Question bank AMC8 2027

Evaluate $4(-1+2-3+4-5+\ldots+1000)$.

Rectangle $ABCD$ and right triangle $CDE$ have equal areas. They fit together to form a trapezoid. What is the length of $DE$?

Pythagoras Middle School's mathematics club has $100$ girls and $80$ boys. Its chemistry club has $80$ girls and $100$ boys. Sixty girls belong to both clubs, and the clubs together have $230$ distinct members. How many boys belong to the mathematics club but not the chemistry club?

A basketball league has two groups of 6 teams. Teams in the same group play twice; teams in different groups play once. How many games are played?

Find the sum of the mean, median, and mode of 3, 3, 0, 1, 4, 0, 3.

Walter has 1/8 of a tank of fuel. He buys 7.5 gallons for\$10 and now has 5/8 of a tank. What is the tank capacity in gallons?

Nonnegative integers $w$, $x$, $y$, $z$ satisfy 2^w·3^x·5^y·7^z=588. Find 2 w+3 x+5 y+7 z.

Alice computes $19-(5+4)$, while Jacky ignores the parentheses and computes $19-5+4$. If Alice's answer is $A$ and Jacky's answer is $J$, what is $A+J$?

Square $ABCD$ has side length $3$. Segments $CM$ and $CN$ divide the square into three regions of equal area. Given $CM=CN$, find $CM$.

Three teachers named Toán, Lý, and Hoá meet at a conference. The physics teacher says, "Interestingly, one of us teaches mathematics, one physics, and one chemistry, but none teaches the subject corresponding to his name." Teacher Toán agrees. What subject does teacher Hoá teach?

How many triangles have vertices among the six points shown in two rows of three?

Roll a fair die twice. What is the probability that the first result is at least the second?

Dallas buses leave on the hour, and each trip takes 5 hours. Consider a Houston departure at half past an hour, traveling the same route. How many Dallas buses does it meet strictly between the terminals?

Multiply all even numbers from 2 through 98 except those ending in 0. What is the units digit of the product?

For nonzero real numbers, define $a\otimes b=\frac{a^2}{b}$. Evaluate $[(1\otimes2)\otimes3]-[1\otimes(2\otimes3)]$.

Triangle $ABC$ is isosceles with $AB=AC$ and $\angle BAC=36^\circ$. Segment $CD$ bisects $\angle ACB$. Find $\angle BDC$.

Five runners $P,Q,R,S,T$ compete in a race. $P$ is faster than $Q$ and $R$. $Q$ is faster than $S$. $T$ is slower than $P$ but faster than $Q$. Which runners cannot finish third?

How many V-shaped triominoes (the illustrated L triomino) can be cut from a $5\times5$ grid?

Among 36 classmates, 12 prefer oranges, 8 apples, 6 strawberries, and the remainder split equally between cherries and kiwi. What pie-chart angle represents cherries?

Sales tax in Bergville is 6% and coats are 20% off. Jack adds 6% tax to a\$90 coat and then discounts 20%. Jill discounts 20% first and then adds 6% tax. What is the difference?