A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.<br><br>Question: There are three different weights. All the weights are integers and their sum is a prime number. What are the weights ?<br><br>Statement-I: One of the weights is twice the another weight<br><br>Statement-II: One of the weights is thrice the another weight<br><br>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 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

Explanation

Using both statements, let the weights be a, b, c such that a=2b and a=3c (the only configuration yielding a valid solution). This means a=6k, b=3k, c=2k. The sum is 11k. Since the sum must be prime, k=1, making the weights 6, 3, and 2 (sum is 11). Either statement alone yields infinitely many prime sums, so both are required.

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