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2017 AMC 12B problems

All 25 problems from the 2017 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 1Kymbrea’s comic book collection currently has 30 comic books in it, and she is adding to her collection at the rate of 2 comic books per month…Algebra
  2. 2Problem 2Real numbers x, y, and z satisfy the inequalities 0 < x < 1, -1 < y < 0, and 1 < z < 2. Which of the following numbers is necessarily positive?Algebra
  3. 3Problem 3Suppose that x and y are nonzero real numbers such that 3x + y/x - 3y = -2. What is the value of x + 3y/3x - y?Algebra
  4. 4Problem 4Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had gone half the distance to her…Algebra
  5. 5Problem 5The data set [6, 19, 33, 33, 39, 41, 41, 43, 51, 57] has median Q_2 = 40, first quartile Q_1 = 33, and third quartile Q_3 = 43. An outlier in a data…Algebra
  6. 6Problem 6The circle having (0, 0) and (8, 6) as the endpoints of a diameter intersects the x-axis at a second point. What is the x-coordinate of this point?Geometry
  7. 7Problem 7The functions sin (x) and cos (x) are periodic with least period 2π. What is the least period of the function cos (sin (x))?Algebra
  8. 8Problem 8The ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. What is the square of the…Algebra
  9. 9Problem 9A circle has center (-10, -4) and radius 13. Another circle has center (3, 9) and radius √(65). The line passing through the two points of…Geometry
  10. 10Problem 10At Typico High School, 60% of the students like dancing, and the rest dislike it. Of those who like dancing, 80% say that they like it, and the rest…Counting & Probability
  11. 11Problem 11Call a positive integer monotonous if it is a one-digit number or its digits, when read from left to right, form either a strictly increasing or a…Counting & Probability
  12. 12Problem 12What is the sum of the roots of z^12 = 64 that have a positive real part?Algebra
  13. 13Problem 13In the figure below, 3 of the 6 disks are to be painted blue, 2 are to be painted red, and 1 is to be painted green. Two paintings that can be…
  14. 14Problem 14An ice-cream novelty item consists of a cup in the shape of a 4-inch-tall frustum of a right circular cone, with a 2-inch-diameter base at the bottom…Geometry
  15. 15Problem 15Let ABC be an equilateral triangle. Extend side AB beyond B to a point B' so that BB' = 3 · AB. Similarly, extend side BC beyond C to a point C' so…Geometry
  16. 16Problem 16The number 21! = 51,090,942,171,709,440,000 has over 60,000 positive integer divisors. One of them is chosen at random. What is the probability that…Number Theory
  17. 17Problem 17A coin is biased in such a way that on each toss the probability of heads is 2/3 and the probability of tails is 1/3. The outcomes of the tosses are…Counting & Probability
  18. 18Problem 18The diameter AB of a circle of radius 2 is extended to a point D outside the circle so that BD = 3. Point E is chosen so that ED = 5 and line ED is…Geometry
  19. 19Problem 19Let N = 123456789101112ldots 4344 be the 79-digit number that is formed by writing the integers from 1 to 44 in order, one after the other. What is…Number Theory
  20. 20Problem 20Real numbers x and y are chosen independently and uniformly at random from the interval (0, 1). What is the probability that ⌊ log _2 x ⌋ = ⌊ log _2…Algebra
  21. 21Problem 21Last year Isabella took 7 math tests and received 7 different scores, each an integer between 91 and 100, inclusive. After each test she noticed that…Algebra
  22. 22Problem 22Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls…Counting & Probability
  23. 23Problem 23The graph of y = f(x), where f(x) is a polynomial of degree 3, contains points A(2, 4), B(3, 9), and C(4, 16). Lines AB, AC, and BC intersect the…Algebra
  24. 24Problem 24Quadrilateral ABCD has right angles at B and C, △ ABC sim △ BCD, and AB > BC. There is a point E in the interior of ABCD such that △ ABC sim △ CEB…Geometry
  25. 25Problem 25A set of n people participate in an online video basketball tournament. Each person may be a member of any number of 5-player teams, but no two teams…Number Theory

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