If the HCF of p and q (p > q) is G, then which of the following statements is/are correct? I. HCF of p and (p + q) is G. II. HCF of p, (p - q) is G.

If HCF(p, q) = G, then p = Ga and q = Gb where gcd(a, b) = 1. Then p + q = G(a + b) and p - q = G(a - b). Since gcd(a, b) = 1, we also have gcd(a, a+b) = gcd(a, b) = 1 and gcd(a, a-b) = gcd(a, b) = 1. So HCF(p, p+q) = G·gcd(a, a+b) = G and HCF(p, p-q) = G·gcd(a, a-b) = G. Both statements are correct.