2014 AMC 12B Problems/Problem 10
Problem
Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, miles was displayed on the odometer, where
is a 3-digit number with
and
. At the end of the trip, the odometer showed
miles. What is
.
$\textbf{(A)}\ 26\qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}}\ 37\qquad\textbf{(E)}\ 41$ (Error compiling LaTeX. Unknown error_msg)
Solution
We know that the number of miles she drove is divisible by , so
and
must either be the equal or differ by
. We can quickly conclude that the former is impossible, so
and
must be
apart. Because we know that
and
and
, we find that the only possible values for
and
are
and
, respectively. Because
,
. Therefore, we have