AMC 12 Mock Exam 5 Problem 2

Problem 2 of 25

The lockers in a school hallway are numbered $1$ through $199$ . A locker receives a blue sticker if its number is a multiple of $6$ but not a multiple of $4$ . How many lockers receive a blue sticker?

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Solution

There are $\lfloor 199/6\rfloor=33$ multiples of $6$ up to $199$ . A multiple of $6$ is also a multiple of $4$ exactly when it is a multiple of $\operatorname{lcm}(6,4)=12$ , and there are $\lfloor199/12\rfloor=16$ of those. So $33-16=\boxed{17}$ lockers get a blue sticker.

Tagged: counting multiples (inclusion-exclusion)

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