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15th AMC 8 199921. (6 ? 3) 4 (2 1) 5. To make this statement true, the question markbetween the 6 and the 3 should be replaced by(A) (B) (C) (D) (E) None of these2. What is the degree measure of the smaller angleformed by the hands of a clock at 10 o’clock?(A) 30(D) 75(B) 4511121210(C) 603948(E) 907563. Which triplet of numbers has a sum NOT equal to 1 ?1 1 1(A) ( , , )2 3 6(B) (2, 2, 1)(D) (1.1, 2.1, 1.0)(C) (0.1, 0.3, 0.6)3 5(E) ( , , 5)2 24. The diagram shows the miles traveled by bikersAlberto and Bjorn. After four hours about howmany more miles has Alberto biked then Bjorn?(A) 15(B) 20(D) 30(E) 35(C) 25MILES756045rtobeAlrnBjo301500132HOURS455. A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. Tomake the garden larger, while using the same fence, its shape is changed to asquare. By how many square feet does this enlarge the garden?(A) 100(B) 200(C) 300(D) 400(E) 5006. Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bohas as much money as Flo. Both Bo and Coe have more than Moe. Jo has morethan Moe, but less than Bo. Who has the least amount of money?(A) Bo(B) Coe(C) Flo(D) Jo(E) Moe

15th AMC 8 199937. The third exit on a highway is located at milepost 40 and the tenth exit is atmilepost 160. There is a service center on the highway located three-fourthsof the way from the third exit to the tenth exit. At what milepost would youexpect to find this service center?(A) 90(B) 100(C) 110(D) 120(E) 1308. Six squares are colored, front and back, (R red, B blue,O orange, Y yellow, G green, and W white). Theyare hinged together as shown, then folded to form a cube.The face opposite the white face is(A) B(B) G(C) O(D) R(B) 1000(C) 1150BGYOW(E) Y9. Three flower beds overlap as shown. Bed A has500 plants, bed B has 450 plants, and bed C has350 plants. Beds A and B share 50 plants, whilebeds A and C share 100. The total number ofplants is(A) 850(E) 1450RACB(D) 130010. A complete cycle of a traffic light takes 60 seconds. During each cycle the light isgreen for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomlychosen time, what is the probability that the light will NOT be green?(A)14(B)13(C)512(D)12(E)71211. Each of the five numbers 1,4,7,10, and 13 is placed in oneof the five squares so that the sum of the three numbersin the horizontal row equals the sum of the three numbersin the vertical column. The largest possible value for thehorizontal or vertical sum is(A) 20(B) 21(C) 22(D) 24(E) 30

15th AMC 8 1999412. The ratio of the number of games won to the number of games lost(no ties) bythe Middle School Middies is 11/4. To the nearest whole percent, what percentof its games did the team lose?(A) 24(B) 27(C) 36(D) 45(E) 7313. The average age of the 40 members of a computer science camp is 17 years.There are 20 girls, 15 boys, and 5 adults. If the average age of the girls is 15and the average age of the boys is 16, what is the average age of the adults?(A) 26(B) 27(C) 28(D) 29(E) 3014. In trapezoid ABCD, the side AB and CD areequal. The perimeter of ABCD is8BC3(A) 27(B) 30(D) 34(E) 48(C) 32A15. Bicycle license plates in Flatville each contain three letters.The first is chosen from the set {C,H,L,P,R}, the secondfrom {A,I,O}, and the third from {D,M,N,T}.D16PAMWhen Flatville needed more license plates, they addedtwo new letters. The new letters may both be added to one set or one letter maybe added to one set and one to another set. What is the largest possible numberof ADDITIONAL license plates than can be made by adding two letters?(A) 24(B) 30(C) 36(D) 40(E) 6016. Tori’s mathematic test had 75 problems: 10 arithmetic, 30 algebra, and 35geometry problems. Although she answered 70% of the arithmetic, 40% of thealgebra, and 60% of the geometry problems correctly, she did not pass the testbecause she got less than 60% of the problems right. How many more questionswould she have needed to answer correctly to earn a 60% passing grade?(A) 1(B) 5(C) 7(D) 9(E) 11

