BDMO 2018 National Olympiad: Problemsets
Posted: Tue Jan 08, 2019 4:43 pm
Bangladesh Mathematical Olympiad 2018 : Primary
problem 1
The average age of the $5$ people in a Room is $30$. The average age of the $10$ people in another Room is $24$. If the two groups are combined, what is the average age of all the people?
http://matholympiad.org.bd/forum/viewto ... =13&t=5372
Problem 2
Two-thirds of the people in a room sat in three-fourths of the chairs. The rest of the people remained standing. If there were $6$ empty chairs, how many people were there in the room ?
http://matholympiad.org.bd/forum/viewto ... =13&t=5373
Problem 3
The area of a rectangle is $120$. All the lengths of the sides of this rectangle are integer, what can be the lowest possible perimeter of this rectangle ?
http://matholympiad.org.bd/forum/viewto ... =13&t=5374
Problem 4
In square $ABCE$, $AF=3FE$ & $CD=3ED$. What is the ratio of the area of triangle $\triangle BFD$ and square $ABCE$ ? http://matholympiad.org.bd/forum/viewto ... =13&t=5375
Problem 5
A singles tournament had six players. Each player played every other player only once, with no ties. If Pritom won $3$ games, Monisha won $2$ games, Sadman won $3$ games, Richita won $3$ games and Somlota won $2$ games, how many games did Zubayer win?
http://matholympiad.org.bd/forum/viewto ... =13&t=5376
Problem 6
An even number is called a ‘good’ even number if its first and last digits are also an even number. How many $3$-digit ‘good’ even numbers are there? Try to find their number without writing all such number!
http://matholympiad.org.bd/forum/viewto ... =13&t=5377
Problem 7
abc is a three digit number. abc is appended to abc to create a six digit number abcabc. If abcabc is divisible by abc $\times$ abc, then determine the abc .
http://matholympiad.org.bd/forum/viewto ... =13&t=5378
Problem 8
From $1$ to $6$ nodes, one can go only right side and downward. From $7$ to $11$ nodes, one can go right side or along the diagonal. If you start from $1$, in how many ways can you reach $12$ ? http://matholympiad.org.bd/forum/viewto ... =13&t=5379
problem 1
The average age of the $5$ people in a Room is $30$. The average age of the $10$ people in another Room is $24$. If the two groups are combined, what is the average age of all the people?
http://matholympiad.org.bd/forum/viewto ... =13&t=5372
Problem 2
Two-thirds of the people in a room sat in three-fourths of the chairs. The rest of the people remained standing. If there were $6$ empty chairs, how many people were there in the room ?
http://matholympiad.org.bd/forum/viewto ... =13&t=5373
Problem 3
The area of a rectangle is $120$. All the lengths of the sides of this rectangle are integer, what can be the lowest possible perimeter of this rectangle ?
http://matholympiad.org.bd/forum/viewto ... =13&t=5374
Problem 4
In square $ABCE$, $AF=3FE$ & $CD=3ED$. What is the ratio of the area of triangle $\triangle BFD$ and square $ABCE$ ? http://matholympiad.org.bd/forum/viewto ... =13&t=5375
Problem 5
A singles tournament had six players. Each player played every other player only once, with no ties. If Pritom won $3$ games, Monisha won $2$ games, Sadman won $3$ games, Richita won $3$ games and Somlota won $2$ games, how many games did Zubayer win?
http://matholympiad.org.bd/forum/viewto ... =13&t=5376
Problem 6
An even number is called a ‘good’ even number if its first and last digits are also an even number. How many $3$-digit ‘good’ even numbers are there? Try to find their number without writing all such number!
http://matholympiad.org.bd/forum/viewto ... =13&t=5377
Problem 7
abc is a three digit number. abc is appended to abc to create a six digit number abcabc. If abcabc is divisible by abc $\times$ abc, then determine the abc .
http://matholympiad.org.bd/forum/viewto ... =13&t=5378
Problem 8
From $1$ to $6$ nodes, one can go only right side and downward. From $7$ to $11$ nodes, one can go right side or along the diagonal. If you start from $1$, in how many ways can you reach $12$ ? http://matholympiad.org.bd/forum/viewto ... =13&t=5379