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Question

# Presidential elections are held every four years. U.S. senators are elected to b-year terms, but only $\frac{1}{3}$ of the Senate is up for election every two years. If $\frac{1}{3}$ of the Senate is elected during a presidential election year, how many years must pass before these same senate seats are up for election during another presidential election year?

Solution

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We need to determine when will a presidential election and when the senators' term will be terminated occur at the same time.

Since presidential elections occur every 4 years and the senators are elected to 6-year terms, then we need to find the first common multiple of 4 and 6 which is 12. Hence, $\text{\color{#c34632}12 years}$ must pass.

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