- A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- B. The Question can be answered by using either Statement alone
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- D. The Question cannot be answered even by using both the Statements together
Answer: C
Explanation
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.