15th AMC 8 19995Problems 17, 18, and 19 refer to the following:Cookies For a CrowdAt Central Middle School the 108 students who takethe AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walterand Gretel are baking Bonnie’s Best Bar Cookies thisyear. Their recipe, which makes a pan of 15 cookies,list these items:1 21 cups of flour, 2 eggs, 3 tablespoons butter, 43 cups sugar, and 1 package ofchocolate drops. They will make only full recipes, not partial recipe.17. Walter can buy eggs by the half-dozen. How many half-dozens should be buyto make enough cookies? (Some eggs and some cookies may be left over.)(A) 1(B) 2(C) 5(D) 7(E) 1518. They learn that a big concert is scheduled for the same night and attendancewill be down 25%. How many recipes of cookies should they make for theirsmaller party?(A) 6(B) 8(C) 9(D) 10(E) 1119. The drummer gets sick. The concert is cancelled. Walter and Gretel must makeenough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stickof butter. How many sticks of butter will be needed? (Some butter may be leftover, of course.)(A) 5(B) 6(C) 7(D) 8(E) 920. Figure 1 is called a ”stack map.” The numberstell how many cubes are stacked in each position. Fig. 2 shows these cubes, and Fig. 3shows the view of the stacked cubes as seenfrom the front.Which of the following is the front view for thestack map in Fig. 4 ?(A)(B)(C)(D)3421Figure 1Figure 2212 43 1Figure 4(E)Figure 3

15th AMC 8 1999621. The degree measure of angle A is(A) 20(B) 30(C) 35(D) 40(E) 45A100 110 40 22. In a far-off land three fish can be traded for two loaves of bread and a loaf ofbread can be traded for four bags of rice. How many bags of rice is one fishworth?(A)38(B)12(C)34(D) 223(E) 31323. Square ABCD has sides of length 3. Segments CMand CN divide the square’s area into three equal part.How long is segment CM ? (A) 10(B) 12(C) 13 (D) 14(E) 15BCMADN24. When 19992000 is divided by 5, the remainder is(A) 4(B) 3(C) 2(D) 1(E) 025. Points B, D, and J are midpoints of the sides ofright triangle ACG. Points K, E, I are midpoints ofthe sides of triangle JDG, etc. If the dividing andshading process is done 100 times(the first three areshown) and AC CG 6, then the total area of theshaded triangles is nearest(A) 6(B) 7(C) 8(D) 9GHFEILJDK(E) 10ABC

16th AMC 8 200021. Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Briannais half as old as Aunt Anna. How old is Caitlin?(A) 15(B) 16(C) 17(D) 21(E) 372. Which of these numbers is less than its reciprocal?(A) 2(B) 1(C) 0(D) 1(E) 23. How many whole numbers lie in the interval between(A) 2(B) 3(C) 4(D) 553and 2π ?(E) infinitely many%%%4. In 1960 only 5% of the working adults in Carlin City worked at home. By 1970the “at-home” work force had increased to 8%. In 1980 there were approximately 15% working at home, and in 1990 there were 30%. The graph that bestillustrates this 19601970198019901960(E)1970198019905. Each principal of Lincoln High School serves exactly one 3-year term. Whatis the maximum number of principals this school could have during an 8-yearperiod?(A) 2(B) 3(C) 4(D) 5(E) 86. Figure ABCD is a square. Inside this square three smallersquares are drawn with side lengths as labeled. the area ofthe shaded L-shaped region is(A) 7(B) 10(C) 12.5(D) 14D 1A133(E) 1511CB

16th AMC 8 200037. What is the minimum possible product of three different numbers of the set{ 8, 6, 4, 0, 3, 5, 7}?(A) 336(B) 280(C) 210(D) 192(E) 08. Three dice with faces numbered 1 through 6 are stacked asshown. Seven of the eighteen faces are visible, leaving elevenfaces hidden(back, bottom, between). The total number ofdots NOT visible in this view is(A) 21(B) 22(C) 31(D) 41(E) 539. Three-digit powers of 2 and 5 are used in this cross-number 1puzzle. What is the only possible digit for the outlined square?2ACROSS2. 2m(A) 0(B) 2(C) 4DOWN1. 5n(D) 6(E) 810. Ara and Shea were once the same height. Since then Shea has grown 20% whileAra has grown half as many inches as Shea. Shea is now 60 inches tall. Howtall, in inches, is Ara now?(A) 48(B) 51(C) 52(D) 54(E) 5511. The number 64 has the property that it is divisible by its units digit. How manywhole numbers between 10 and 50 have this property?(A) 15(B) 16(C) 17(D) 18(E) 20

