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 : Can we have a common solution which is prime ?<br><br>Statement-I : x^2-26x+133=0<br><br>Statement-II: x^2-44x+475=0<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

To check for a "common solution", we must compare both equations. Solving I: x^2-26x+133=0 \implies (x-7)(x-19)=0 \implies x=7, 19. Solving II: x^2-44x+475=0 \implies (x-19)(x-25)=0 \implies x=19, 25. The common root is 19, which is prime. Thus, both statements are required to answer the question.

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