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?

since 20 can write, 18 can design, and 23 can program then if we wanted to find the amount of people that can do at least one then we would add these 3 values togeather and subtract the various intersections.  the total is 61,  we know 3 of the 4 intersections.  the first 3 are the intersections of writers+designers, writers and programers, and designers and programers.  those values are 6,7, and 4 respectively.  so we subtract each of these once from 61 because these are the applicants that were counted twice (because of the intersections).  now we are down to 44.  all we must subtract now is the intersection of writers+designers+programmers which happens to be what we are looking for.  lets call this quantity x.  since these applicants are actually counted 3 times we must subtract 2x from 44 to get the known value of 30.  thus
44-2x=30
2x=14
x=7

Posted by Daniel on 2006-07-04 09:36:06