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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?

enter image description here


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Wildly off-topic (sorry!), but have you seen this joke, taken from wikipedia? A physicist, a biologist and a mathematician are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty." –  Srivatsan Nov 3 '11 at 14:34
Are you sure that is the statement? Your diagram looks correct. –  robjohn Nov 3 '11 at 14:42
There may be problems in the translation. But it is more likely that, as @discipulus says, it is simply a bad question. So was at least one earlier one along similar lines. It takes a surprising amount of care to make up a "word problem" that makes sense physically and mathematically. –  André Nicolas Nov 3 '11 at 17:08
It created by my teacher. Could be wrong.. –  Fahad Uddin Nov 3 '11 at 17:23
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1 Answer

up vote 2 down vote accepted

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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