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1、Speed Questions, Grade 52022 Math League International Summer Challenge (Unofficial version, for reference only)Note:Listed below are the four types of coins currently being minted in United States.a. Penny: 1b. Nickel: 5c. Dime: 10d. Quarter: 251. 1% of 1% =A) 1B) 1%C) 1 1000D) 1 %100Answer: D2. 20
2、0% of ?is a prime.A) 1B) 2C) 3D) 5 Answer: A13.1=12+2+2A) 1 3B) 2 5C) 2 9D) 5 12Answer: D164. Find the missing number: 4455 = 4 5.?A) 11B) 22C) 45D) 121Answer: D5. The average of six consecutive whole numbers could be A)36 13B) 44 16C) 48 12D) 54 Answer: C6. If 5% of a certain number is 16, then 25%
3、 of half the number isA) 2B) 4C) 40D) 80 Answer: C7. Alis crystal ball grants two-fifths of one-fifth of all wishes. This is ？ of all wishes.A) 3 5B) 2 25C) 8D) 60 Answer: C8. After a girl spends 13of her money and loses 12of the remainder, she then has $10left. She started withA)$30B) $45C) $50D) $
4、60 Answer: A9. Which of the following fractions has the greatest value?A)51 100B) 152300C) 52 103D) 50 99Answer: A10. If 5 apples cost the same as 4 oranges, find the ratio of the cost of 1 apple to the cost of 1 orange.A)5: 9B) 4:9C) 5:4D) 4:5Answer: D11. The least common multiple of 1, 2, 3, 4, 5,
5、 6, 7, 8, 9, and 10 isA)1B) 1260C) 2520D) 3628800Answer: C12. By what fractional part of 45does 35exceed 2?5A) 1 5B) 1 4C) 2 5D) 3 5Answer: B13. In a right triangle whose area is 12, each leg is as long as the side of a certain square. What is the area of the square?A) 12B) 24C) 48D) 144Answer: B14.
6、 Find the last digit of 19831984.A) 1B) 2C) 3D) 9 Answer: A15. I have 5 coins of equal value in my left pocket, and 2 coins of equal value in my right pocket. If the total value of the coins in each pocket is the same, my left pocket containsA) penniesB) nickelsC) dimesD) quarters Answer: C16. A cir
7、cle has an area of 36. What is the area of the smallest square that can surround this circle?A) 18B) 48C) 72D) 144Answer: D17. The number 1000 has only 16 positive whole number factors. The product of all 16 of these factors isA)108B) 1016C) 1024D) 1032Answer: C18. (-1)1 + (-1)2 + (-1)3 + +(-1)2021
8、+ (-1)2022 =A) -1B) 0C) 1D) 1011Answer: B19. If Bos score was 8/10 of Als, and Cys score was 3/4 of Bos, then the ratio of Als score to the average of Bos and Cys scores wasA)10:7B) 7:10C) 5:3D) 3:5Answer: A20. Jack picks 3 liters of berries in 8 minutes. Jill pick 4 liters of berries in 10 minutes.
9、 Working together, how many berries can they pick in 1 minute?A) 7 9B) 7 18C) 8 19D) 31 40Answer: D21. 5% is what percent of 0.1? A)10%B) 50%C) 200%D) 500%Answer: B22. The length of a radius of a circle is decreased by 10%. This causes the area to be decreased byA)19%B) 20%C) 21%D) 25%Answer: A99999
10、923. The hundreds digit ofisA) 3B) 5C) 7D) 9 Answer: D24. An ant crawls outside a square of side 1 cm, at all times remaining exactly 1 cm from the boundary of the square. In square cm, the area bounded by one complete circuit of the ant is most nearly equal toA) 7B) 8C) 9D) 10 Answer: B25. From noo
11、n one day till noon 2 days later, how many times will the hour hand of a clock pass the 1 oclock mark?A) 2B) 3C) 4D) 48 Answer: C26. The reciprocal of 1.01 is A)0.101B) 1.01C) 0.99D) 100101Answer: D27. If, every 2 seconds, a unicycle wheel of radius 1 m rolls once around without slipping, what is th
12、e wheels average ground speed?A) 0.5p m/secB) p m/secC) 2p m/secD) 4p m/secAnswer: B28. The volume of cube is 331 m3 less than the volume of cube . If an edge ofcube is 10 meters, an edge of cube isA) 14 metersB) 13 metersC) 12 metersD) 11meters Answer: D29. 72 + 72 + 72 + 72 + 72 + 72 + 72 = 7 ?A)
13、72B) 73C) 77D) 78Answer: A30. Which of the following figures can not be folded along the dotted lines to form a cube?A)B)C)D)Answer: D31. When I turn my calculator upside down, the digits 0, 1, 2, 5, 6, 8, and 9 still appear as digits. For example, When I turn my calculator upside down, 65259 remain
14、s the samethat is, it stays 65259. How many whole numbers between 100 and 1000 remain the same when I turn my calculator upside down?A)67B) 65C) 656D) 676Answer: B32. For each whole number n 1 , list all the fractions between 0 and 1 withdenominator n and a whole number numerator. The list, which be
