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2024 AMC 10A problems

All 25 problems from the 2024 AMC 10A, 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 1What is the value of 9901 · 101 - 99 · 10101?Algebra
  2. 2Problem 2A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form T = aL + bG, where a and b are constants…Algebra
  3. 3Problem 3What is the sum of the digits of the smallest prime that can be written as a sum of 5 distinct primes?Number Theory
  4. 4Problem 4The number 2024 is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write…Algebra
  5. 5Problem 5What is the least value of n such that n! is a multiple of 2024?Number Theory
  6. 6Problem 6What is the minimum number of successive swaps of adjacent letters in the string ABCDEF that are needed to change the string to FEDCBA? (For example…Counting & Probability
  7. 7Problem 7The product of three integers is 60. What is the least possible positive sum of the three integers?Algebra
  8. 8Problem 8Amy, Bomani, Charlie, and Daria work in a chocolate factory. On Monday Amy, Bomani, and Charlie started working at 1:00 PM and were able to pack 4…Algebra
  9. 9Problem 9In how many ways can 6 juniors and 6 seniors form 3 disjoint teams of 4 people so that each team has 2 juniors and 2 seniors?Counting & Probability
  10. 10Problem 10Consider the following operation. Given a positive integer n, if n is a multiple of 3, then you replace n by n/3. If n is not a multiple of 3, then…Algebra
  11. 11Problem 11How many ordered pairs of integers (m, n) satisfy √(n^2 - 49) = m?Algebra
  12. 12Problem 12Zelda played the Adventures of Math game on August 1 and scored 1700 points. She continued to play daily over the next 5 days. The bar chart below…Algebra
  13. 13Problem 13Two transformations are said to commute if applying the first followed by the second gives the same result as applying the second followed by the…Algebra
  14. 14Problem 14One side of an equilateral triangle of height 24 lies on line ℓ. A circle of radius 12 is tangent to ℓ and is externally tangent to the triangle. The…Geometry
  15. 15Problem 15Let M be the greatest integer such that both M + 1213 and M + 3773 are perfect squares. What is the units digit of M?Algebra
  16. 16Problem 16All of the rectangles in the figure below, which is drawn to scale, are similar to the enclosing rectangle. Each number represents the area of the…Geometry
  17. 17Problem 17Two teams are in a best-two-out-of-three playoff: the teams will play at most 3 games, and the winner of the playoff is the first team to win 2…Algebra
  18. 18Problem 18There are exactly K positive integers b with 5 ≤ b ≤ 2024 such that the base-b integer 2024_b is divisible by 16 (where 16 is in base ten). What is…Number Theory
  19. 19Problem 19The first three terms of a geometric sequence are the integers a, 720, and b, where a < 720 < b. What is the sum of the digits of the least possible…Algebra
  20. 20Problem 20Let S be a subset of {1, 2, 3, …, 2024} such that the following two conditions hold: • If x and y are distinct elements of S, then |x - y| > 2. • If…Algebra
  21. 21Problem 21The numbers, in order, of each row and the numbers, in order, of each column of a 5 × 5 array of integers form an arithmetic progression of length 5…Algebra
  22. 22Problem 22Let mathcal K be the kite formed by joining two right triangles with legs 1 and sqrt 3 along a common hypotenuse. Eight copies of mathcal K are used…Geometry
  23. 23Problem 23Integers a, b, and c satisfy ab + c = 100, bc + a = 87, ca + b = 60. What is ab + bc + ca?Algebra
  24. 24Problem 24A bee is moving in three-dimensional space. A fair six-sided die with faces labeled A^+, A^-, B^+, B^-, C^+, and C^- is rolled. Suppose the bee…Geometry
  25. 25Problem 25The figure below shows a dotted grid 8 cells wide and 3 cells tall consisting of 1'' × 1'' squares. Carl places 1-inch toothpicks along some of the…Counting & Probability

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