2025 AMC 8 Problems/Problem 16
Five distinct integers from to
are chosen, and five distinct integers from
to
are chosen. No two numbers differ by exactly
. What is the sum of the ten chosen numbers?
Solution
Note that for no two numbers to differ by , every number chosen must have a different units digit. To make computations easier, we can choose
from the first group and
from the second group. Then the sum evaluates to
.
~Soupboy0
Similar solution
One efficient method is to quickly add , which is 55. Then because you took 50 in total away from
, you add 50. 55+50= \boxed{\text{(C)\ 105}}$
~Bepin999