The sum of two numbers is 1224 and their HCF is 68 The number of pairs of numbers satisfying the abo...........

Quantitative Aptitude (CPO) LCM, HCF

The sum of two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:

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SSC CPO 9th Nov 2022 Shift 2

- The sum of two numbers is 1224.

- The highest common factor (HCF) of the numbers is 68.

- Let the two numbers be 68a and 68b, where a and b are co-prime numbers.

- Therefore, 68a + 68b = 1224 simplifies to a + b = 18.

- We find pairs of (a, b) such that they add up to 18: (1, 17), (2, 16), (3, 15), (4, 14), (5, 13), (6, 12), (7, 11), (8, 10), (9, 9).

- Only (1, 17), (3, 15), and (5, 13) are pairs of co-prime numbers.

- Number of valid pairs: 3.

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