Discussion

The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there?

Answer: B

Let the numbers be 27a and 27b, where a and b are co-prime.

Sum = 27a + 27b = 216

27(a + b) = 216

a + b = 216 / 27 = 8.

We need to find pairs of co-prime numbers that sum to 8.

The pairs are (1, 7) and (3, 5). The pair (2, 6) is not co-prime, and (4, 4) is not co-prime.

There are 2 such pairs.

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