The other tutor is correct. But here is the whole thing with the
Venn diagram drawn and step by step procedure for filling it in.
there are 80 students in a class. Some take Mathematics, some Physics and
others biology. All students take at least one course and some two or three. 40
students take Mathematics and 31 biology. 7 students take mathematics and
Physics only, 8 take Biology and physics only and 3 take mathematics and
Biology only. 5 take all three courses how many take physics?
We draw three overlapping circles inside a rectangle.
Label the circles M,P and B for Mathematics, Physics and Biology.
There are 8 regions and we must put a number in each of the 8.
In this type of problem, the clues are nearly always given
in the REVERSE order that we put the numbers into the Venn
diagram.
We look for the most inclusive clue first, which
is the very last one:
>> 5 take all three courses <<
The only region which is part of all three circles is
right in the center, so we put a 5 there:
The next to the last clue is
>>3 take mathematics and Biology only<<
So we put a 3 in the only region that is common to
both circle M and circle B and not P, like this:
Still going backwards in the listing of the clues:
>8 take Biology and physics only<<
So we put an 8 in the only region that is common to
both circle B and circle P and not M, like this:
Still going backwards in the listing of the clues:
>7 students take mathematics and Physics only<<
So we put a 7 in the only region that is common to
both circle M and circle P and not B, like this:
Still going backwards in the listing of the clues:
>and 31 (take) biology<<
In circle B we now have three of the regions with
numbers filled in them. We have a 3, a 5 and an 8.
So we add those 3+5+8 and get 16, and since the whole
circle B must contain 31, we subtract 31-16 = 15, and
so we put 15 in the bottom part of circle B, and now
circle B is complete:
Still going backwards in the listing of the clues:
>40 students take Mathematics<<
In circle M we have three of the regions with
numbers filled in them. We have a 7, a 5 and an 3.
So we add those 7+5+3 and get 15, and since the whole
circle M must contain 40, we subtract 40-15 = 25, and
so we put 25 in the left part of circle M, and now
circle M is complete:
Still going backward we come to:
>>All students take at least one course<<
This tells us that there are no students who aren't taking any of
the three courses. In lots of this type problem there are some
that are not in any of the three sets. They go outside the three
circles but inside the rectangle. So we put 0 in the area outside
all the circles, in the lower left corner of the rectangle.
Now there is just one region to fill in. We
finally come to the very first clue:
>>there are 80 students in a class.<<
So we add up all the other 7 numbers we've filled in
and subtract from 80: 25+7+3+5+8+15+0 = 63, then
80-63=17. So we put 17 in the right region of circle
P.
Now we are asked
how many take physics?<<
So we add up the four numbers in the
regions of circle P and get:
7+5+8+17 = 37
That's the answer:
Edwin
