Which of the following is the same as2-4 + 6-8 + 10-12 + 143-6 + 9-12 + 15-18 + 21?(A)-1(B)-23(C)23(D)1(E)1432003 AMC 10 B, Problem #1—2003 AMC 12 B, Problem #1—“Can you find any common factor in numerator anddenominator .”Difficulty:EasyNCTM Standard:Number and Operations Standard for Grades 9-12: Compute fluently and makereasonable estimates.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
Al gets the disease algebritis and must take one greenpill and one pink pill each day for two weeks. A greenpill costs1 more than a pink pill, and Al’s pills costa total of546 for the two weeks. How much doesone green pill cost?2003 AMC 10 B, Problem #2—2003 AMC 12 B, Problem #2—“The cost of each day’s pills is546/14 = 39dollars .”Difficulty:Medium-easyNCTM Standard:Algebra Standard for Grades 9–12: Use mathematical models to represent andunderstand quantitative relationships.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
The sum of 5 consecutive even integers is 4 lessthan the sum of the first 8 consecutive odd countingnumbers. What is the smallest of the even integers?(A)6(B)8(C)10(D)12(E)142003 AMC 10 B, Problem #3—“Thesumofthefirst8consecutiveoddcountingnumbers is 64 .”Difficulty:Medium-easyNCTM Standard:Number and Operations Standard for Grades 9–12: Compute fluently and makereasonable estimates.Mathworld.com Classification:Number Theory>Arithmetic>General ArithmeticNumber Theory>Integers>Consecutive Numbers
Rose fills each of the rectangular regions of her rectangular flower bed with
a different type of flower. The lengths, in feet, of the rectangular regions inher flower bed are as shown in the figure. She plants one flower per squarefoot in each region.Asters cost1 each, begonias1.50 each, cannas2 each, dahlias2.50 each, and Easter lilies3 each. What is the leastpossible cost, in dollars, for her garden?15473356(A)108(B)115(C)132(D)144(E)1562003 AMC 10 B, Problem #4—2003 AMC 12 B, Problem #3—“To minimize the cost, Rose should place the most expensive flowers inthe smallest region.”SolutionAnswer (A):To minimize the cost, Rose should place the most expensive flowers in the smallestregion, the next most expensive in the second smallest, etc. The areas of the regions are shown in thefigure, so the minimal total cost, in dollars, is(3)(4) + (2.5)(6) + (2)(15) + (1.5)(20) + (1)(21) = 108.1542021415673356Difficulty:EasyNCTM Standard:Geometry Standard for Grades 9–12: Use geometric models to gain insightsinto, and answer questions in, other areas of mathematics.
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Natural number, Prime number, Geometric progression