2024 · Q63
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option. Question : Can we have a common solution which is prime?
Statement Ix² − 26x + 133 = 0
Statement IIx² − 44x + 475 = 0 Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsAlgebra
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
x²−26x+133 = 0 gives x = 19 or 7; x²−44x+475 = 0 gives x = 25 or 19. Each statement alone leaves two candidates, but together they fix the common solution 19, which is prime. Both statements are needed — option C.