One can holds 12 ounces of soda.What is theminimum number of cans needed to provide a gallon(128 ounces) of soda?(A)7(B)8(C)9(D)10(E)112009 AMC 10 A, Problem #1—“Number of cans is an integer.”SolutionAnswer (E):Because12812= 1023, there must be 11 cans.Difficulty:EasyNCTM Standard:Number and Operations Standard:judge the effects of such operations asmultiplication, division, and computing powers and roots on the magnitudes of quantities.Mathworld.com Classification:Number Theory>Arithmetic>Multiplication and Division>Division
Four coins are picked out of a piggy bank that containsa collection of pennies, nickels, dimes, and quarters.Which of the following couldnotbe the total value ofthe four coins, in cents?2009 AMC 10 A, Problem #2—2009 AMC 12 A, Problem #4—“Thevalueofanycombinationoffourcoinsthatincludes pennies cannot be a multiple of 5 cents.”Difficulty:EasyNCTM Standard:Number and Operations Standard:compare and contrast the properties ofnumbers and number systems, including the rational and real numbers, and understand complexnumbers as solutions to quadratic equations that do not have real solutions.Mathworld.comClassification:Foundations of Mathematics>Mathematical Problems>Unsolved Problems>Coin Problem
Which of the following is equal to1 +11 +11+1?(A)54(B)32(C)53(D)2(E)32009 AMC 10 A, Problem #3—2009 AMC 12 A, Problem #2—“NEED HINT.”SolutionAnswer (C):Simplifying the expression,1 +11 +11+1= 1 +11 +12= 1 +132= 1 +23=53.Difficulty:Medium-easyNCTM Standard:Number and Operations Standard:understand meanings of operations andhow they relate to one another.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Fraction
Eric plans to compete in a triathlon. He can average 2miles per hour in the14-mile swim and 6 miles per hourin the 3-mile run. His goal is to finish the triathlon in 2hours. To accomplish his goal what must his averagespeed, in miles per hour, be for the 15-mile bicycleride?