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The sum of two numbers is 552 and their HCF is 23. What is the minimum number of pairs that satisfy these conditions?

The sum of two numbers is 552 and their HCF is 23. What is the minimum number of pairs that satisfy these conditions? Correct Answer 4

Let the two numbers be 23x and 23y. Given, 23x + 23y = 552. So, x + y = 24. Now, co-prime pairs with sum 24 is (1,23), (5,19), (7,17) and (11,13). Hence, there are 4 pairs that satisfy the conditions.

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