If n and p are positive integers, n is a factor of p, and neither n

If n and p are positive integers, n is a factor of p, and neither n nor p is a multiple of 8, is p/n an odd number ?

(1) p is a multiple of 4
(2) n is a multiple of 4

Evaluating statement (1) alone: n=1 and p=4 satisfies the criteria in both the question stem and statement and results in p/n = 4, which is even. n=4 and p=12 also satisfies both the question stem and statement and results in p/n = 3, which is odd. So, does statement (1) alone give us enough information to answer the question whether p/n is odd? No. BCE

Evaluating statement (2) alone: n is a multiple of 4 but not a multiple of 8. That means that n is an odd multiple of 4, since all the even multiples of 4 are also multiples of 8. Since n is a factor of p, p must also be a multiple of 4. And since p is also not a multiple of 8, it must also be an odd multiple of 4. Evaluating p/n, then, we know that the numerator p is 4 multiplied by an odd number and denominator n is also 4 multiplied by an odd number. Reducing both the numerator and denominator by a factor of 4 leaves us with an odd number in both the numerator and the denominator. Odd divided by odd must be odd, so p/n is odd. Does statement (2) alone give us enough information to answer the question whether p/n is odd? Yes. B

Answer choice B.