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 chairs. The rest of the people remained standing. If there were 6 empty chairs, how many people were there in the room?
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?
Problem 4: In square 𝐀𝐁𝐂𝐄, 𝐀𝐅 = 𝟑𝐅𝐄 and 𝐂𝐃 = 𝟑𝐄𝐃. What is the ratio of the area of triangle 𝐁𝐅𝐃 and square ABCE?
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?
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-digits ‘good’ even numbers are there? Try to find their number without writing all such number!
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 × 𝒂𝒃𝒄, then determine the 𝒂𝒃𝒄.
Problem 8: From 1 – 6 nodes, one can go only right side and downward. From 7 – 11 nodes, one can go right side or along the diagonal. If you start from 1, in how many ways can you reach 12?