A Question is given followed by two Statements I and II. Consider the Questions and the Statements.…
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?
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Solution
Statement I alone: $m + n > mn$ with $m > n$ holds for many cases (e.g. n = 1 with various m), so not sufficient. Statement II alone: $mn = 24$ allows (24,1), (12,2), (8,3), (6,4) - not sufficient. Combining: $m + n > mn = 24$ requires $m + n > 24$, satisfied only by $24 + 1 = 25 > 24$, giving m = 24, n = 1 uniquely. Hence both statements together are needed.