Tokyo University Entrance Exam Math Problems 001

The following is a problem from 1956 Tokyo University STEM major's 1st test Comprehension I part. We have translated and uploaded it for people interested in math, education, and history. Please take a look and comment or post your own solutions.

 * CLA note : There is a long way to solve this problem and also a short, quick way. It is very important to be able to solve this problem in both ways.