2010/11 AHSMC Part 1 Problem 3

Problem 3 of 16

The greatest common divisor and least common multiple of two positive integers are $1$ and $10$ respectively. If neither of them is equal to $10$ , their sum is equal to

Show solution

Solution

Since the least common multiple is even, at least one number is even. Since the greatest common divisor is odd, exactly one number is even. We can show in a similar manner that exactly one of the two numbers is divisible by $5$ . Since neither is $10$ , one of them is $2$ and the other is $5$ , yielding a sum of $7$ . The answer is (C).

University of Alberta

Answer choices

Solution