QUESTION

CSAT

Medium

Reasoning

Prelims 2024

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

Question: What are the values of mm and nn, where mm and nn are natural numbers?

Statement-I: m+n>mnm + n > mn and m>nm > n. Statement-II: The product of mm and nn is 2424.

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

Select an option to attempt

Explanation

Statement-I: m+n>mnm + n > mn and m>nm > n

  • For m=2m = 2, n=1n = 1: 2+1=3>2×1=22 + 1 = 3 > 2 \times 1 = 2, and 2>12 > 1, which satisfies both conditions.
  • For m=3m = 3, n=1n = 1: 3+1=4>3×1=33 + 1 = 4 > 3 \times 1 = 3, and 3>13 > 1, which satisfies both conditions. This gives multiple possible pairs for mm and nn, so it is not sufficient to uniquely determine mm and nn.

Statement-II: mn=24mn = 24

Possible pairs are:

  • 1×24=241 \times 24 = 24
  • 2×12=242 \times 12 = 24
  • 3×8=243 \times 8 = 24
  • 4×6=244 \times 6 = 24

This also gives multiple possible pairs, so it is not sufficient alone.

Combining Statement-I and Statement-II: From Statement-II, mm and nn must be pairs where the product is 24. Using Statement-I, we check:

  • (24,1)(24, 1): 24+1=25>2424 + 1 = 25 > 24, also 24 is greater than 1, so this pair statisfy all the conditions.
  • Other pairs like (2,12)(2, 12), (3,8)(3, 8), and (4,6)(4, 6) fail to meet the condition m+n>mnm + n > mn.

Hence, both statements together provide the unique solution (m,n)=(24,1)(m, n) = (24, 1).

Conclusion: The question can be answered by using both statements together, but not either statement alone.

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