Competition problem — Combinatorics

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Combinatorics Difficulty 3.9 AMC 10/12 Find the answer South Africa

In a group of $108$ people, $1$ in $4$ of them has a pen and $1$ in $3$ has a pencil. What is the minimum possible number of people that have something to write with?

Your answer

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

Solution

$36$ people must have a pen and $36$ must have a pencil. If all the people with pens also have pencils, this could be as few as $36$ people in all.

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