**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**.

- Tue Jan 08, 2019 1:45 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/7
- Replies:
**1** - Views:
**970**

- Tue Jan 08, 2019 1:32 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/6
- Replies:
**1** - Views:
**920**

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!

- Tue Jan 08, 2019 1:29 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/5
- Replies:
**1** - Views:
**918**

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?

- Tue Jan 08, 2019 1:27 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/4
- Replies:
**4** - Views:
**1753**

In square $ABCE$, $AF=3FE$ & $CD=3ED$. What is the ratio of the area of triangle $\triangle BFD$ and square $ABCE$ ?

- Tue Jan 08, 2019 1:21 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/3
- Replies:
**1** - Views:
**927**

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 ?

- Tue Jan 08, 2019 1:19 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/2
- Replies:
**1** - Views:
**878**

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 ?

- Tue Jan 08, 2019 1:18 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Primary 2018/1
- Replies:
**1** - Views:
**913**

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?

- Tue Jan 08, 2019 1:16 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Junior 2018/6
- Replies:
**4** - Views:
**1451**

Given $8$ lines on a plane and no two of them are parallel. Prove that, at least two of them form an angle less than 23°.

- Tue Jan 08, 2019 1:08 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Junior 2018/5
- Replies:
**1** - Views:
**1026**

$3x^2 + y^2 = 108$ ;

Determine all the positive integer values of $x$ and $y$.

Determine all the positive integer values of $x$ and $y$.

- Tue Jan 08, 2019 1:05 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO National Junior 2018/4
- Replies:
**1** - Views:
**986**

The squares of three positive numbers add up to $2018$. The biggest of these three numbers is the sum of the smaller two. If the difference between the smaller two numbers is $2$, what is the difference between the cubes of the smaller two numbers?