Multiple choice

If the sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers is

  1. 2

  2. 3

  3. 4

  4. 5
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C Correct answer
Explanation

Let the numbers be 81a and 81b, where a and b are coprime. 81(a+b) = 1215, so a+b = 15. Pairs (a,b) such that gcd(a,b)=1 are (1,14), (2,13), (4,11), (7,8). There are 4 such pairs.

AI explanation

Let the two numbers be 81a and 81b, where a and b are coprime natural numbers. Their sum gives 81 times a plus b equals 1215, meaning a plus b equals 15. The coprime pairs that sum to 15 are (1, 14), (2, 13), (4, 11) and (7, 8). Counting these sets gives exactly 4 possible pairs of numbers.

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