## Task 2 - 310722

Susann wants to calculate the sum $s$ of all four-digit natural numbers that are divisible by 4.

Tamara determines the sum $t$ of all four-digit natural numbers that are divisible by 2 but not by 4.

a) Are $s$ and $t$ equal, or if not, which of the two numbers is the larger one?

b) What is the amount of the difference between $s$ and $t$? Justify your answers!
$s$ is the sum of the numbers 1000, 1004, ..., 9996; $t$ is the sum of the numbers 1002, 1006, ..., 9998.

a) From each summand in $s$, by increasing it by 2, a summand in $t$ is obtained, and each summand in $t$ is obtained exactly once. Therefore, both sums contain the same number of summands.

Furthermore, each summand in $t$ is greater than the corresponding summand in $s$. Hence, $t$ is greater than $s$.

b) The difference between the first and last summands is 8996 in both sums, and the summands follow each other at intervals of 4. The number of summands (in each of the two sums) is therefore $8996: 4 + 1 = 2250$.

From this and because each summand in $t$ is 2 greater than the corresponding summand in $s$, it follows:

The difference between $s$ and $t$ has the magnitude $2250 \cdot 2 = 4500$.