International Team Mathematical Competition
Description: This quiz consists of 15 questions related to the International Team Mathematical Competition (ITMC). These questions cover various topics from algebra, geometry, number theory, and combinatorics. The questions are designed to challenge and stimulate the mathematical thinking of participants. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: itmc mathematics algebra geometry number theory combinatorics |
In a certain country, the sum of the first 100 positive integers is equal to the sum of the first 100 even integers. What is the sum of the first 100 odd integers?
A regular hexagon has side length 6 cm. What is the area of the hexagon?
In a group of 10 people, there are 4 men and 6 women. In how many ways can a committee of 3 people be formed if it must include at least 1 man and 1 woman?
What is the value of the expression (2 + 3i)² - (2 - 3i)²?
A farmer has 120 acres of land. He plants corn on 40% of the land, soybeans on 30% of the land, and wheat on the remaining land. How many acres of land does he plant wheat on?
In a triangle, the ratio of the lengths of two sides is 3:4. If the perimeter of the triangle is 42 cm, what is the length of the third side?
A train leaves a station at 10:00 AM and travels at a speed of 60 mph. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 75 mph. At what time will the second train overtake the first train?
A rectangular garden has a length of 12 meters and a width of 8 meters. What is the area of the garden in square meters?
A company has 100 employees, of which 60% are men and 40% are women. If 20% of the men and 30% of the women leave the company, what percentage of the remaining employees are women?
A circle has a radius of 10 cm. What is the circumference of the circle in centimeters?
A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that it is a red ball?
A farmer has 100 acres of land. He plants corn on 40% of the land, soybeans on 30% of the land, and wheat on the remaining land. How many acres of land does he plant corn on?
A train leaves a station at 10:00 AM and travels at a speed of 60 mph. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 75 mph. How far apart are the two trains at 12:00 PM?
A rectangular garden has a length of 12 meters and a width of 8 meters. What is the perimeter of the garden in meters?
A company has 100 employees, of which 60% are men and 40% are women. If 20% of the men and 30% of the women leave the company, how many employees remain in the company?