I was working on a problem from one of the TIA sample exams and I am having a hard time coming up how to solve this venn diagram question. Unfortunately I can't watch the video solution because it already expired last month so I am just left with the pdf solution which doesn't help me much. Besides, I wanted to see the different ways people approach this type of problem.

In Old Crobuzon, there were three subway lines. On a typical day, 7,500 people take the Red line, 5,500

take the Orange line, and 6,500 take the Green line. The number of people who take both the Red and

Green line is 500 greater than the number who take both the Red and Orange lines, and the number of

people who take the Red and Green line is 1600 greater than the number that take both the Orange and

Green lines. If one-seventh of those who take the Red and Green lines also take the Orange line and 4,100

take only the Red line, how many people take more than one subway line?

The answer is 3600

Thanks

In Old Crobuzon, there were three subway lines. On a typical day, 7,500 people take the Red line, 5,500

take the Orange line, and 6,500 take the Green line. The number of people who take both the Red and

Green line is 500 greater than the number who take both the Red and Orange lines, and the number of

people who take the Red and Green line is 1600 greater than the number that take both the Orange and

Green lines. If one-seventh of those who take the Red and Green lines also take the Orange line and 4,100

take only the Red line, how many people take more than one subway line?

The answer is 3600

Thanks

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