The sum of two numbers is 98 and their HCF is 14. How many such pairs can be formed?

Correct option is C

Given:

Sum of two numbers = 98
HCF of the two numbers = 14

Concept Used:
Number of co-prime pairs (x, y) such that x + y = k

Solution:

14 x + 14 y = 98

We have x + y = 7, and gcd(x, y) = 1.

Possible positive integer pairs for (x, y) such that x + y = 7:
(1, 6), (2, 5), (3, 4)

Now check for co-primality:

gcd(1, 6) = 1

gcd(2, 5) = 1

gcd(3, 4) = 1

So, 3 valid pairs.