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2025 AMC 10B problems

All 25 problems from the 2025 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 1The instructions on a 350-gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What…Algebra
  2. 2Problem 2Jerry wrote down the ones digit of each of the first 2025 positive squares: 1, 4, 9, 6, 5, 6, … What is the sum of all the numbers Jerry wrote down?Number Theory
  3. 3Problem 3A Pascal-like triangle has 10 as the top row and 10 followed by 1 as the second row. In each subsequent row the first number is 10, the last number…Algebra
  4. 4Problem 4The value of the two-digit number a b in base seven equals the value of the two-digit number b a in base nine. What is a + b?Number Theory
  5. 5Problem 5In △ ABC, AB = 10, AC = 18, and ∠ B = 130°. Let O be the center of the circle containing points A, B, and C. What is the degree measure of ∠ CAO?Geometry
  6. 6Problem 6The line y = 1/3x + 1 divides the square region defined by 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2 into an upper region and a lower region. The line x = a divides…Geometry
  7. 7Problem 7Frances stands 15 meters directly south of a locked gate in a fence that runs east-west. Immediately behind the fence is a box of chocolates, located…Geometry
  8. 8Problem 8Emmy says to Max, “I ordered 36 math club sweatshirts today.” Max asks, “How much did each shirt cost?” Emmy responds, “I’ll give you a hint. The…Number Theory
  9. 9Problem 9How many ordered triples of integers (x, y, z) satisfy the following system of inequalities? -x - y - z ≤ -2 -x + y + z ≤ 2 x - y + z ≤ 2 x + y - z ≤…Algebra
  10. 10Problem 10Let f(n) = n^3 - 5n^2 + 2n + 8, and let g(n) = n^3 - 6n^2 + 5n + 12. What is the sum of all integer values of n for which f(n)/g(n) is also an…Algebra
  11. 11Problem 11On Monday, 6 students went to the tutoring center at the same time, and each one was randomly assigned to one of the 6 tutors on duty. On Tuesday…Counting & Probability
  12. 12Problem 12The figure below shows an equilateral triangle, a rhombus with a 60° angle, and a regular hexagon, each of them containing some mutually tangent…Geometry
  13. 13Problem 13The altitude to the hypotenuse of a 30-60-90° right triangle is divided into two segments of lengths x < y by the median to the shortest side of the…Geometry
  14. 14Problem 14Nine athletes, no two of whom are the same height, try out for the basketball team. One at a time, they draw a wristband at random, without…Counting & Probability
  15. 15Problem 15The sum sum _k=1^∞ 1/k^3 + 6k^2 + 8k can be expressed as a/b, where a and b are relatively prime positive integers. What is a + b?Algebra
  16. 16Problem 16A circle has been divided into 6 sectors of different sizes. Then 2 of the sectors are painted red, 2 painted green, and 2 painted blue so that no…Counting & Probability
  17. 17Problem 17Consider a decreasing sequence of n positive integers x_1 > x_2 > x_3 > … > x_n that satisfies the following conditions. The average of the first 3…Algebra
  18. 18Problem 18What is the ones digit of the sum ⌊√(1)⌋ + ⌊√(2)⌋ + ⌊√(3)⌋ + … + ⌊√(2024)⌋ + ⌊√(2025)⌋? (Recall that ⌊ x ⌋ denotes the greatest integer less than or…Algebra
  19. 19Problem 19A container has a 1 × 1 square bottom, a 3 × 3 open square top, and four congruent trapezoidal sides, as shown. Starting when the container is empty…Geometry
  20. 20Problem 20Four congruent semicircles are inscribed in a square of side length 1 so that their diameters are on the sides of the square, one endpoint of each…Geometry
  21. 21Problem 21Each of the 9 squares in a 3 × 3 grid is to be colored red, blue, or yellow in such a way that each red square shares an edge with at least one blue…Counting & Probability
  22. 22Problem 22A seven-digit positive integer is chosen at random. What is the probability that the number is divisible by 11, given that the sum of its digits is…Counting & Probability
  23. 23Problem 23A rectangular grid of squares has 141 rows and 91 columns. Each square has room for two numbers. Horace and Vera each fill in the grid by putting the…Number Theory
  24. 24Problem 24A frog hops along the number line according to the following rules. It starts at 0. If it is at 0, then it moves to 1 with probability tfrac 12 and…Counting & Probability
  25. 25Problem 25Square ABCD has sides of length 4. Points P and Q lie on AD and CD, respectively, with AP = 8/5 and DQ = 10/3. A path begins along the line segment…Geometry

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