## Euclid 2024 Question 6, CEMC UWaterloo

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#### Difficulty: 7

#### This problem is tagged with euclid, euclid24, highschool.

**(Euclid 2024, Question 6, CEMC - UWaterloo)**

(a) There are $M$ integers between $10000$ and $100000$ that are multiples of $21$ and whose units (ones) digit is $1$. What is the value of $M$?

(b) There are $N$ students who attend Strickland S.S., where $500 < N < 600$. Among these $N$ students, $\frac{2}{5}$ are in the physics club and $\frac{1}{4}$ are in the math club. In the physics club, there are $2$ times as many students who are not in the math club as there are students who are in the math club. Determine the number of students who are not in either club.

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