1975 AMC 12 Problem 17

Question

A man can commute either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon; and if he comes home in the afternoon on the train, he took the bus in the morning. During a total of

x

working days, the man took the bus to work in the morning

8

times, came home by bus in the afternoon

15

times, and commuted by train (either morning or afternoon)

9

times. Find

x.

19

18

17

16

not enough information given to solve the problem

Answer: D

Concepts:basic counting

Difficulty rating: 1380

Small hint:

There are exactly two one-way trips on every working day

Big hint:

Count all bus trips and all train trips together

Solution:

There were

8+15=23

bus trips and

9

train trips, hence

32

one-way trips in all. Since each working day contributes two trips,

2x=32

and

x=16.

The conditional statements are consistent but not needed for this count.

Therefore, the correct answer is D.