How many people are working on the project?

Question

Each person, in an IT department of 60 people, works on at least one of 3 major projects: system security (ss), program implementation (pi), platform development. 23 people work on (ss), 28 on (pi), and 26 on (pd). 7 people work on (ss) and (pd). 12 work on (pi) and (pd). 6 people work on all 3 projects. How many people work only on (ss) and (pi)? (i.e. not all 3 projects)

Answer 1

We can assign variables to numbers of people involved in one or more projects:

A ss only

B pi only

C pd only

D ss+pi

E ss+pd

F pi+pd

G all three projects

We know that each person is involved in at least one project, so:

A+B+C+D+E+F+G=60

A+D+E=23 (ss) }

B+D+F=28 (pi)  } excludes those working on all three*

C+E+F=26 (pd) }

E=7, F=12, G=6

A+D=23-7=16=28-12=B+D so B=A, D=16-A

C=26-(7+12)=7

2A+7+(16-A)+7+12+6=60,

A+7+16+7+12+6=60,

A=60-48=12 and D=16-A=16-12=4.

So (A,B,C,D,E,F,G)=(12,12,7,4,7,12,6), therefore 12 work on each of ss and pi and 7 work on pd.

* If the figures were to include those involved on all 3 projects, we get a negative result for one group of people, so there would be no sensible solution. The solution to this question depends on the interpretation of the figures provided.