A job opening for a Webmaster has three desirable skills: writing, design, and programming. Of the received applications, 30 have at least one of these skills: 18 know design, 20 can write well, and 23 have programming ability. There are 6 with writing and design skills only, 7 with just writing and programming, and 4 who can design and program but can't write. Only those with all three skills are interviewed. How many interviews are there?

Seven (7) persons were interviewed for the Webmaster job.

[w&d] + [w&p] + [d&p] + W + D + P + C = 30
W + D + P + C = 30 - ( 6 + 7 + 4 ) = 13

Where [w&d], [w&p], and [d&p] represent the number of applicants that have only two skills; and W, D, P correspond to the quantity of persons with only one skill and C corresponds to the number of candidates with all three skills.

C + W + [w&d] + [w&p] = 20     <--- writers
C + W = 20 - (6 + 7) = 7

C + D + [w&d] + [d&p] = 18      <--- designers
C + D = 18 - (6 + 4) = 8

C + P + [w&p] + [d&p] = 23       <--- programmers
C + P = 23 - (7 + 4) = 12

By substitution we then find...
D + P = 13 - (C + W) = 13 - 7 = 6
W + P = 13 - (C + D) = 13 - 8 = 5
D + W = 13 - (C + P) = 13 - 12 = 1

and then it can be deduced... 
D = 1, W = 0, P = 5, therefore C = 7

Posted by Dej Mar on 2006-07-04 09:12:45