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4 February, 04:10

The mayor gets elected every four years. Treasurer gets elected every six years. Both were elected this year. How many years before the election happens in the same year.

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  1. 4 February, 05:08
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    There are 11 years before both the elections happen in the same year.

    Step-by-step explanation:

    The mayor gets selected once in every 4 years.

    So, the number of years the mayor elections takes place

    = 1, 4,8, 12, 16, 20, 24, 28, ...

    Now, the Treasurer gets selected once in every 6 years.

    So, the number of years the Treasurer elections takes place

    = 1, 6, 12, 18, 24, 30

    Now, as we can see from both statements, the year in which both elections happen are the common factors of 4 and 6.

    The first common factor of 4 and 6 is 12.

    So, in twelfth year both elections happen in the same year again.

    Hence, there are 11 years before the elections happen in the same year.
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