MathMania 2025

  1. How much of a 10% acid solution and a 15% acid solution must you use to get 20 liters of 12% acid sollution?
  2. What is the measure (in degrees) of a interior angle of a regular polygon with 30 sides?
  3. A box contains 3 red balls, 4 blue balls, and 5 green balls. If three balls are selected at random from the box, what is the probability that one ball of each color is selected? Please give your answer as a reduced fraction.
  4. What is the angle (in degrees) between the minute hand and hour hand of a clock at 2:15?
  5. In the figure shown, ABCD is a square, AB = 1, and ABE is an equilateral triangle. What is the area of triangle CDE to 5 decimal places?
    square with triangles inside

  6. What is the radius of the circle inscribed in a triangle with sides of length 13,20, and 21? Give your answer as a reduced fraction.

  7. Solve log4(log3(log2 x)) = − 1/2.

  8. As it inflates, the surface area of a spherical balloon increases 21%. By what percentage does its volume increase?

  9. From a pool of 7 women and 6 men, a committee with 5 members is to be chosen. In how many ways can this be done if there must be at least one man and at least one woman on the committee?

  10. What are the first three digits of 20252025