Find the value of a ........

Quantitative Aptitude (SBI-PO) Quadratic Equations

Directions: Answer the questions based on the information given below.

Equation (i) : ax² + bx + c = 0

Equation (ii) : py²+ qy + c = 0

'c' is a single-digit prime number greater than 2. 'p' and 'b' are 2-digit prime numbers less than 20. 'p' is greater than 11 and 'b' is greater than 'p'. The smallest roots of both the equations are same and none of the roots for any given equation is irrational. '3c' is greater than 'b' and q = b + 1

Find the value of a?

This questions was previously asked in

SBI PO Mains (30 Jan, 2023)

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Explanation:

- The value of 'c' is a single-digit prime number greater than 2. Possible values are 3, 5, or 7.

- 'p' and 'b' are two-digit numbers less than 20, so they can be 11, 13, 17, or 19. 'p' is greater than 11, leaving 13, 17, and 19 as options. 'b' is greater than 'p'.

- Given that '3c' is greater than 'b', if we set c = 5, then 'b' should be less than 15. But 'b' is a two-digit number, which is not possible. So, c cannot be 5.

- If c = 7, then 3c = 21. Thus, 'b' should be less than 21 and still greater than 'p'.

- Select smallest primes for 'p', as p > 11: this gives p = 13.

- Then, for 'b' to be greater than 13, we can choose b = 17 or 19. But as 3c = 21, choose b = 17.

- Given q = b + 1, so q = 18.

- The smallest roots of both equations are the same; hence, factor pairs need to match.

- Roots are integers: solving with possible values: a = 9.

- Correct answer: Option 1, 9.

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