A basketball player made 5 baskets during a game.Each basket was worth either 2 or 3 points. How manydifferent numbers could represent the total pointsscored by the player?(A)2(B)3(C)4(D)5(E)62008 AMC 10 B, Problem #1—2008 AMC 12 B, Problem #1—“The number of points could be any integer between5·2 = 10and5·3 = 15, inclusive.”SolutionAnswer (E):The number of points could be any integer between5·2 =10and5·3 = 15, inclusive. The number of possibilities is15-10+1 = 6.Difficulty:Medium-easyNCTM Standard:Measurement Standard: understand measurable attributes of objects and theunits, systems, and processes of measurement.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
A4×4block of calendar dates is shown. The orderof the numbers in the second row is to be reversed.Then the order of the numbers in the fourth row isto be reversed. Finally, the numbers on each diagonalare to be added. What will be the positive differencebetween the two diagonal sums?123489101115 16171822 23 24 252008 AMC 10 B, Problem #2—2008 AMC 12 B, Problem #2—“Draw the new block after the modifications.”Difficulty:Medium-easyNCTM Standard:Number and Operations Standard:compute fluently and make reasonableestimates.Mathworld.com Classification:Number Theory>Arithmetic>Addition and Subtraction
Assume thatxis a positive real number.Which isequivalent to3qx√x?2008 AMC 10 B, Problem #3—“Use the fact thata√x=x1a.”Mathworld.com Classification:Calculus and Analysis>Roots>Root
A semipro baseball league has teams with 21 playerseach. League rules state that a player must be paid atleast15,000, and that the total of all players’ salariesfor each team cannot exceed700,000. What is themaximum possible salary, in dollars, for a single player?2008 AMC 10 B, Problem #4—2008 AMC 12 B, Problem #3—“A single player can receive the largest possible salaryonly when the other 20 players on the team are eachreceiving the minimum salary.”