Algebra and Number Sense
Geometry
Probability
Riddles :)
Modular Arithmetic
100
Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need? (AMC 8 2020)
24
100
Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest? (AMC 8 2020)
1920
100
You roll two six-sided dice. What is the probability that the sum of the numbers rolled is either 7 or 11?
2/9
100
I am an odd number. Take away one letter and I become even. What number am I?
Seven
100
What is 17 mod 5?
2
200
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive? (AMC 8 2020 - Problem 5)
15
200
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?
(AMC 8 2020 - Problem 4)
37
200
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 a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this? (AMC 8 Problem 10)
12
200
If you have two coins that add up to 30 cents, and one is not a nickel, what are the coins?
quarter and a nickel
200
Calculate 38 mod 7
3
300
How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.). (AMC 8 2020 Problem 7)
15
300
Rectangle ABCD is inscribed in a semicircle with diameter 
as shown in the figure. Let DA=16 and let FD=AE=9. What is the area of ABCD? (AMC 8 2020 - Problem 18)
240
300
Jamal has a drawer containing 6 green socks, 18 purple socks, and 12 orange socks. After adding more purple socks, Jamal noticed that there is now a 60% chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add? (AMC 8 2020 Problem 13)
9
300
A man walked into a room and found 2 doors. One leads to a treasure, the other to certain doom. There are two guards. One always tells the truth, the other always lies. What question should he ask to find the treasure?
What is "Which door would the other guard say leads to the treasure?" and go through the opposite door.
300
Find the smallest positive integer x that satisfies both of these conditions: x ≡ 2 (mod 3) x ≡ 3 (mod 5)
8
400
Suppose 15% of x equals 20% of y. What percentage of x is y? (AMC 8 2020 - Problem 15)
75
400
In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?
AMC 8 2018 - Problem 15
1
400
When a certain unfair die is rolled, an even number is 
times as likely to appear as an odd number. The die is rolled twice. What is the probability that the sum of the numbers rolled is even?
(AMC 2021 10A - Problem 9)
5/8
400
A farmer needs to cross a river with a wolf, a goat, and a cabbage. He can only carry one at a time. How can he get all three across the river without the wolf eating the goat or the goat eating the cabbage?
Take the goat across first, go back, take the wolf across, bring the goat back, take the cabbage across, then go back and bring the goat.
400
Using the squaring method, find the remainder when 381 is divided by 5.
3
500
AMC 10 - Problem 3
-1
500
2022 AMC 10B - Problem 2
20
500
A radio program has a quiz consisting of multiple-choice questions, each with 3 choices. A contestant wins if he or she gets 2 or more of the questions right. The contestant answers randomly to each question. What is the probability of winning? (2017 - AMC 10B - Problem 9)
7/27
500
A man is looking at a portrait. He says, "Brothers and sisters, I have none, but this man’s father is my father’s son." Who is in the portrait?
What is the man’s son?
500
Using the squaring method, determine the last digit of 72023
The last digit of a number is the number mod 10. So let's think about 72023mod10. We'll use the squaring method and Euler's theorem. Solution: First, we need to find the pattern of last digits of powers of 7: 7¹ ≡ 7 (mod 10) 7² ≡ 9 (mod 10) 7³ ≡ 3 (mod 10) 7⁴ ≡ 1 (mod 10)
We see the pattern repeats every 4 steps. So we can use 7²⁰²³ ≡ 7²⁰²³ mod 4 (mod 10)
2023 ≡ 3 (mod 4)
So 7²⁰²³ will have the same last digit as 7³, which is 3.
Therefore, the last digit of 7²⁰²³ is 3.