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$([[2008 AMC 10B Problems/Problem 3|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?$ (Error compiling LaTeX. Unknown error_msg)\textbf{(A)} 270,000 \qquad \textbf{(B)} 385,000 \qquad \textbf{(C)} 400,000 \qquad \textbf{(D)} 430,000 \qquad \textbf{(E)} 700,000 $([[2008 AMC 10B Problems/Problem 4|Solution]]) ==Problem 5== For [[real number]]s$ 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$