2025 AMC 8 Problems/Problem 13
Problem
Each of the even numbers is divided by
. The remainders are recorded. Which histogram displays the number of times each remainder occurs?
Solution
Writing down all of the numbers modulo , we have
. Notice how the the cycle
repeats itself 3 times (because
). Then, we have
,
,
, and
remaining, which are
,
,
, and
mod 7, respectively. After adding them to our total count, the remainder
occurs
times,
occurs
times,
occurs
times,
occurs
times,
occurs
times,
occurs
times, and
occurs
times, which corresponds to histogram
.
~mrtnvlknv