BdMO National Primary 2016/3

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Primary 2016/3

Unread post by samiul_samin » Thu Feb 15, 2018 11:11 am

The sum of the digits of some two digits number is $11$ and these number can be written as the product of only two prime numbers.What is the sum of these two digits numbers?

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samiul_samin
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Re: BdMO National Primary 2016/3

Unread post by samiul_samin » Thu Feb 15, 2018 8:01 pm

Hint
Let,$11=a+b$ find all $(a,b)$ such that $0<a<10,0<b<10$
Answer
$177$

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samiul_samin
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Re: BdMO National Primary 2016/3

Unread post by samiul_samin » Thu Feb 15, 2018 8:07 pm

Solution
$11=2+9=3+8=4+7=5+6=6+5=7+4=8+3=9+2$
So, the numbers are $29,38,47,56,65,74,83,92$
Here, $29,47,83$ are primes
And $56,92 $ can not be written as the product of only two primes.
So,the desired numbers are$38,74,65$
Now,$38+74+65=177$
The answer is $\fbox {177}$

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