[Math] Count of a quantity coming negative in this Venn diagram

algebra-precalculuselementary-set-theory

Here is a question:

There are $140$ students in a batch. $10$ reserved stalls at the spring festival, $20$ sang on the stage and $45$ played games at various stalls. $8$ had reserved a stall and sang on the stage, $14$ sang and played games, $5$ who played games also had stalls reserved on their names. $2$ had stalls, sang and played games. How many did not go to the spring festival?

I tried to solve the problem with the Venn diagram but a set (people who just reserved stalls) is coming out to be $-1$. Can anyone help me out why?

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Thanks.

Best Answer

Your Venn diagram appears to agree with the statement. As you've noticed (and Srivatsan joked about), a negative number in this context doesn't have a physical interpretation.

Depending on where this question is from, it's possible that the statement is simply wrong. It's also possible that it is meant to say

There are 140 students in a batch. 10 reserved stalls at the spring event and did not play games or sing, 20 sang on the stage and did not reserve a stall or play games, etc.

in which case all of the Venn diagram counts will make sense; but this is not the usual interpretation.

I guess the answer is that this is just a bad question.

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