Problem:
A number is chosen at random from among the first positive integers, and a positive integer divisor of that number is then chosen at random. What is the probability that the chosen divisor is divisible by ?
Answer Choices:
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Solution:
There are 9 multiples of 11 among the first 100 positive integers, and the probability of choosing any particular one of them is . For each of these multiples of 11 , the probability that\
a randomly chosen divisor is a multiple of 11 is because each divisor that is a multiple of 11 can be paired with a divisor that is not a multiple of 11 . Therefore the requested probability is
The problems on this page are the property of the MAA's American Mathematics Competitions