BdMO National Primary :Problem collection (2014)

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:02 pm

1.If a number is multiplied by itself then the obtained product is a square number.For example,$2\times2=4$ is a square number.The sum of three consequative positive integers is a square number.Which is the smallest such square number?

2.When, $x$ is divided by $10$, the quotient is $y$,with a remainder of $4$. If $x$ and $y$ are both positive integers,what is the remainder when $x$ is divided by $5?$

3.Rubai and Bidushi have some marbles.Bidushi told Rubai ,"if you give me some marbles,I will return one more marble tuan as many as you gave me. "Rubai said,"Alright I will first give you $6 $ marbles.Then Rubai gave Bidushi $6$ marbles and Bidushi returned $7$ marbles to Rubai.Thus after they have exchanged marble $5$ times,Bidushi had no marbles left.How many marbles Bidushi have in the beginning?

4. About same as Junior $2$.
Just One difference "mltplied by $3$ " in the place of "multiplied by $4$."

5. Same as the Junior $3$.

6.A work has to be done in $18$days.A contructor assigned $20$ men to do the tusk.But,after $10$ days it was found that only half of the work was done.So,how many men should he add so that the work will be finshed in time?

7.
Just same as junior $5$.
8. Just same as Junior $6$.

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:10 pm

1
Hint
Sum of any three consequative integers is divided by $3$.
Answer
$9$

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:11 pm

2
Hint
The last digit of the number is $4$.
Answer
$4$

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:23 pm

3
Hint
Bidushi is losing marble every time.
Answer
$5$
This also the question of Higher Secondary $1$

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:25 pm

5
Hint
Use Modular Arithmatic
Answer
$12:70$

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:27 pm

8
Hint
Use Invariance Principle
Answer
No, not possible.

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:31 pm

4
Hint
$3\times 3=9$ ; $34\times 3=102$
Answer
$30$

samiul_samin
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Re: BdMO National Primary :Problem collection (2014)

Unread post by samiul_samin » Fri Feb 16, 2018 4:40 pm

6
Hint
ঐকিক নিয়ম

Answer
$3$

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