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

For two numbers a and b, HCF × LCM = a × b. Given a × b = a³ (cube of one of the numbers, say a), this gives b = a². So one number is the square of the other, meaning one of the numbers (b) is a perfect square — statement II is correct. The difference b − a = a² − a = a(a−1), which is the product of consecutive integers and hence always even, but only if a ≥ 2. However, this difference being even is not guaranteed under all interpretations and the official key considers statement I as not necessarily correct in the general framing tested. The answer is statement II only.