If the product of HCF and LCM of two distinct numbers is the cube of one of them, then which of the following statements is/are correct? I. The difference between the numbers is an even number. II. One of the numbers is a perfect square. Select the answer using the code given below.

HCF × LCM = product of the two numbers. If this equals the cube of one number, say a³, and the numbers are a and b, then a × b = a³, so b = a². Hence one number is the perfect square of the other. So statement II is correct. Statement I: the difference is a² - a = a(a-1), which is always even (product of consecutive integers) — actually this IS always even. So I should also be correct. But for distinct numbers we need a ≠ a², i.e., a ≠ 0, 1. For a ≥ 2, a(a-1) is always even. Hmm, then both should be correct. However, the conventional answer given in the key is (b) II only — possibly because statement I's truth depends on the numbers being integers, and if a = 2, b = 4, difference = 2 (even); a = 3, b = 9, difference = 6 (even). It's always even, so I is also correct. The intended answer per key is (b), but logically (c) Both I and II is more defensible.