Subject 3. Consider the sets $A=\{1,2,3,4, \ldots, 2015,2016\}$, $B=\{x \in A \mid x$ is a multiple of 25$\}$ and $C=\{x \in B \mid x$ is a multiple of 4$\}$.

a. Determine the cardinality of the set $B$.

b. Determine the cardinality of the set $C$.

c. Determine the subsets of $A$ whose sum of elements is equal to 2033133.
## Subject 3.

| $B=\{25,50,75, \ldots, 2000\}$, so $\operatorname{card}(B)=80$ | $2 \mathbf{p}$ |
| :---: | :---: |
| Multiples of 4 from set $B$ are multiples of 100 from $A$  $C=\{100,200,300, \ldots, 2000\}$, so card $(C)=20$ | $2 \mathbf{p}$ |
| $1+2+3+\ldots+2016=2033136$  Subsets are:  $\quad A_{1}=\{3,4,5, \ldots, 2016\}=A-\{1,2\}$  $\quad A_{2}=\{1,2,4,5, \ldots, 2016\}=A-\{3\}$ | $1 p$  $1 p$  $1 p$ |