# Math

In a class of students, 80 spoke English, 110 spoke spanish, 100 spoke french, 50 spoke english & spanish, 30 spoke english & french, 20 spoke french & spanish, 10 spoke english & frnech, but no spanish.

How many spoke spanish & french, but not english?

The answer is 0. I was wondering how this is the case.

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1. Mistyped it should say "10 spoke english & french" not "10 spoke english & frnech"

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posted by Sally
2. If 30 spoke E&F and 10 spoke E&F but not S, then that means 20 spoke E,F,S.

So, in your Venn diagram, the small triple intersection in the center has a 20 in it.

But, since only 20 spoke French and Spanish, and all of them also spoke English, there are 0 who spoke no English.

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posted by Steve
3. Thank you!

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posted by Sally

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