MATHCOUNTS 2020 Countdown Round #11-20

Front

What is the ratio of green to blue marbles if there are 10 green and 24 blue marbles?

Back

The ratio is 5:12.

Front

If a movie is released 102 days from a Saturday, what day of the week is it 102 days earlier?

Back

It is a Tuesday.

Front

Calculate the value of the expression (1 − 8) ÷ (2 − 7) + (3 − 6) ÷ (4 − 5).

Back

The value is 4.4.

Front

What is the area of a triangle with side lengths 5, 5, and 6?

Back

The area is 12 square units.

Front

What is the product of the least common multiple and the greatest common factor of 10 and 15?

Back

The product is 150.

Front

Define the least common multiple (LCM).

Back

The least common multiple of two numbers is the smallest multiple that is evenly divisible by both numbers.

Front

Define the greatest common factor (GCF).

Back

The greatest common factor of two numbers is the largest number that divides both of them without leaving a remainder.

Front

How do you find the area of a triangle using Heron's formula?

Back

Heron's formula: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.

Front

What is the formula for calculating the ratio of two quantities?

Back

Ratio = Quantity 1 : Quantity 2.

Front

What is the significance of the order of operations in mathematics?

Back

The order of operations determines the sequence in which calculations are performed to ensure accurate results.