Problem:
How many positive three-digit integers have a remainder of when divided by , a remainder of when divided by , and a remainder of when divided by
Answer Choices:
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E.
Solution:
Let be a positive three-digit integer that satisfies the conditions stated in the problem. Note that because has a remainder of when divided by , is divisible by . Similarly, is divisible by and . Hence is divisible by the least common multiple of , and , which is . Thus = where or . So , or , and there are therefore five positive three-digit integers satisfying the given conditions.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions