Question

Out of 200 kids, 100 had a T-Rex, 70 had iPads and 140 had a cell phone. 40 of them had both, a T-Rex and a iPad, 30 had both, a iPad and a cell phone and 60 had both, a T-Rex and cell phone and 10 had all three. How many kids had none of the three?

Answer 1

`10` have none of the three.

Explanation:

`10` students have all three.
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Of the `40` students who have a T-Rex and an iPad, `10` students also have a cell phone (they have all three). So `30` students have a T-Rex and an iPad but not all three.

Of the `30` students who had an iPad and a cell-phone, `10` students have all three. So `20` student have an iPad and a cell-phone but not all three.

Of the `60` students who had a T-Rex and a cell-phone, `10` students have all three. So `50` students have a T-Rex and a cell-phone but not all three.
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Of the `100` students who have a T-Rex, `10` have all three, `30` also have (only) an iPad, and `50` also have (only) a cell-phone.
So `100-(10+30+50)=10` have only a T-Rex.

Similarly, `70-(10+30+20)=10` have only an iPad.

And `140-(10+20+50)=60` have only a cell-phone.
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`{: ("T-Rex","iPad","cell-phone",,"number of students"), ("Y","Y","Y",,10), ("Y","Y","N",,30), ("N","Y","Y",,20), ("Y","N","Y",,50), ("Y","N","N",,10), ("N","Y","N",,10), ("N","N","Y",,60), (,,,"total:",190) :}`

So out of `200` students `190` have at least one of these devices.

`rArr 200-190=10` students do not have any of these devices.

Here is how the distribution would appear in a Venn diagram: