Rangpur Secondary 2011/6
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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.
Rangpur Secondary 2011/6
Problem 6:
When $N$ is divided by $7$, the quotient is twice the remainder. What is the number greater than $7$ that must divide $N$?
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
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 Tahmid Hasan
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 Joined: Thu Dec 09, 2010 5:34 pm
 Location: Khulna,Bangladesh.
Re: Rangpur Secondary 2011/6
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
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

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Re: Rangpur Secondary 2011/6
N=15a then must be divided by 15
 leonardo shawon
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 Joined: Sat Jan 01, 2011 4:59 pm
 Location: Dhaka
Re: Rangpur Secondary 2011/6
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 .....
BRAC University.
long way to go .....

 Posts: 78
 Joined: Thu Jan 20, 2011 10:46 am
Re: Rangpur Secondary 2011/6
For any natural number it is true.U should read the question carefully.
 leonardo shawon
 Posts: 169
 Joined: Sat Jan 01, 2011 4:59 pm
 Location: Dhaka
Re: Rangpur Secondary 2011/6
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.
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.
Re: Rangpur Secondary 2011/6
Here,$N$ must be equal to $15x$ where $x\neq7y$.Then $15$ is the answer.
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