Problem:
The product of two positive numbers is . The reciprocal of one of these numbers is times the reciprocal of the other number. What is the sum of the two numbers?
Answer Choices:
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Solution:
Let be the first number, and let be the second number. The first statement implies . The second statement implies , so . Substitution yields , so . Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions