Competition · AMC preparation · step 4 of 4

AMC 10 2024B: all 25 problems

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

AMC 10 2024B #1 grade 4+ arithmetic
In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the righ…
AMC 10 2024B #2 grade 5+ arithmetic
What is 10! - 7! · 6!
AMC 10 2024B #3 grade 8+ arithmetic
For how many integer values of x is |2x| ≤ 7 π
AMC 10 2024B #4 grade 6+ arithmetic
Balls numbered 1, 2, 3, ... are deposited in 5 bins, labeled A, B, C, D, and E, using the following procedure. Ball 1 is…
AMC 10 2024B #5 grade 6+ algebra
In the following expression, Melanie changed some of the plus signs to minus signs: 1+3+5+7+...+97+99 When the new expre…
AMC 10 2024B #6 grade 8+ geometry-2d
A rectangle has integer length sides and an area of 2024. What is the least possible perimeter of the rectangle?
AMC 10 2024B #7 grade 6+ number-theory
What is the remainder when 7²⁰²⁴+7²⁰²⁵+7²⁰²⁶ is divided by 19?
AMC 10 2024B #8 grade 8+ arithmetic
Let N be the product of all the positive integer divisors of 42. What is the units digit of N?
AMC 10 2024B #9 grade 8+ arithmetic
Real numbers a, b, and c have arithmetic mean 0. The arithmetic mean of a², b², and c² is 10. What is the arithmetic mea…
AMC 10 2024B #10 grade 8+ geometry-2d
Quadrilateral ABCD is a parallelogram, and E is the midpoint of the side AD. Let F be the intersection of lines EB and A…
AMC 10 2024B #11 grade 8+ geometry-2d
In the figure below WXYZ is a rectangle with WX=4 and WZ=8. Point M lies XY, point A lies on YZ, and ∠ WMA is a right an…
AMC 10 2024B #12 grade 8+ arithmetic
A group of 100 students from different countries meet at a mathematics competition. Each student speaks the same number…
AMC 10 2024B #13 grade 8+ algebra
Positive integers x and y satisfy the equation √x + √y = √1183. What is the minimum possible value of x+y?
AMC 10 2024B #14 grade 8+ probability
A dartboard is the region B in the coordinate plane consisting of points (x, y) such that |x| + |y| ≤ 8. A target T is t…
AMC 10 2024B #15 grade 6+ arithmetic
A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, and 7, as well as x, y , and z with x ≤ y ≤ z. The range of…
AMC 10 2024B #16 grade 4+ rate-ratio
Jerry likes to play with numbers. One day, he wrote all the integers from 1 to 2024 on the whiteboard. Then he repeatedl…
AMC 10 2024B #17 grade 7+ arithmetic
In a race among 5 snails, there is at most one tie, but that tie can involve any number of snails. For example, the resu…
AMC 10 2024B #18 grade 8+ arithmetic
How many different remainders can result when the 100th power of an integer is divided by 125?
AMC 10 2024B #19 grade 8+ arithmetic
In the following table, each question mark is to be replaced by "Possible" or "Not Possible" to indicate whether a nonve…
AMC 10 2024B #20 grade 7+ counting
Three different pairs of shoes are placed in a row so that no left shoe is next to a right shoe from a different pair. I…
AMC 10 2024B #21 grade 8+ geometry-2d
Two straight pipes (circular cylinders), with radii 1 and 1/4, lie parallel and in contact on a flat floor. The figure b…
AMC 10 2024B #22 grade 8+ counting
A group of 16 people will be partitioned into 4 indistinguishable 4-person committees. Each committee will have one chai…
AMC 10 2024B #23 grade 5+ arithmetic
The Fibonacci numbers are defined by F₁ = 1, F₂ = 1, and F_n = F_(n-1) + F_(n-2) for n ≥ 3. What is F₂/F₁ + F₄/F₂ + F₆/F…
AMC 10 2024B #24 grade 6+ arithmetic
Let P(m)=m/2+m²/4+m⁴/8+m⁸/8 How many of the values P(2022), P(2023), P(2024), and P(2025) are integers?
AMC 10 2024B #25 grade 8+ number-theory
Each of 27 bricks (right rectangular prisms) has dimensions a × b × c, where a, b, and c are pairwise relatively prime p…

A parent dashboard for the family lives at sensimlab.com.