AoPSWiki
Art of Problem Solving holds many free classes called Math Jams.
Click here for transcripts to past Math Jams.
Personal tools

2008 AMC 10B Problems

From AoPSWiki

Contents

Problem 1

A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?

\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 3\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 5\qquad\mathrm{(E)}\ 6

Solution

Problem 2

A block of calendar dates has the numbers through in the first row, though in the second, though in the third, and through in the fourth. The order of the numbers in the second and the fourth rows are reversed. The numbers on each diagonal are added. What will be the positive difference between the diagonal sums?

\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 6\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 10

Solution

Problem 3

Assume that is a positive real number. Which is equivalent to ?

\mathrm{(A)}\ x^{1/6}\qquad\mathrm{(B)}\ x^{1/4}\qquad\mathrm{(C)}\ x^{3/8}\qquad\mathrm{(D)}\ x^{1/2}\qquad\mathrm{(E)}\ x

Solution

Problem 4

A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least $15,000 and that the total of all players' salaries for each team cannot exceed $700,000. What is the maximum possible salary, in dollars, for a single player?

\mathrm{(A)}\ 270,000\qquad\mathrm{(B)}\ 385,000\qquad\mathrm{(C)}\ 400,000\qquad\mathrm{(D)}\ 430,000\qquad\mathrm{(E)}\ 700,000

Solution

Problem 5

For real numbers and , define . What is ?

\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ x^2+y^2\qquad\mathrm{(C)}\ 2x^2\qquad\mathrm{(D)}\ 2y^2\qquad\mathrm{(E)}\ 4xy

Solution

Problem 6

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 7

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 8

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 9

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 10

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 11

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 12

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 13

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 14

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 15

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 16

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 17

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 18

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 19

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 20

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 21

Ten chairs are evenly spaced around a round table. 5 married couples are to sit in the chairs with men and women alternating, and no one is to sit either across from or next to his/her spousse. How many seating arrangements are possible?

Solution

Problem 22

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 23

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 24

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

Problem 25

This problem has not been edited in. If you know this problem, please help us out by adding it.Solution

See also

Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us