16th AMC 8 2000412. A block wall 100 feet long and 7 feet high will be constructedusing blocks that are 1 foot high and either 2 feet long or 1foot long (no blocks may be cut). The vertical joins in theblocks must be staggered as shown, and the wall must beeven on the ends. What is the smallest number of blocksneeded to build this wall?(A) 344(B) 347(C) 350(D) 353(E) 35613. In triangle CAT , we have ACT AT C and CAT 36 .If T R bisects AT C, then CRT (A) 16 (B) 51 (C) 72 (D) 90 A(E) 108 RCT14. What is the units digit of 1919 9999 ?(A) 0(B) 1(C) 2(D) 8(E) 915. Triangle ABC, ADE, and EF G are all equilateral. Points Dand G are midpoints of AC and AE, respectively. If AB 4,what is the perimeter of figure ABCDEF G?(A) 12(B) 13(C) 15(D) 18CDE(E) 21GBA16. In order for Mateen to walk a kilometer(1000m) in his rectangular backyard, hemust walk the length 25 times or walk its perimeter 10 times. What is the areaof Mateen’s backyard in square meters?(A) 40(B) 200(C) 400(D) 500(E) 1000F

16th AMC 8 2000517. The operation is defined for all nonzero numbers by a b [(1 2) 3] [1 (2 3)].(A) 23(B) 14(C) 0(D)14(E)a2. Determineb2318. Consider these two geoboard quadrilaterals. Which of the following statements is true?I(A) The area of quadrilateral I is more than the area of quadrilateral II.II(B) The area of quadrilateral I is less than the area of quadrilateral II.(C) The quadrilaterals have the same area and the same perimeter.(D) The quadrilaterals have the same area, but the perimeterof I is more than the perimeter of II.(E) The quadrilaterals have the same area, but the perimeterof I is less than the perimeter of II.19. Three circular arcs of radius 5 units bound the region shown.Arcs AB and AD are quarter-circles, and arc BCD is a semicircle. What is the area, in square units, of the region?(A) 25(B) 10 5π(C) 50CDB(D) 50 5πA(E) 25π20. You have nine coins: a collection of pennies, nickels, dimes, and quarters havinga total value of 1.02, with at least one coin of each type. How many dimesmust you have?(A) 1(B) 2(C) 3(D) 4(E) 5

16th AMC 8 2000621. Keiko tosses one penny and Ephraim tosses two pennies. The probability thatEphraim gets the same number of heads that Keiko gets is(A)14(B)38(C)12(D)23(E)3422. A cube has edge length 2. Suppose that we glue a cube ofedge length 1 on top of the big cube so that one of its facesrests entirely on the top face of the larger cube. The percentincrease in the surface area (sides, top, and bottom) from theoriginal cube to the new solid formed is closest to:(A) 10(B) 15(C) 17(D) 21(E) 2523. There is a list of seven numbers. The average of the first four numbers is 5, andthe average of the last four numbers is 8. If the average of all seven numbers is6 47 , then the number common to both sets of four numbers is(A) 537(B) 6(C) 647(D) 7(E) 73724. If A 20 and AF G AGF , Then B D (A) 48 (B) 60 (C) 72 (D) 80 (E) 90 BGACFDE25. The area of rectangle ABCD is 72. If point A and the midpoints of BC and CD are joined to form a triangle, the areaof that triangle is(A) 21(B) 27(C) 30(D) 36(E) 40ABDC

