Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number N? Statement I : N + M = 33 Statement II: N > M

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone ✓
  4. D. The Question can be answered even without using any of the Statements

Correct Answer: C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Explanation

Let N = 10a + b and M = 10b + a. Statement I gives 11(a+b) = 33, so a+b = 3. Using MN = 252, testing combinations (1,2) or (2,1) gives 12 and 21. Thus N can be 12 or 21. Statement II specifies N > M, confirming N = 21. Both statements are needed.

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