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2001 AMC 10 problems

All 25 problems from the 2001 AMC 10, 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 median of the list n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15 is 10. What is the mean?Algebra
  2. 2Problem 2A number x is 2 more than the product of its reciprocal and its additive inverse. In which interval does the number lie?Algebra
  3. 3Problem 3The sum of two numbers is S. Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two…Algebra
  4. 4Problem 4What is the maximum number of possible points of intersection of a circle and a triangle?Geometry
  5. 5Problem 5How many of the twelve pentominoes pictured below have at least one line of symmetry?Counting & Probability
  6. 6Problem 6Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23)=6 and S(23)=5. Suppose N is a…Algebra
  7. 7Problem 7When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the…Algebra
  8. 8Problem 8Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works…Number Theory
  9. 9Problem 9The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p+2)% of any amount above $28000…Algebra
  10. 10Problem 10If x, y, and z are positive with xy=24, xz=48, and yz=72, then x+y+z isAlgebra
  11. 11Problem 11Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains 8 unit…Algebra
  12. 12Problem 12Suppose that n is the product of three consecutive integers and that n is divisible by 7. Which of the following is not necessarily a divisor of n?Number Theory
  13. 13Problem 13A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit. The digits in each part of the number are in decreasing…Number Theory
  14. 14Problem 14A charity sells 140 benefit tickets for a total of $2001. Some tickets sell for full price (a whole dollar amount), and the rest sell for half price…Number Theory
  15. 15Problem 15A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between…Geometry
  16. 16Problem 16The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their…Algebra
  17. 17Problem 17Which of the cones below can be formed from a 252° sector of a circle of radius 10 by aligning the two straight sides?Geometry
  18. 18Problem 18The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest toGeometry
  19. 19Problem 19Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are…Counting & Probability
  20. 20Problem 20A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length 2000. What is the length…Geometry
  21. 21Problem 21A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter 10 and altitude 12, and…Geometry
  22. 22Problem 22In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by v, w, x…Algebra
  23. 23Problem 23A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are…Counting & Probability
  24. 24Problem 24In trapezoid ABCD, AB and CD are perpendicular to AD, with AB+CD=BC, AB< CD, and AD=7. What is AB· CD?Geometry
  25. 25Problem 25How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5?Counting & Probability

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