Dhaka Higher Secondary 2010/12

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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Please don't post problems (by starting a topic) in the "Higher 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.
BdMO
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Joined: Tue Jan 18, 2011 1:31 pm

Dhaka Higher Secondary 2010/12

If $\dfrac{x+2}{8}$ is an integer greater than $2$, find the remainder when $x$ is divided by $8$.

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

Re: Dhaka Higher Secondary 2010/12

here x > 14
and the remainder is 1.
(vagsesh) is 2,3,4,5. . . . . . . .
Ibtehaz Shawon
BRAC University.

long way to go .....

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

Re: Dhaka Higher Secondary 2010/12

{x+2}/8 > 8 so x > 14
x is divided by 8.
That means 16,24,32 . . . . . .
For x=16 the answer is 2 and remaminder 1
for x=24 answer 3 remainder 1
for x=32 answer 4 remainder 1
...... So, the remainder is 1
Ibtehaz Shawon
BRAC University.

long way to go .....

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

Re: Dhaka Higher Secondary 2010/12

i dont think its quite a good proof... Im working on it.
Ibtehaz Shawon
BRAC University.

long way to go .....

Moon
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Re: Dhaka Higher Secondary 2010/12

Please don't post more than once at the same time. You can always edit your post within 1 day.
BTW How did you find that the remainder is $1$ . I think we have $x=8k-2$. So the remainder is?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

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

Re: Dhaka Higher Secondary 2010/12

okay i wont. I didnt find the edit option first.
Anyway... As BdMo said
x+2/8 > 2 from their i found that x > 14. And x will always be divided by 8. So, i checked for the multiple of 8 greater then 14. BTW, delete my unusal post if u r so kind.
Is there any problem bhaia?
Ibtehaz Shawon
BRAC University.

long way to go .....

Zzzz
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Location: 22° 48' 0" N / 89° 33' 0" E

Re: Dhaka Higher Secondary 2010/12

leonardo shawon wrote: And x will always be divided by 8.
I think, you meant 'x will be always divisible by 8'

But, why
Every logical solution to a problem has its own beauty.

Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm
$$x+2 \equiv 0(mod 8)$$
or,$$x \equiv -2(mod8)$$
so,$$x \equiv 6(mod8)$$