Question

Five friends sat in a movie theater in a row containing $5$ seats, numbered $1$ to $5$ 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?

$1$

$2$

$3$

$4$

$5$

Answer: B

Concepts:logical deduction invariant

Difficulty rating: 1420

Solution:

The sum of the occupied seat numbers is $1+2+3+4+5=15$ both before and after the moves. Dee and Edie merely switch seats, so their combined displacement is $0.$ Bea's displacement is $+2,$ and Ceci's is $-1.$ Therefore Ada's displacement must be $-1$ so that the total displacement is $0.$

Ada returns to an end seat. Since she moves one seat left, she must move from seat $2$ to seat $1.$

Thus, the correct answer is B .

2016 AMC 10A Problem 13

Answer: B

Difficulty rating: 1420

Solution:

Problem 13 in Other Years