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2024 AMC 12B problems

All 25 problems from the 2024 AMC 12B, 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 6The national debt of the United States is on track to reach 5 · 10^13 dollars by 2033. How many digits does this number of dollars have when written…Algebra
  7. 7Problem 7In 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
  8. 8Problem 8What value of x satisfies log _2 x · log _3 x/log _2 x + log _3 x = 2?Algebra
  9. 9Problem 9A 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
  10. 10Problem 10A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, and 7, as well as x, y, z with x ≤ y ≤ z. The range of the list is 7, and the mean and…Algebra
  11. 11Problem 11Let x_n = sin ^2(n°). What is the mean of x_1, x_2, x_3, …, x_90?Algebra
  12. 12Problem 12Suppose z is a complex number with positive imaginary part, with real part greater than 1, and with |z| = 2. In the complex plane, the four points 0…Algebra
  13. 13Problem 13There are real numbers x, y, h, and k that satisfy the system of equations x^2 + y^2 - 6x - 8y = h x^2 + y^2 - 10x + 4y = k. What is the minimum…Algebra
  14. 14Problem 14How many different remainders can result when the 100th power of an integer is divided by 125?Number Theory
  15. 15Problem 15A triangle in the coordinate plane has vertices A(log _2 1, log _2 2), B(log _2 3, log _2 4), and C(log _2 7, log _2 8). What is the area of △ ABC?Geometry
  16. 16Problem 16A group of 16 people will be partitioned into 4 indistinguishable 4-person committees. Each committee will have one chairperson and one secretary…Number Theory
  17. 17Problem 17Integers a and b are randomly chosen without replacement from the set of integers with absolute value not exceeding 10. What is the probability that…Algebra
  18. 18Problem 18The 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
  19. 19Problem 19Equilateral △ ABC with side length 14 is rotated about its center by angle θ, where 0 < θ < 60°, to form △ DEF. See the figure. The area of hexagon…Geometry
  20. 20Problem 20Suppose A, B, and C are points in the plane with AB = 40 and AC = 42, and let x be the length of the line segment from A to the midpoint of BC…Geometry
  21. 21Problem 21The measures of the smallest angles of three different right triangles sum to 90°. All three triangles have side lengths that are primitive…Geometry
  22. 22Problem 22Let △ ABC be a triangle with integer side lengths and the property that ∠ B = 2∠ A. What is the least possible perimeter of such a triangle?Geometry
  23. 23Problem 23A right pyramid has regular octagon ABCDEFGH with side length 1 as its base and apex V. Segments AV and DV are perpendicular. What is the square of…Geometry
  24. 24Problem 24What is the number of ordered triples (a, b, c) of positive integers, with a ≤ b ≤ c ≤ 9, such that there exists a (non-degenerate) triangle △ ABC…Geometry
  25. 25Problem 25Pablo will decorate each of 6 identical white balls with either a striped or a dotted pattern, using either red or blue paint. He will decide on the…Counting & Probability

Practise the same ideas across every year on the topic pages, or browse the full AMC 12 archive.