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

Home > Numbers
How many oranges? (Posted on 2007-03-22) Difficulty: 3 of 5
Three friends Riley, Sammy and Todd have a certain number of oranges in their possession.

It is known that:

(1) The number of oranges possessed by each of the three friends are two digit positive integers.

(2) The number of oranges possessed by Sammy is obtained by adding the two digits of the number of oranges possessed by Riley and summing the result with the original number of oranges in Riley's possession.

(3) The number of oranges possessed by Todd is obtained by reversing the digits corresponding to the number of oranges in Sammy's possession.

(4) The total number of oranges possessed by the three friends is 272.

Determine analytically the number of oranges possessed by each of the three friends.

See The Solution Submitted by K Sengupta    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
spoiler | Comment 1 of 6

Let (R,S,T) = the number of oranges held by Riley, Sammy, Todd respectively.

If S = 10k + j, by (3) T = 10j + k so S + T = 0 mod11 and then by (4) R = 8 mod11.

Since S + T < 200, R = 74,85 or 96.

R = 74 implies T>100 and R = 96 implies S>100.

(R,S,T) = (85,98,89) satisfies all the problem's conditions.

  Posted by xdog on 2007-03-22 15:14:09
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information