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2024 AMC 10B problems

All 25 problems from the 2024 AMC 10B, with answer choices, worked solutions and hints. Problems are roughly ordered by difficulty: 1–10 are the most approachable, 19–25 the hardest.

Problems

  1. 1Problem 1In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the right. How many people are in the…Counting & Probability
  2. 2Problem 2What is 10! - 7! · 6!?Counting & Probability
  3. 3Problem 3For how many integer values of x is |2x| ≤ 7π?Algebra
  4. 4Problem 4Balls numbered 1, 2, 3, … are deposited in 5 bins, labeled A, B, C, D, and E, using the following procedure. Ball 1 is deposited in bin A, and balls…Algebra
  5. 5Problem 5In the following expression, Melanie changed some of the plus signs to minus signs: 1 + 3 + 5 + 7 + … + 97 + 99 When the new expression was…Algebra
  6. 6Problem 6A rectangle has integer side lengths and an area of 2024. What is the least possible perimeter of the rectangle?Algebra
  7. 7Problem 7What is the remainder when 7^2024 + 7^2025 + 7^2026 is divided by 19?Algebra
  8. 8Problem 8Let N be the product of all the positive integer divisors of 42. What is the units digit of N?Number Theory
  9. 9Problem 9Real numbers a, b, and c have arithmetic mean 0. The arithmetic mean of a^2, b^2, and c^2 is 10. What is the arithmetic mean of ab, ac, and bc?Algebra
  10. 10Problem 10Quadrilateral ABCD is a parallelogram, and E is the midpoint of the side AD. Let F be the intersection of lines EB and AC. What is the ratio of the…Geometry
  11. 11Problem 11In the figure below WXYZ is a rectangle with WX = 4 and WZ = 8. Point M lies on XY, point A lies on YZ, and ∠ WMA is a right angle. The areas of △…Geometry
  12. 12Problem 12A group of 100 students from different countries meet at a mathematics competition. Each student speaks the same number of languages, and, for every…Counting & Probability
  13. 13Problem 13Positive integers x and y satisfy the equation √(x) + √(y) = √(1183). What is the minimum possible value of x + y?Algebra
  14. 14Problem 14A dartboard is the region B in the coordinate plane consisting of points (x, y) such that |x| + |y| ≤ 8. A target T is the region where (x^2 + y^2 -…Geometry
  15. 15Problem 15A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, 7, as well as x, y, z with x ≤ y ≤ z. The range of the list is 7, and the mean and median…Algebra
  16. 16Problem 16Jerry likes to play with numbers. One day, he wrote all the integers from 1 to 2024 on the whiteboard. Then he repeatedly chose four numbers on the…Algebra
  17. 17Problem 17In a race among 5 snails, there is at most one tie, but that tie can involve any number of snails. For example, the result of the race might be that…Counting & Probability
  18. 18Problem 18How many different remainders can result when the 100th power of an integer is divided by 125?Number Theory
  19. 19Problem 19In the following table, each question mark is to be replaced by “Possible” or “Not Possible” to indicate whether a nonvertical line with the given…Geometry
  20. 20Problem 20Three different pairs of shoes are placed in a row so that no left shoe is next to a right shoe from a different pair. In how many ways can these six…Counting & Probability
  21. 21Problem 21Two straight pipes (circular cylinders), with radii 1 and tfrac 14, lie parallel and in contact on a flat floor. The figure below shows a head-on…Geometry
  22. 22Problem 22A group of 16 people will be partitioned into 4 indistinguishable 4-person committees. Each committee will have one chairperson and one secretary…Number Theory
  23. 23Problem 23The Fibonacci numbers are defined by F_1 = 1, F_2 = 1, and F_n = F_n-1 + F_n-2 for n ≥ 3. What is F_2/F_1 + F_4/F_2 + F_6/F_3 + … + frac F_20F_10?Algebra
  24. 24Problem 24Let P(m) = m/2 + m^2/4 + m^4/8 + m^8/8. How many of the values of P(2022), P(2023), P(2024), and P(2025) are integers?Number Theory
  25. 25Problem 25Each of 27 bricks (right rectangular prisms) has dimensions a × b × c, where a, b, and c are pairwise relatively prime positive integers. These…Geometry

Practise the same ideas across every year on the topic pages, or browse the full AMC 10 archive.