# BdMO

## BdMO Higher Secondary Problems and Solutions 2018

Problem 1: Find solutions of the following equation that are real numbers, x2(2 – x)2 = 1 + 2(1 – x)2 Problem 2: AB is the diameter of a circle. Tangents AD and BC are drawn so that AC and BD intersect at a point on the circle. Suppose AD = a and BC = …

## BdMO Secondary Problems and Solutions 2018

Problem 1: Find solutions of the following equation that are real numbers, x2(2 – x)2 = 1 + 2(1 – x)2 Problem 2: AB is the diameter of a circle. Tangents AD and BC are drawn so that AC and BD intersect at a point on the circle. Suppose AD = a and BC = …

## BdMO Junior Problems and Solutions 2018

Problem 1: The area of a rectangle is 240. All the lengths of the sides of this rectangle are integer, what can be the lowest possible perimeter of this rectangle? Problem 2: If the average of first n positive integers is 2018, then find the value of n? Problem 3: Shoumo, Oindry and Esha take …

## BdMO Higher Secondary Problems and Solutions 2019

Problem 1: Find all prime numbers such that the square of the prime number can be written as the sum of cubes of two positive integers. Problem 2: Prove that, if a, b, c are positive real numbers, Problem 3: Let α and ꙍ be 2 circles such that ꙍ goes through the center of …

## BdMO Secondary Problems and Solutions 2019

Problem 1: At some math Olympiad, 72 medals were handed out. Afterwards, it was found that Sumon had lost the receipt! He only remembers that the total price of the medals was a 5-digit number, and the three middle digits were all 9. If the price of all the medals were the same integer, what …

## BdMO Primary Problems and Solutions 2018

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? Problem 2: Two-thirds of the people in a room sat in three-fourths of the …

## BdMO Higher Secondary Problems and Solutions 2020

Problem 1: Lazim rolls two 24-sided dice. From the two rolls, Lazim selects the die with the highest number. N is an integer not greater than 24. What is the largest possible value for N such that there is a more than 50% chance that the die Lazim selects is larger than or equal to …

## BdMO Secondary Problems and Solutions 2020

Problem 1: Let, m be a real number such that the following equation holds: 3m = 4m Compute the sum of all possible distinct values that (3^3^m)) / m4 can take. [xy = yth power of x. 32 = 9] Problem 2: A polygon is called beautiful if you can pick three of its vertices …

## BdMO Junior Problems and Solutions 2020

Problem 1: m and n are positive integers such that 1 + 2m = n2. Find the sum of all possible values of 10m+n. [xy = yth power of x. 32 = 9] Problem 2: Consider rectangle ABCD. Let E be the midpoint of side AD and let F be the midpoint of ED. Let …

## BdMO Primary Problems and Solutions 2020

Problem 1: It’s Ramadan time, and Saad is out buying Iftar! At the store, he can either get 3kg Jilapi and 4kg Halim for 53 Taka or 5kg Jilapi and 2kg Halim for 37 Taka. But Saad really likes Halim and doesn’t like Jilapi at all! How much should it cost him to get 10kg …