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1、A2012Problem 1Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds.Working together,how many cupcakes can they frost in 5 minutes?(A)1 0(B)1 5 (C)2 0(D)2 5 (E)3 0SolutionProblem 2A square with side length 8 is cut in half,creating two congruent rectangles.What a
2、re thedimensions of one of these rectangles?(A)2 4 (B)2 b y 6 (C)2 b y 8 (D)4 b y 4 (E)4 b y 8SolutionProblem 3A bug crawls along a number line,starting at-2.It crawls to-6,then turns around and crawlsto 5.How many units does the bug crawl altogether?(A)9 (B)1 1 (C)1 3 (D)1 4 (E)1 5SolutionProblem 4
3、Let Z.A B C=2 4。and Z.A B D=2 0.What is the smallest possible degree measure forangle CBD?(A)0(B)2 (C)4 (D)6 (E)1 2SolutionProblem 5Last year 100 adult cats,half of whom were female,were brought into the Smallville AnimalShelter.Half of the adult female cats were accompanied by a litter of kittens.T
4、he averagenumber of kittens per litter was 4.What was the total number of cats and kittens received bythe shelter last year?(A)150(B)200(C)250(D)300(E)400SolutionProblem 6The product of two positive numbers is 9.The reciprocal of one of these numbers is 4 timesthe reciprocal of the other number.What
5、 is the sum of the two numbers?(A)y (B)件 (C)7(D)y (E)8SolutionProblem 73In a bag of marbles,5 of the marbles are blue and the rest are red.If the number of redmarbles is doubled and the number of blue marbles stays the same,what fraction of themarbles will be red?(A)|(B)5(C)；(D)|(E)|O I I tJ OSoluti
6、onProblem 8The sums of three whole numbers taken in pairs are 12,17,and 19.What is the middlenumber?(A)4(B)5(C)6(D)7(E)8SolutionProblem 9A pair of six-sided dice are labeled so that one die has only even numbers(two each of 2,4,and 6),and the other die has only odd numbers(two of each 1,3,and 5).The
7、 pair of dice isrolled.What is the probability that the sum of the numbers on the tops of the two dice is 7?(A)(B)1(C)1(D)|(E)1O 4 u ZSolutionProblem 10Mary divides a circle into 12 sectors.The central angles of these sectors,measured in degrees,are all integers and they form an arithmetic sequence.
8、What is the degree measure of thesmallest possible sector angle?(A)5(B)6(C)8(D)10(E)12SolutionProblem 11Externally tangent circles with centers at points A and B have radii of lengths 5 and 3,respectively.A line externally tangent to both circles intersects ray AB at point C.What is BC?(A)4(B)4.8(C)
9、10.2(D)12(E)14.4SolutionProblem 12A year is a leap year if and only if the year number is divisible by 400(such as 2000)or isdivisible by 4 but not 1 00(such as 2012).The 200th anniversary of the birth of novelistCharles Dickens was celebrated on February 7,2012,a Tuesday.On what day of the weekwas
10、Dickens born?(A)Friday(B)Saturday(C)Sunday(D)Monday(E)TuesdaySolutionProblem 13An iterative average of the numbers 1,2,3,4,and 5 is computed the following way.Arrangethe five numbers in some order.Find the mean of the first two numbers,then find the meanof that with the third number,then the mean of
11、 that with the fourth number,and finally themean of that with the fifth number.What is the difference between the largest and smallestpossible values that can be obtained using this procedure?(A)禁(B)2 (C)y (D)3(E)SolutionProblem 14Chubby makes nonstandard checkerboards that have 31 squares on each s
12、ide.Thecheckerboards have a black square in every corner and alternate red and black squares alongevery row and column.How many black squares are there on such a checkerboard?(A)480(B)481(C)482(D)483(E)484SolutionProblem 15Three unit squares and two line segments connecting two pairs of vertices are
13、 shown.Whatis the area of/B Cr?(A)i (B)|(C)|(D)|(E)苧O D y o 4SolutionProblem 16Three runners start running simultaneously from the same point on a 500-meter circulartrack.They each run clockwise around the course maintaining constant speeds of 4.4,4.8,and 5.0 meters per second.The runners stop once
14、they are all together again somewhere onthe circular course.How many seconds do the runners run?(A)1,000(B)L250(C)2,500(D)5.000(E)10.000SolutionProblem 1 7标-标 7 3Let fl and b be relatively prime integers with a fe 0 and(a 一办 =3 whatis Q -b?(A)1 (B)2(C)3(D)4(E)5SolutionProblem 1827rThe closed curve i
15、n the figure is made up of 9 congruent circular arcs each of length 3,where each of the centers of the corresponding circles is among the vertices of a regularhexagon of side 2.What is the area enclosed by the curve?(A)2TT+6(B)2T T+4/3(C)3;r+4(D)2万+3通+2(E)汗 +6禽SolutionProblem 19Paula the painter and
16、 her two helpers each paint at constant,but different,rates.Theyalways start at 8:00 AM,and all three always take the same amount of time to eat lunch.OnMonday the three of them painted 50%of a house,quitting at 4:00 PM.On Tuesday,whenPaula wasnt there,the two helpers painted only 24%of the house and quit at 2:12 PM.OnWednesday Paula worked by herself and finished the house by working until 7:12 P.M.Howlong,in minutes,was each days lunch break?(A)30(B)36(C)42(D)48(E)60SolutionProblem 20A 3 x 3 s
