Word Problem

Question

Each person in an IT department of 25 people work on at least one of the 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. How many people work on system security and program implementation?

Answer 1

Draw 3 overlapping circles:

Labelled as security, implementation, development...

 

The area where all 3 overlap has value 2

 

overlap of security and development has value 4

but 2 is accounted for in the all 3 area so 2 work in security/development overlap

 

The area for overlap of implementation and development has value 5

but, again, 2 are in the all 3 area so implementation/development overlap has value 3

 

Label the area of overlap of security/implementation but not development as x

 

Security only:  10 - (x+4) = 6-x

Implementation only: 13 - (x+5) = 8-x

Development only:  12 - (2+2+3) = 12 - 7 = 5

 

The total of all areas is 25

2 + 2 + 3 + x + (6-x) + (8-x) + 5 = 25

26 + x - 2x = 25

-x = -1

x = 1

 

1 person does security/implementation but not development.

Add to that the 2 that do all 3.

The total that work on security and implementation is:

2 + 1 = 3