2008 AMC 10 A, Problem #4—2008 AMC 12 A, Problem #3—“One banana is worth as much as8·320=65oranges.”SolutionAnswer (C):Note that23of 10 bananas is203bananas, which are worthas much as 8 oranges.So one banana is worth as much as8·320=65oranges. Therefore12of 5 bananas are worth as much as52·65= 3oranges.Difficulty:MediumNCTMStandard:Measurement Standard:make decisions about units and scales that areappropriate for problem situations involving measurement.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
Which of the following is equal to the product84·128·1612· · · · ·4n+ 44n· · · · ·20082004?2008 AMC 10 A, Problem #5—2008 AMC 12 A, Problem #4—“Each denominator except the first can be canceledwith the previous numerator.”Difficulty:Medium-hardNCTM Standard:Number and Operations Standard: understand numbers, ways of representingnumbers, relationships among numbers, and number systems.Mathworld.com Classification:Number Theory>Arithmetic>Fractions
A triathlete competes in a triathlon in which theswimming, biking, and running segments are all ofthe same length. The triathlete swims at a rate of 3kilometers per hour, bikes at a rate of 20 kilometersper hour, and runs at a rate of 10 kilometers per hour.Which of the following is closest to the triathlete’saverage speed, in kilometers per hour, for the entirerace?2008 AMC 10 A, Problem #6—“Average Speed=Total DistanceTotal Time.”Difficulty:Medium-hardNCTM Standard:Algebra Standard:use mathematical models to represent and understandquantitative relationships.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
The fraction(32008)2-(32006)2(32007)2-(32005)2simplifies to which of the following?2008 AMC 10 A, Problem #7—“Factor92005from each term.”Mathworld.com Classification:Calculus and Analysis>Special Functions>Powers>Exponent
Heather compares the price of a new computer at twodifferent stores.Store A offers 15% off the stickerprice followed by a90 rebate, and store B offers 25%off the same sticker price with no rebate.Heathersaves15 by buying the computer at store A insteadof store B. What is the sticker price of the computer,in dollars?2008 AMC 10 A, Problem #8—2008 AMC 12 A, Problem #6—“Letxdenote the sticker price, in dollars.Write thecost at each store in terms ofx.”