All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
WWW (Posted on 2006-07-04) Difficulty: 2 of 5
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?

No Solution Yet Submitted by alex    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution Comment 6 of 6 |
(In reply to Answer by K Sengupta)

Let us represent writing, design and programming respectively by a, b and c.

Let us denote union and intersection respectively by (+) and (*).
Then, in terms of the inclusion-exclusion principle, we must have:

N(a+b+c) = N(a) + N(b) + N(c) + N(a*b) + N(b*c) + N(c*a) - N(a*b*c)     .......(i)

Let, N(a*b*c) = t (say)

Then, by the given conditions, we have:

N(a+b+c) = 30
N(a) = 18
N(b) = 20
N(c) = 23
N(a*b) = 6+t
N(b*c) = 7+t
N(c*a) = 4+t

Acordingly, in terms of (i), we obtain:

30 = 18+20+23 - (6+t) - (7+t) - (4+t) + t
-> 2t = 14
-> t = 7

Consequently, the required number of interviews is 7.

Edited on December 9, 2008, 7:00 am
  Posted by K Sengupta on 2008-12-09 06:17:54

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information