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

Home > Just Math
Rational Sum (Posted on 2016-02-15) Difficulty: 3 of 5
Find the sum of all possible values of a rational number R of the form N/30, where N is a positive integer with gcd (N, 30) = 1 and, R < 10.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Very rational (spoiler) Comment 1 of 1
1) If N/30 < 10, then N < 300
2) 30 = 2*3*5, so N is not a multiple of 2 or 3 or 5
3) Between 1 and 30, N can only be 1,7,11,13,17,19,23 and 29.  Sum = 120.
   So sum(R) where R < 1 = 120/30 = 4
4) There are 8 terms, so sum(R) where 1 < R < 2 is 4 + 8 = 12
5) Desired sum = 4 * (1+3+5+...+19) = 4*10*20/2 = 400

  Posted by Steve Herman on 2016-02-15 09:49:30
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 (4)
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