17. Jeroen writes a list of 2019 consecutive integers. The sum of his integers is 2019 . What is the product of all the integers in Jeroen's list?
A $2019^{2}$
B $\frac{2019 \times 2020}{2}$
C $2^{2019}$
D 2019
E 0
Solution
$\mathbf{E}$

In a list of 2019 consecutive positive integers, at least one of them will be greater than or equal to 2019, and therefore the sum of these integers will be greater than 2019. So the integers in Jeroen's list are not all positive.
The sum of 2019 negative integers is negative and therefore cannot be equal to 2019 . So the integers in Jeroen's list are not all negative.
We deduce that Jeroen's list of consecutive integers includes both negative and positive integers.
Because the integers in the list are consecutive it follows that one of them is 0 .
Therefore the product of all the numbers in Jeroen's list is 0 .