1. Vittorio calculates the sum of the numbers from 1 to 2024, but he skips one by mistake! Knowing that he gets a multiple of 5, which of the following can be the number he skipped?
(A) 1
(B) 100
(C) 222
(D) 2023
(E) 2024
1. The answer is (B). First, we notice that the sum of the numbers from 1 to 2024 is a multiple of 5. This can be observed directly knowing that the sum of the numbers from 1 to $n$ is $\frac{n(n+1)}{2}$; alternatively, one can notice that each of the following numbers is a multiple of 5: $1+2024$, $2+2023, \ldots, 1012+1013$, and therefore so is the sum of these. Since the sum calculated by Vittorio is a multiple of 5, the missing number must also be a multiple of 5. The answer is therefore 100.