ABMC
AMC 8
Countdown round
Mathcounts
Miscellaneous
100
Joshua hates writing essays for homework, but his teacher Mr. Meesh assigns two essays every 3 weeks. However, Mr. Meesh favors Joshua, so he allows Joshua to skip one essay out of every 4 that are assigned. How many essays does Joshua have to write in a 24-week school year?
What is 12?
100
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?
What is 88?
100
The Sharks have a win-loss record of 36-14. What percent of the games played have the Sharks won?
What is 72%?
100
What is the least common multiple of 143 and 1001?
What is 1001?
100
6 ÷ 2(1+2)=?
(Rules before 1917)
What is 1?
200
6. Anuj has a circular pizza with diameter A inches, which is cut into B congruent slices, where A, B are positive integers. If one of Anuj’s pizza slices has a perimeter of 3pi + 30 inches, find A + B.
What is 40?
200
What is the largest power of 2 that is a divisor of 134-114?
What is 32?
200
Jin has scores of 80, 91 and 96 on his tests this term. What is the lowest score that he can get on the next test that will raise his average to at least 90?
What is 93?
200
How many of the first one thousand perfect fourth powers have either 1 or 6 as their units digit?
What is 800?
200
Convert 122 in the base of 6 to the base of 4
What is 302?
300
How many consecutive zeroes are at the end of 12! when it is expressed in base 6?
What is 5?
300
The "Middle School Eight" basketball conference has 8 teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 4 games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight" teams?
What is 88?
300
What is the sum of the solutions of the equation 4x2 = 12x + 7?
What is 3?
300
What is the greatest integer k such that 2k is a factor of 67!?
What is 64?
300
What is the median of the following list of 4040 numbers? 1, 2, 3, ..., 2020, 12, 22, 32, ..., 20202
What is 1976.5?
400
There is a sphere-container, filled to the brim with fruit punch, of diameter 6. The contents of this container are poured into a rectangular prism container, again filled to the brim, of dimensions 2pi by 4 by 3. However, there is an excess amount in the original container. If all the excess drink is poured into conical containers with diameter 4 and height 3, how many containers will be used?
What is 3?
400
An integer between 1000 and 9999, inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
What is 56/225?
400
What is the remainder when 1 + 3 + 32 + 33 + ⋯ + 32020 is divided by 81?
What is 40?
400
How many of the first 1024 positive integers are neither perfect squares nor perfect fifth-powers?
What is 990?
400
Two people(A and B) are meeting at the airport between 9:00 am and 10:00 am. Person A will go at a random time and stay there for 30 minutes, but Person B is less patient and will stay there for only 10 minutes. They will meet if one is leaving the airport and the other is entering the airport. What is the probability they will meet?
What is 19/36?
500
Let z(n) represent the number of trailing zeroes of n!. What is z(z(6!))? (Note: n! = n·(n−1)· · · 2 · 1)
What is 43?
500
How many perfect cubes lie between 28+1 and 218+1, inclusive?
What is 58?
500
What is the value of 20202− 2020 × 2019 + 20192 − 2019 × 2020?
What is 1?
500
How many of the first 2019 positive integers have no odd single-digit prime factors?
What is 923?
500
The roots of the polynomial 
are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by 
units. What is the volume of the new box?
A)24/5 B)42/5 C)81/5 D)30 E)48
What is D or 30? Additional question who's batman?