Rangpur Secondary 2011/6

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
User avatar
Moon
Site Admin
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Location: Dhaka, Bangladesh
Contact:

Rangpur Secondary 2011/6

Unread post by Moon » Wed Feb 02, 2011 6:49 pm

Problem 6:
When $N$ is divided by $7$, the quotient is twice the remainder. What is the number greater than $7$ that must divide $N$?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

User avatar
Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm
Location: Khulna,Bangladesh.

Re: Rangpur Secondary 2011/6

Unread post by Tahmid Hasan » Wed Feb 02, 2011 7:51 pm

is the wanted number a prime?
if it isn't there is no soln.
let's express $N=7.2a+a$
let's input the possible values of $a=1,2,3,4,5,6$
then the numbers are not divisible by any prime greater than 7 :(
বড় ভালবাসি তোমায়,মা

Mehfuj Zahir
Posts: 78
Joined: Thu Jan 20, 2011 10:46 am

Re: Rangpur Secondary 2011/6

Unread post by Mehfuj Zahir » Thu Feb 03, 2011 4:46 am

N=15a then must be divided by 15

User avatar
leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

Re: Rangpur Secondary 2011/6

Unread post by leonardo shawon » Thu Feb 03, 2011 11:36 am

no..actually it is if $N=15x$ [$x=1,2] and divisible by 7 then quotient is twice the remainder.
Ibtehaz Shawon
BRAC University.

long way to go .....

Mehfuj Zahir
Posts: 78
Joined: Thu Jan 20, 2011 10:46 am

Re: Rangpur Secondary 2011/6

Unread post by Mehfuj Zahir » Thu Feb 03, 2011 11:58 am

For any natural number it is true.U should read the question carefully.

User avatar
leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

Re: Rangpur Secondary 2011/6

Unread post by leonardo shawon » Thu Feb 03, 2011 6:41 pm

sorry. Mistake
Ibtehaz Shawon
BRAC University.

long way to go .....

User avatar
Moon
Site Admin
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Location: Dhaka, Bangladesh
Contact:

Re: Rangpur Secondary 2011/6

Unread post by Moon » Thu Feb 03, 2011 8:07 pm

No problem. We are here so that we may discuss and learn from our mistakes. :)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

User avatar
*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
Contact:

Re: Rangpur Secondary 2011/6

Unread post by *Mahi* » Thu Feb 03, 2011 9:07 pm

Here,$N$ must be equal to $15x$ where $x\neq7y$.Then $15$ is the answer.
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

Post Reply