SOLUTION: out of 30 job applicants,11 are female,17 are college graduates,7 are bilingual,3 are female college graduates,2 are bilingual women,6 are bilingual college graduates,and 2 are bil

Question 513369: out of 30 job applicants,11 are female,17 are college graduates,7 are bilingual,3 are female college graduates,2 are bilingual women,6 are bilingual college graduates,and 2 are bilingual female college graduates:
(a) how many college graduates are male?
(b) how many female college graduates are not bilingual?
(c) how many women who are not college graduates are bilingual?
(d) how many applicants are either female or bilingual?
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
Let's break this problem down: each of our 30 job applicants can be characterized by:
1) female or male;
2) college graduate or not college graduate;
3) bilingual or not bilingual
We are told the following:
11 of the job applicants are female;
17 are college graduates;
7 are bilingual;
3 are female college graduates;
2 are bilingual women;
6 are bilingual college graduates; and
2 are bilingual female college graduates.
How do we make sense of all of this?
a) There are 17 college graduates, 3 of which are female. Thus 14 college graduates are male.
b) There are 3 female college graduates, and 2 bilingual female college graduates. Thus only 1 female college graduate is not bilingual.
c) There are 2 bilingual women total among the applicants, and 2 bilingual female college graduates. So none of the applicants are female, bilingual, and not college graduates.
d) Either typically means in this context "one or the other, but not both." So we are looking for job applicants that are female, bilingual, but not both female and bilingual. We already know that there are 11 female job applicants and 7 bilingual applicants, so 18 applicants are female, bilingual, or both. We need to subtract then the 2 bilingual women from that list, making 16 applicants who are female, bilingual, but not both.

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