greater or equal to b? otherwise, if b>, then a!/b! will not be an integer.

1 - b^2 - a^2 = 7!+1

so we know that both are positive integers, and b^2 is greater than a^2. it means that b is greater than a, and we know for sure that a!/b! is not an integer.

B, C, and E - out.

2 - b+a=11.

if a=6, b=5, then it is an integer

if a=5, b=6, then not.

B is out, so the answer is:

A.