BdMO National Junior 2010/1

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Junior 2010/1

Unread post by samiul_samin » Sun Feb 24, 2019 9:21 am

The three digit number $1*3$ is divided by $11$.Find with proof the missing digit(represented by the asterik).

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Junior 2010/1

Unread post by samiul_samin » Sun Feb 24, 2019 1:46 pm

Answer:$\fbox 4$
Solution:
$1×3=3$
So,the given $3$ digit number must be $11×(10a+3)$where $a=0,1,2,3,...$
If $a =0$ ;$11×3=33<100$
If $a =1$ ;$11×13=143>100$ & $143<200$
If $a =2$ ;$11×23=253>200$
So $4$ is the answer.

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