Problem Set Workbook
Access the downloadable workbook for 2002 AMC 12B problems here.
Discussion Forum
Engage in discussion about the 2002 AMC 12B math contest by visiting Random Math AMC 12B 2002 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2002 AMC 12B problems, please refer below:
Problem 1: The arithmetic mean of the nine numbers in the set is a -digit number , all of whose digits are distinct. The number does not contain the digit
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Problem 2: What is the value of
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Problem 3: For how many positive integers is a prime number?
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A. none
B. one
C. two
D. more than two, but finitely many
E. infinitely many
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Problem 4: Let be a positive integer such that is an integer. Which of the following statements is not true:
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A. divides
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Problem 5: Let , and be the degree measures of the five angles of a pentagon. Suppose and , and form an arithmetic sequence. Find the value of .
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Problem 6: Suppose that and are nonzero real numbers, and that the equation has solutions and . Then the pair is
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Problem 7: The product of three consecutive positive integers is times their sum. What is the sum of their squares?
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Problem 8: Suppose July of year has five Mondays. Which of the following must occur five times in August of year ? (Note: Both months have days.)
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A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
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Problem 9: If are positive real numbers such that form an increasing arithmetic sequence and form a geometric sequence, then is
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Problem 10: How many different integers can be expressed as the sum of three distinct members of the set ?
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Problem 11: The positive integers , and are all prime numbers. The sum of these four primes is
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A. even
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E. prime
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Problem 12: For how many integers is the square of an integer?
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Problem 13: The sum of consecutive positive integers is a perfect square. The smallest possible value of this sum is
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Problem 14: Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
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Problem 15: How many four-digit numbers have the property that the three-digit number obtained by removing the leftmost digit is one ninth of ?
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Problem 16: Juan rolls a fair regular octahedral die marked with the numbers through . Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of ?
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Problem 17: Andy's lawn has twice as much area as Beth's lawn and three times as much area as Carlos' lawn. Carlos' lawn mower cuts half as fast as Beth's mower and one third as fast as Andy's mower. If they all start to mow their lawns at the same time, who will finish first?
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A. Andy
B. Beth
C. Carlos
D. Andy and Carlos tie for first.
E. All three tie.
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Problem 18: A point is randomly selected from the rectangular region with vertices , . What is the probability that is closer to the origin than it is to the point ?
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Problem 19: If , and are positive real numbers such that , and , then is
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Problem 20: Let be a right-angled triangle with . Let and be the midpoints of legs and , respectively. Given that and , find .
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Problem 21: For all positive integers less than , let
Calculate .
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Problem 22: For all integers greater than , define . Let and . Then equals
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Problem 23: In , we have and . Side and the median from to have the same length. What is ?
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Problem 24: A convex quadrilateral with area contains a point in its interior such that , and . Find the perimeter of .
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Problem 25: Let , and let denote the set of points in the coordinate plane such that
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The problems on this page are the property of the MAA's American Mathematics Competitions