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Dutch Mathematical Olympiad

Algebra Difficulty 4.4 AIME Find the answer Netherlands

For the integers $a$ , $b$ , $c$ , and $d$ the difference between $a$ and $b$ equals $2$ , the difference between $b$ and $c$ equals $3$ , and the difference between $c$ and $d$ equals $4$ . Which of the following values cannot be the difference between $a$ and $d$ ?

A) $1$ B) $3$ C) $5$ D) $7$ E) $9$

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is D, and the solution below works it through.

Solution

D) $7$

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