Competition · AMC preparation · step 4 of 4

AMC 8 2020: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 8 2020 #1 grade 4+ rate-ratio
Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as…
AMC 8 2020 #2 grade 3+ arithmetic
Four friends do yardwork for their neighbors over the weekend, earning 15, 20, 25, and $40, respectively. They decide to…
AMC 8 2020 #3 grade 4+ arithmetic, geometry-2d
Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Car…
AMC 8 2020 #4 grade 4+ pattern
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon con…
AMC 8 2020 #5 grade 4+ rate-ratio
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice in…
AMC 8 2020 #6 grade 1+ logic
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in…
AMC 8 2020 #7 grade 4+ counting
How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is on…
AMC 8 2020 #8 grade 5+ arithmetic
Ricardo has 2020 coins, some of which are pennies (1-cent coins) and the rest of which are nickels (5-cent coins). He ha…
AMC 8 2020 #9 grade 3+ geometry-3d, counting
Akash's birthday cake is in the form of a 4 × 4 × 4 inch cube. The cake has icing on the top and the four side faces, an…
AMC 8 2020 #10 grade 7+ counting
Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on…
AMC 8 2020 #11 grade 6+ rate-ratio
After school, Maya and Naomi headed to the beach, 6 miles away. Maya decided to bike while Naomi took a bus. The graph b…
AMC 8 2020 #12 grade 4+ algebra, number-theory
For a positive integer n, the factorial notation n! represents the product of the integers from n to 1. What value of N…
AMC 8 2020 #13 grade 6+ probability, algebra
Jamal has a drawer containing 6 green socks, 18 purple socks, and 12 orange socks. After adding more purple socks, Jamal…
AMC 8 2020 #14 grade 6+ arithmetic
There are 20 cities in the County of Newton. Their populations are shown in the bar chart below. The average population…
AMC 8 2020 #15 grade 6+ rate-ratio
Suppose 15% of x equals 20% of y. What percentage of x is y?
AMC 8 2020 #16 grade 6+ algebra, logic
Each of the points A,B,C,D,E, and F in the figure below represents a different digit from 1 to 6. Each of the five lines…
AMC 8 2020 #17 grade 6+ number-theory, counting
How many positive integer factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely 1,2,3,4,6,…
AMC 8 2020 #18 grade 8+ geometry-2d
Rectangle ABCD is inscribed in a semicircle with diameter FE, as shown in the figure. Let DA=16, and let FD=AE=9. What i…
AMC 8 2020 #19 grade 4+ number-theory, counting
A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, b…
AMC 8 2020 #20 grade 6+ number-theory, logic
A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that ea…
AMC 8 2020 #21 grade 5+ counting
A game board consists of 64 squares that alternate in color between black and white. The figure below shows square P in…
AMC 8 2020 #22 grade 4+ number-theory, logic
When a positive integer N is fed into a machine, the output is a number calculated according to the rule shown below. Fo…
AMC 8 2020 #23 grade 7+ counting
Five different awards are to be given to three students. Each student will receive at least one award. In how many diffe…
AMC 8 2020 #24 grade 7+ geometry-2d, algebra
A large square region is paved with n² gray square tiles, each measuring s inches on a side. A border d inches wide surr…
AMC 8 2020 #25 grade 8+ geometry-2d, algebra
Rectangles R₁ and R₂, and squares S₁, S₂, and S₃, shown below, combine to form a rectangle that is 3322 units wide and 2…

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