Mathematical Association of AmericaAmerican Mathematics CompetitionsPresented by the Akamai Foundation17th AnnualAMC 8(American Mathematics Contest 8)Tuesday, NOVEMBER 13, 20011. NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLSYOU.This is a twenty-five question multiple choice test. Each question is followedby answers marked A, B, C, D and E. Only one of these is correct.The answers to the problems are to be marked on the AMC 8 Answer Formwith a #2 pencil. Check the blackened circles for accuracy and erase errorsand stray marks completely. Only answers properly marked on the answerform will be graded.There is no penalty for guessing. Your score on this test is the number ofcorrect answers.No aids are permitted other than scratch paper, graph paper, rulers, erasers,and calculators that are accepted for use on the SAT. No problems on the testwill require the use of a calculator.Figures are not necessarily drawn to scale.Before beginning the test, your proctor will ask you to record certain information on the answer form.When your proctor gives the signal, begin working on the problems. You willhave 40 minutes to complete the test.When you finish the exam, sign your name in the space provided on theAnswer Form.The Committee on the American Mathematics Competitions reserves the right to re-examine students beforedeciding whether to grant official status to their scores. The Committee also reserves the right to disqualify allscores from a school if it is determined that the required security procedures were not followed.The publication, reproduction, or communication of the problems or solutions of the AMC 8 during the periodwhen students are eligible to participate seriously jeopardizes the integrity of the results. Duplication at any timevia copier, telephone, e-mail, World Wide Web or media of any type is a violation of the copyright law.Copyright 2001, Committee on the American Mathematics Competitions,Mathematical Association of America

17th AMC 8 200121. Casey’s shop class is making a golf trophy. He hasto paint 300 dimples on a golf ball. If it takes him2 seconds to paint one dimple, how many minuteswill he need to do his job?(A) 4(B) 6(C) 8(D) 10(E) 122. I’m thinking of two whole numbers. Their product is 24 and their sumis 11. What is the larger number?(A) 3(B) 4(C) 6(D) 8(E) 123. Granny Smith has 63. Elberta has 2 more than Anjou and Anjou hasone-third as much as Granny Smith. How many dollars does Elbertahave?(A) 17(B) 18(C) 19(D) 21(E) 234. The digits 1, 2, 3, 4 and 9 are each used once to form the smallestpossible even five-digit number. The digit in the tens place is(A) 1(B) 2(C) 3(D) 4(E) 95. On a dark and stormy night Snoopy suddenly saw aflash of lightning. Ten seconds later he heard the soundof thunder. The speed of sound is 1088 feet per secondand one mile is 5280 feet. Estimate, to the nearest halfmile, how far Snoopy was from the flash of lightning.(A) 1(B) 1 12(C) 2(D) 2 12(E) 36. Six trees are equally spaced along one side of a straight road. Thedistance from the first tree to the fourth is 60 feet. What is the distancein feet between the first and last trees?(A) 90(B) 100(C) 105(D) 120(E) 140

17th AMC 8 20013KITES ON PARADEProblems 7, 8 and 9 are about these kites.To promote her school’s annual Kite Olympics,Genevieve makes a small kite and a large kite fora bulletin board display. The kites look like theone in the diagram. For her small kite Genevievedraws the kite on a one-inch grid. For the largekite she triples both the height and width of theentire grid.7. What is the number of square inches in thearea of the small kite?(A) 21(B) 22(C) 23(D) 24(E) 258. Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing materialdoes she need?(A) 30(B) 32(C) 35(D) 38(E) 399. The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inchesof waste material are cut off from the four corners?(A) 63(B) 72(C) 180(D) 189(E) 26410. A collector offers to buy state quarters for 2000% of their face value.At that rate how much will Bryden get for his four state quarters?(A) 20(B) 50(C) 200(D) 50011. Points A, B, C and D have these coordinates:A(3, 2), B(3, 2), C( 3, 2) and D( 3, 0). The areaof quadrilateral ABCD is(A) 12(B) 15(C) 18(D) 21(E) 24(E) 2000

