How many students studied math only?

Question

In a second year college class of 100 students, 40 studied mathematics, 64 studied psychology, 50 studied chemistry, 20 studied both math and chemistry, 24 studied both math and psychology, 8 studied chemistry but neither math nor psychology, 10 studied all 3 subjects, while 12 did not take any of the three.

Answer 1

 

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.)