2016 AMC 10A Problem 13
Problem 13 of 25Intermediate
Five friends sat in a movie theater in a row containing seats, numbered to from left to right. (The directions “left” and “right” are from the point of view of the people as they sit in the seats.)
During the movie Ada went to the lobby to get some popcorn. When she returned, she found that Bea had moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada been sitting before she got up?
Answer choices
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Solution
The sum of the occupied seat numbers is both before and after the moves. Dee and Edie merely switch seats, so their combined displacement is Bea’s displacement is and Ceci’s is Therefore Ada’s displacement must be so that the total displacement is
Ada returns to an end seat. Since she moves one seat left, she must move from seat to seat
Thus, the correct answer is B .