To solve draw a large circle to represent 100 students. Inside the circle draw three smaller interlocking circles each representing a subject, represented by and labelled M, P, C. These circles produce 7 regions or areas caused by the overlaps and the region surrounding the three circles inside the larger circle is an 8th region. These are given letters a to h and represent the numbers of students in each region:
a. M only
b. P only
c. C only
d. M, P only
e. M, C only
f. All 3
g. P, C only
h. None
The combination of letters below represents addition of the quantities represented by the individual letters.
abcdefgh=100; adef=40; bdfg=64; cefg=50; ef=20; df=24; c=8; f=10. (h=12, but this can be calculated as shown below.)
abdefgh=92 and efg=42 (because c=8), so g=22 (because ef=20); ad=20; bg=40 (because df=24), so b=18 (because g=22); h=12 (because abdefgh=92, b=18, ad=20, efg=42); d=14 (because f=10), so a=6.
There are a=6 students taking math only; b=18 students taking psychology only; g=22 taking psychology and chemistry only. (e=10 took math and chemistry only.)