SOLUTION: In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra, and geometry 25 liked calculus 15 liked geometry

Let A = the set of all students who liked algebra, regardless
of whether they liked the other two subjects.
Let G = the set of all students who liked geometry, regardless
of whether they liked the other two subjects.
Let C = the set of all students who liked calculus, regardless
of whether they liked the other two subjects.


 
The most inclusive clue we have is this one:

Those 4 are in all three circles, and the only
region that is common to all three circles is
the middle region f, so we put 4 for f



Now we look at this:

4 of these 12 are in the middle region,
so the other 12-4 or 8 are in j, so
we put 8 in region j:



Next we look at this clue:

So 18 are in circle C but not in circle A.

8 of these 18 we just got through finding so
the other 18-8 or 10 must be in region k,
since they do not like algebra.  So we put
10 in region k:



Next we look at:

Now we can complete the circle C, 
because we have accounted for the
numbers in three of its four regions
of its regions, that's 4+8+10, or 22,
so the other 25-22 or 3 are in region h.
So we put 3 in region h:



Next we look at this clue:

These 10 are all in region d because they are the
only ones in the algebra circle who are not also
in either of the other two circles.  So we can
put 10 in region d



Next clue:

These 2 are in region e because that region is
part of the geometry and algebra circles but
not part of the calculus circle,  So we put
2 in region e:



Next clue:

So there are 15 students in the geometry cirle,
and we have accounted for 2+4+8 or 14 of the 15
in the geometry circle, so that leaves 15-14 or
just 1 student in region i. So we put 1 student
in region i:




Finally we look at,

So of these 50 math majors, we have accounted for
10+2+1+3+4+8+10=38 of them, so the remaining 50-38
or 12 math majors are in the region outside all
three circles, which is m.  So we put 12 in region
m.



So 12 math majors didn't like any of
the three math subjects, so those 12
had better change their major to history
or English or a foreign language, don't
you think!!

Anyway you only have to answer this:

Of those surveyed, how many liked calculus and algebra?

Those are the students in the two region with 3 
and 4 in them for they are in both the calculus and
the algebra circles. So the only thing you have to
answer is 3+4 or 7.

Yes, I know, we could have answered that long before we 
finished all the regions.  However I went through the 
whole Venn diagram anyway, because in other Venn diagram 
problems you will likely have to complete the whole Venn 
diagram to answer the question asked.

Answer: 7

Edwin