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

Home > Just Math
Divisibility rule (Posted on 2013-02-13) Difficulty: 2 of 5
abcde is five digit number. Show that abcde is divisible by 7 if and only if the number abcd-(2*e) is divisible by 7 (* means Multiplication)

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

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

Denote concatenation  xyzw by bold letters ,-and multiplication    xyzw by regular font.

n1 = abcde= 10*abcd +e

 n2 =10* (abcd -2e)=10*abcd -20e

n1-n2= 21*e    is divisible by 7.

 

Reading the 3 lines to fro makes it if and only if.


  Posted by Ady TZIDON on 2013-02-13 11:05:20
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