MATHCOUNTS 2020 Countdown Round #11-20

What is the value of the expression (1 − 8) ÷ (2 − 7) + (3 − 6) ÷ (4 − 5)? Express your answer as a decimal to the nearest tenth.

Carl received a text notifying him that the release date for “102 Dachshunds” would be 102 days from the notification date. If the movie release day will be a Saturday, on what day of the week did Carl receive the text?

A jar contains 8 red, 10 green, 36 yellow and some blue marbles. If the ratio of green to blue marbles is 5:12, how many blue marbles are in the jar?

What is the area of the triangle with side lengths 5, 5 and 6, in square units?

If a  b =  $a^2-b$ , what is the value of 12  12?

A math club for seventh and eighth graders starts with 14 seventh graders and 8 eighth graders. Each week, 3 new seventh graders and 4 new eighth graders join the club. What will be the total number of members when the club has an equal number of seventh graders and eighth graders?

What is the surface area, in square centimeters, of a cube with volume  $1000\ cm^2$ ? 

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

The product of three distinct prime numbers is 130. What is the greatest of the three prime numbers?

How many distinct Halloween costumes can be made by choosing one of three different capes, one of two different wigs and two of four different accessories?