Problem:
A palindrome between 1000 and 10,000 is chosen at random. What is the probability that it is divisible by 7 ?
Answer Choices:
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E.
Solution:
Each four-digit palindrome has digit representation with and . The value of the palindrome is . Because 1001 is divisible by 7 and 110 is not, the palindrome is divisible by 7 if and only if or . Thus the requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions