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1、 2018年美国数学大联盟杯六年级初赛竞赛数学试卷一、选择题（每小题5分，答对加5分，答错不扣分，共200分）1.Pick any integer greater than . Double it twice, then triple the result. The final outcome is（）of your starting integer.B.A.C.D.2.3.4.Barry listened to the radio for hours andminutes . Rounded to the nearestminutes ,for how many minutes was Ba
2、rry listening ?（ ）.A.B.C.D.Dividebyto get a quotient and remainder. Divide that remainder by thatquotient, and the new remainder is（ ）A. B.C.D.A man had five pieces of chain, each made up of three links, figure below. He wanted to join thefive pieces together to make a big chain of fifteen links and
3、 went to a blacksmith to see howmuch it would cost. Well, said the blacksmith,I will charge youcents for cutting a link andfor welding a link. Any bending that is required is free. Given those prices, what is thesmallest amount of money for which the job could be done?（ ）Note: In a chain, each link
4、is connected to one or two other links.A.B.C.D.5.A bee sat on the head of a horse rider whose horse was trotting eastbound at a steady fivemiles per hour. Some distance ahead on the same path, another horse and rider wereapproaching westbound, also at five miles per hour. When the two horses weremil
5、es apart,the bee left the first horse rider and flew toward the second horse at a rate of ten miles per hour.1/6 Upon reaching the second horse, the bee immediately turned around and flew back at the samerate to the first horse. If the bee kept up this performance until the two riders met, how far (
6、inmiles) did he travel from the moment he left the first horse rider?（ ）A.C.B.D. None of the above6.Which of the following is the sum of the prime factors ofA. B. C.?（ ）D.7If the length of the longest side of a triangle is 18, which of the following could not be the lengthof its second-longest side（
7、 ）A.B.C.D.8.My final score in a competition is the average of my scores on rounds. To get a final score ofafter gettinglast rounds?A., andon the first rounds, what must be my average score for theB.C.D.9.Mr. Rice had breakfast one day at a restaurant with Mr. Wheat. When it came time to pay thebill,
8、 it was found that Mr. Rice had as many one-dollar bills as Mr. Wheat had quarters. (Mr. Ricehad one-dollar bills only, and Mr. Wheat had quarters only.) Rather than each man payingseparately, Mr. Rice paid his share of the bill, to Mr. Wheat. At that point, Mr. Wheat hadfour times as much money as
9、Mr. Rice. How much money did Mr. Rice have at the beginning?（）A.B.C.D.10. Professor Peach teaches chemistry to clever kids.The ratio of fresh men to other students in hisclass isA. The total number of students in Professor Peachs class could be（ ）B.C.D.11.（ ）A.B.C.D.12. Mr. Bogs worth once left a wi
10、ll which read:2/6 To Bob, twice as much as to Betty.To Brian, twice as much as to Bob.To Bill, twice as much as to Brian.If his estate was valued at, how much money did Betty, one of his four heirs, receive?C. D.A.B.13. I paidand got quarters, dimes, and nickels in change. I spent（ ）A.B.C.D.14. One
11、side of Todds truck is a perfect rectangle with an area ofwidth, then its perimeter is（ ）. If its length is times itsA.B.C.D.1111125. If a bird in the hand is worth two in the bush, and a bird in the bush is worth four in the sky, thenbirds in the hand are worthB.birds in the sky.C.A.D.6. On each of
12、 the four shelves of my bookcase is a different prime number of books. There couldbe a total of （ ） books on my shelves.A.B.C.D.7. Seven years ago I realized that my age would be tripled twelve years from then. How old am Inow （ ）?A.B.C.D.8. How many fractions with a numerator of and a whole-number
13、denominator are greater thanand less than （ ）A.B.C.D.9. If I write the letters R-E-P-E-A-T repeatedly, stopping when I have written exactlyhow many times do I write the letter E?（ ）letters,A.B.C.D.0.3/6 On my map,represents. If a park shown on the map is a rectangle that isbyA., the area of the actu
14、al park is （ ）.B.C.D.2221. Gloomy Guss Tuesday rain cloud shows up every Tuesday at. and everyminutes after that. Its last appearance on Tuesday is at（ ） .A.B.C.D.2. If my lucky number divided by its reciprocal is, then the square of my lucky number is（）A.B.C.D.3. A boy and his sister were walking d
15、own the street one afternoon when they met a kind old man.When the old man asked them about the size of their family, the boy quickly answered. I haveas many brothers as I have sisters, he proudly stated. Not to be left out, the girl added, I havethree times as many brothers as I have sisters. Can y
16、ou tell how many boys and girls in totalthere were in their family?（ ）A.B.C.D.24. A farmer was asked how many pigs he had. Well, he said, if I had just as many more again,plus half as many more, plus anothertimes more, I would have three dozen. How manypigs did he have?（ ）A.B.C.C.D.D.25.ofisof（ ）A.B
17、.26. It took meminutes to cyclekm to the beach. Later I got a ride from the beach to the parkat twice my cycling speed. If the ride to the park tookminutes, what distance did I travel fromthe beach to the park?（ ）A.B.C.D.27. Ted, Rack, and Sam painted a wall together. Ted paintedpainted. Sam painted
18、 less than Rick. Ted paintedmore of the wall than Samof the amount that Rick painted.4/6 A.B.C.D.D.D.D.223338. The greatest integer power ofthat is a divisor ofC.is（ ）A. B.9. The ones digit of the sum of all even integers from tois（ ）A.B.C.0. The median of，andis（）A.B.C.1. The average of all positive
19、 even integers from tois（ ）A.B.C.D.2. Pirate Percy hascoins in his chest. Of the Spanish coins,are gold. Ifof the coinsare gold but not Spanish andof the coins are neither gold nor Spanish, how many Spanishgold coins are in Percys chest?（ ）A. B.C.D.33333. When I divided the population of my city by
20、the number of streets in the city, I got a remainder of.If the exact quotient on my calculator wasB., how rnany streets are there in my city?D.A.C.4. What is the greatest number of -by- rectangle that can be placed inside anrectangle with no overlapping（ ）?-by-A.B.C.D.5. How many four-digit whole nu
21、mbers have four different even digits and a ones digit greater thanits thousands digit?A.B.C.D.6. Both arcsandare quarter circles of radius , figure on the right. Arcis a asemi-circle of radius . What is the area of the region?5/6 A.B.C.D.37. In the figure on the right, the side-length of the smalle
22、r square is . The four arcs are four semi-circles. Each side of squareis tangent to one of the semi-circles. The area ofis（ ）A.B.C.D.38. A million is a large number, a followed by zeros. A googol is a large number, a followed by one hundred zeros. A googolplex is a large number, a followed by a goog
23、ol ofzeros. A googolplexian is a large number, a followed by a googolplex of zeros. Agoogolplexian is（ ）A.C.B.D. none of the above39. If the total number of positive integral divisors of isnumber of positive integral divisors of？（ ）A. B. C.，whatisthegreatestpossibletotalD.40. Of all the isosceles triangle whose perimeter isand whose side-lengths are integers, what isthe length of the base of the triangle with the largest area?（ ）A. B. C.D.6/6