Q59. A Question is given followed by two Statements I and
II. Consider the Questions 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?

We need to find unique natural numbers m and n. **Statement I: m + n > mn and m > n.** Let's test some natural number pairs where m > n: - If m=2, n=1: 2+1 = 3, 2*1 = 2. Since 3 > 2, (2,1) is a possible pair.

- If m=3, n=1: 3+1 = 4, 3*1 = 3. Since 4 > 3, (3,1) is a possible pair. Since there are multiple possibilities, Statement I alone is insufficient. **Statement II: The product of m and n is 24 (mn = 24).** Possible pairs of natural numbers (m,n): - (1,24), (2,12), (3,8), (4,6), (6,4), (8,3), (12,2), (24,1).

Since there are multiple possibilities, Statement II alone is insufficient. **Combining Statement I and Statement II:** We need to find a pair (m,n) from the list in Statement II that satisfies m + n > mn and m > n.

From Statement II, mn = 24. So the condition m + n > mn becomes m + n > 24. Let's check the pairs from Statement II that also satisfy m > n: 1. (24,1): m+n = 25. Is 25 > 24? Yes.

So (24,1) is a solution. 2. (12,2): m+n = 14. Is 14 > 24? No. 3. (8,3): m+n = 11. Is 11 > 24? No. 4. (6,4): m+n = 10. Is 10 > 24? No. Only the pair (24,1) satisfies both conditions.

Thus, m=24 and n=1 are uniquely determined. Therefore, both statements together are sufficient to answer the question. This question tests data sufficiency and number properties.