Q. 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?

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

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

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

## What are the values of m and n ?

1) Statement I: m + n > mn and m > n

2) Statement II: The product of m and n is 24

3) Using both statements together:

– From Statement II, m * n = 24

– The possible (m,n) pairs are: (24,1), (12,2), (8,3), (6,4)

– From Statement I, m > n, so we can eliminate (4,6)

– We also need to check m + n > mn for the remaining pairs:

(24,1): 24 + 1 = 25, which is > 24 * 1 = 24

(12,2): 12 + 2 = 14, which is not > 12 * 2 = 24

(8,3): 8 + 3 = 11, which is not > 8 * 3 = 24

4) After this correct analysis, we find that (24,1) satisfies all conditions.

Therefore, the correct answer is c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

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