17th AMC 8 200112. If a b (A) 44a b, then (6 4) 3 a b(B) 13(C) 15(D) 30(E) 7213. Of the 36 students in Richelle’s class, 12 preferchocolate pie, 8 prefer apple, and 6 prefer blueberry.Half of the remaining students prefer cherry pie andhalf prefer lemon. For Richelle’s pie graph showing this data, how many degrees should she use forcherry pie?(A) 10(B) 20(C) 30(D) 50(E) 7214. Tyler has entered a buffet line in which he chooses one kind of meat,two different vegetables and one dessert. If the order of food items isnot important, how many different meals might he choose?Meat: beef, chicken, porkVegetables: baked beans, corn, potatoes, tomatoesDessert: brownies, chocolate cake, chocolate pudding, icecream(A) 4(B) 24(C) 72(D) 80(E) 14415. Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes perminute. Four minutes later Christen joined him and peeled at the rateof 5 potatoes per minute. When they finished, how many potatoeshad Christen peeled?(A) 20(B) 24(C) 32(D) 3316. A square piece of paper, 4 inches on a side, isfolded in half vertically. Both layers are then cut inhalf parallel to the fold. Three new rectangles areformed, a large one and two small ones. What is theratio of the perimeter of one of the small rectanglesto the perimeter of the large rectangle?(A)13(B)12(C)34(D)45(E)56(E) 40

17th AMC 8 2001517. For the game show Who Wants To Be A Millionaire?, thedollar values of each question are shown in the following table(where K 1000).QuestionValue1234 5 6 7 8910 1112131415100 200 300 500 1K 2K 4K 8K 16K 32K 64K 125K 250K 500K 1000KBetween which two questions is the percent increase of the value thesmallest?(A) From 1 to 2(D) From 11 to 12(B) From 2 to 3(E) From 14 to 15(C) From 3 to 418. Two dice are thrown. What is the probability that the product of thetwo numbers is a multiple of 5?(A)136(B)118(C)16(D)1136(E)1319. Car M traveled at a constant speed for a given time. This is shownby the dashed line. Car N traveled at twice the speed for the samedistance. If Car N’s speed and time are shown as solid line, whichgraph illustrates espeedMNtimeMNtime(E)N(C)

17th AMC 8 2001620. Kaleana shows her test score to Quay, Marty and Shana, but the otherskeep theirs hidden. Quay thinks, “At least two of us have the samescore.” Marty thinks, “I didn’t get the lowest score.” Shana thinks,“I didn’t get the highest score.” List the scores from lowest to highestfor Marty (M), Quay (Q) and Shana (S).(A) S,Q,M(B) Q,M,S(C) Q,S,M(D) M,S,Q(E) S,M,Q21. The mean of a set of five different positive integers is 15. The medianis 18. The maximum possible value of the largest of these five integersis(A) 19(B) 24(C) 32(D) 35(E) 4022. On a twenty-question test, each correct answer is worth 5 points, eachunanswered question is worth 1 point and each incorrect answer isworth 0 points. Which of the following scores is NOT possible?(A) 90(B) 91(C) 92(D) 9523. Points R, S and T are vertices of an equilateral triangle, and points X, Y and Z are midpoints of itssides. How many noncongruent triangles can bedrawn using any three of these six points as vertices?(A) 1(B) 2(C) 3(D) 4(E) 20(E) 97SYRZXT24. Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. Whenthe upper half is folded down over the centerline, 2pairs of red triangles coincide, as do 3 pairs of bluetriangles. There are 2 red-white pairs. How manywhite pairs coincide?(A) 4(B) 5(C) 6(D) 7(E) 925. There are 24 four-digit whole numbers that use each of the four digits2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is amultiple of another one. Which of the following is it?(A) 5724(B) 7245(C) 7254(D) 7425(E) 7542

SOLUTIONSYour School Manager will be sent at least one copy of the 2001 AMC 8 Solutions Pamphlet. It is meant to be loaned to students (but not duplicated).WRITE TO USComments about the problems and solutions for this AMC 8 should

15th AMC ! 8 1999 5 Problems 17, 18, and 19 refer to the following: Cookies For a Crowd At Central Middle School the 108 students who take the AMC! 8 meet in the evening to talk about prob-lems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie’s Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, list these items: 11 2 cups of our, 2 eggs .

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