Math Gold Medalist

Lor

2023 AMC 10A

Problem 14

A number is chosen at random from among the first $100$ 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 $11$?

$\textbf{(A)}~\frac{4}{100}\qquad\textbf{(B)}~\frac{9}{200} \qquad \textbf{(C)}~\frac{1}{20} \qquad\textbf{(D)}~\frac{11}{200}\qquad\textbf{(E)}~\frac{3}{50}$

Casework

Probability

First number should be 11 or 22 … or 99

case1)11 -> 1/2

case2)22 -> 2/4

case3)33 -> 1/2

…

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   Solution