Question: Let mn=k, where m and n are prime numbers and k is an even number. What is the value of mn-n+1?<br>Statement-I: m \gt n<br>Statement-II: One of the numbers is 2.

Consider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions : Choose option (a) If the Question can be answered by one of the Statements alone, but not by the other. (b) If the Question can be answered by either Statement alone. (c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone. (d) If the Question cannot be answered even by using both Statements together.

  1. A. If the Question can be answered by one of the Statements alone, but not by the other.
  2. B. If the Question can be answered by either Statement alone.
  3. C. If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
  4. D. If the Question cannot be answered even by using both Statements together. ✓

Correct Answer: D. If the Question cannot be answered even by using both Statements together.

Explanation

The product k = mn is given as an even number, which means at least one of the prime factors must be 2. Statement-II explicitly states this, making it redundant information. Statement-I tells us that m \gt n, which securely implies n = 2 and m is some odd prime number. However, since the exact value of the odd prime m remains unknown, we cannot determine a specific numerical value for the mathematical expression mn - n + 1. Thus, the question cannot be answered even with both statements.

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