Competition problem — Number theory

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Number theory Difficulty 4.3 AIME Find the answer Philippines

Problem:
What is the probability that a randomly chosen positive divisor of $2010$ has two digits?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$\frac{1}{4}$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.