Competition problem — Combinatorics

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

How many of the integers between $97$ and $199$ are multiples of $2$ or $3$ ?

Pick one

Solution

E Between (and including) $98$ and $200$ there are $51$ multiples of $2$ ; between $98$ and $199$ there are $34$ multiples of $3$ . Between $102$ and $198$ there are $17$ multiples of $6$ . The number we seek is $51 + 34 - 17 = 68$

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