In a group of 25, 13 can speak Latin, 15 can speak French,
and 6 don’t speak either. How many of these speak both Latin
and French?
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Answer Posted / jig
(A Venn diagram can easily confirm the answer below.)
6 out of 25 don't speak both Latin and French, so only 19 speak EITHER Latin OR French OR both.
25 - 6 = 19.
Of the 19 who speak either or both languages, 13 speak Latin, so 6 speak French but not Latin.
19 - 13 = 6.
Of the 19 who speak either or both languages, 15 speak French, so 4 speak Latin but not French.
19 - 15 = 4.
So out of the 25, we have:
6 who don't speak both Latin and French
6 who speak French but not Latin
4 who speak Latin but not French
Therefore, those who speak both Latin and French are 25 - 6 - 6 - 4 = 9.
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