A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:
What are the values of m and n, where m and n are natural numbers?

Statement-I:
m + n > mn and m > n.

Statement-II:
The product of m and n is 24.

Which one of the following is correct in respect of the above Question and the Statements?

Correct Option: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

We are asked to find the values of natural numbers m and n. From Statement-I: m + n > mn and m > n. For natural numbers, if both m, n ≥ 2, we must have mn ≥ m + n. The inequality m + n > mn can only hold if at least one of the numbers is 1. Since m > n, we must have n = 1. Thus, Statement-I implies n = 1 and m > 1, but we do not know the exact value of m. Hence, Statement-I alone is insufficient. From Statement-II: mn = 24. There are multiple factor pairs for 24, such as (24, 1), (12, 2), (8, 3), and (6, 4). Hence, Statement-II alone is insufficient. Combining both statements: We have mn = 24 and from Statement-I, we must have n = 1. Substituting n = 1 gives m × 1 = 24, which means m = 24. This yields a unique solution: m = 24, n = 1. Thus, both statements together are sufficient. Hence, the correct option is (c).