Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
GET READY FOR THE AMC 10 WITH AoPS
Learn with outstanding instructors and top-scoring students from around the world in our AMC 10 Problem Series online course.
CHECK SCHEDULE

Difference between revisions of "2008 AMC 10B Problems"

m (Problem 5 - Fixed LaTeX)
Line 110: Line 110:
  
 
==Problem 21==
 
==Problem 21==
−
{{problem}}
+
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?
  
 
[[2008 AMC 10B Problems/Problem 21|Solution]]
 
[[2008 AMC 10B Problems/Problem 21|Solution]]

Revision as of 12:54, 20 December 2008

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 $4\times 4$ block of calendar dates has the numbers $1$ through $4$ in the first row, $8$ though $11$ in the second, $15$ though $18$ in the third, and $22$ through $25$ 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 $x$ is a positive real number. Which is equivalent to $\sqrt[3]{x\sqrt{x}}$?

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

Solution

Problem 4

A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least <dollar/>15,000 and that the total of all players' salaries for each team cannot exceed <dollar/>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 $a$ and $b$, define $a$$b=(a-b)^2$. What is $(x-y)^2$$(y-x)^2$?

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

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2008_AMC_10B_Problems&oldid=28655"