Problem:
The sum of two natural numbers is . One of the two numbers is divisible by . If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?
Answer Choices:
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Solution:
Let be the number that is known to be a multiple of . Then the other number is . The sum condition says that , which can be rewritten as . Multiplying both sides by gives . The requested difference is .
Let be the lesser number. Then the greater number is and the sum of the two numbers is . This gives , and the difference of the two numbers is .
The problems on this page are the property of the MAA's American Mathematics Competitions