2008 AMC 10B Problems

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?

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

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

Problem 3

Assume that $x$ is a positive real number. Which is equivalent to $\sqrt[3]{x\sqrt{x}}$ ?

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

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

Problem 5

For real numbers $a$ and $b$ , define $a$ b=(a-b)^2 $. What is$ (x-y)^2\ $(y-x)^2$ ?

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

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2008 AMC 10B Problems

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25