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.