15、gins1 , 1 ,232 , 1 ,342 , 3 ,441 , , continues in increasing order for each denominator. The 100th such5fraction isA) 8 46B) 9 46C) 10 46D) 11 46Answer: C33. If the hands on a round clock moved counter clockwise, to what number would the minute hand point 20 minutes before the hour hand pointed to t
16、he 3?A) 4B) 7C) 8D) 11 Answer: A34. If M and N are positive two-digit numbers, then, of the following fractions, the one with the largest value isA) N MB) N +1M -1C) N -1MD) N M +1Answer: B35. Find the area of the trapezoid below.A) 44B) 48C) 90D) 100Answer: A36. If A)a 0- a bandb 0 , which of the f
17、ollowing must be true?B) a -bC) b - a 0Answer: C37. 299 + (-2)99 =A)099B) 299C) 2198D) 499Answer: A38. The first 1000 primes are multiplied together. This number must be divisible byA)10B) 100C) 1000D) 101000Answer: A39. Two sides of a triangle have lengths 9 and 11. If no two sides of the triangle
18、have equal lengths, the perimeter could beA) 21B) 23C) 29D) 31 Answer: B40. To form a certain sequence, the rules are:If a number is even, divide by 2 to get the next number;If a number is odd, multiply by 3, then add 1 to the next number.Starting with 12, the first few terms are 12, 6, 3, 10, 5, 16
19、, In this particular sequence, the 100th term isA) 1B) 2C) 3D) 4 Answer: A41. Ifx + 3represents an even number, then which of the following will alwaysrepresent an odd number?A) x +1B) 6x + 4C) 3x + 5D) 5x + 8Answer: D42. A number is rounded to the nearest whole number. The original number is then r
20、ounded to the nearest ten. The difference between the 2 new numbers formed cannot beA) 3B) 4C) 5D) 6 Answer: D43. How many of the first 1992 prime numbers have reciprocals which are less than 0.05?A)1972B) 1984C) 1985D) 1988Answer: B44. If x people can do a job in d days, how long would it take y pe
21、ople to do the same job?A) xydB) xd yC) y xdD) yd xAnswer: B45. There are 2 red, 3 blue, and 4 green marbles in a bag. I take one marble at a time out of the bag without looking. What is the least number of marbles I must take out to be sure that I have 3 of the same color?A) 3B) 5C) 7D) 9 Answer: C
22、46. If Pat is A)20%B) 25%C) 30%331 % taller than Lee, then Lee is what percent shorter than Pat?3D) 331 %3Answer: B47. How many different integers have reciprocals whose values are greater than19and less than1998A) 78B) 79C) 84D) 85 Answer: D98 ?199848. What is the remainder when the product of all
23、the prime numbers between 1 and 100 is divided by 4?A) 3B) 2C) 1D) 0 Answer: B49. As shown, a vertex of a square with sides of length 2, and the center of a circlewith a radius of 2, coincide. What is the area of the shaded region?A)4p - 4B) 2p + 4C) 3p - 4D) pAnswer: B50. What is the quotient of th
24、e least common multiple of the first 40 positive integers divided by the least common multiple of the first 30 positive integers?A)1147B) 2294C) 36704D) 89466Answer: B51. In Professor Tuffguys mathematics class, 36 students took the final exam. If the average passing grade was 78, the average failin
25、g grade was 60, and the class average was 71, how many of these students passed the final?A) 14B) 22C) 24D) 29 Answer: B52. Frank and Alice went to a “Bring a Snack” party. Frank spent 10 pennies + 16 dimes. Alice spent as much as Frank, but her 26 coins consisted of only quarters and nickels. How m
26、any nickels did Alice spend?A) 16B) 20C) 22D) 24 Answer: D53. In the ordered sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, , each positive integer n occurs in a block of n terms. If I add the reciprocals of all the terms, in order beginning with the first term, then at some point the sum will beA)98.1B) 99
27、.25C) 100.5D) 102.75Answer: B54. If n is a positive integer, n！ is the product of the first n positive integers. Forexample,4！= 4 3 2 1 = 24 . If u and v are positive integers andu!= v!56 , then vcould equalA) 6B) 8C) 56D) 57 Answer: A55. If the lengths of the sides of a rectangle are integers, and
28、if one sides is 2 more than another, then the perimeter could equalA)1998B) 1999C) 2000D) 2002Answer: C56. I found the product of n different positive prime numbers. Of the following, which could be the number of positive integers that are factors of this product?A)1024B) 1000C) 676D) 400Answer: A57
29、. If I add together ?different positive odd numbers, the value of the sum can be 12321, but it can never be less than 12321.A)111B) 121C) 131D) 221Answer: A58. The productA)1999B) 2000C) 2001D) 2002Answer: B1.25 10nis the cube of an integer when n =59. If3x : 5 y = 7 :11 , thenx : y =A)2:3B) 21:55C) 35:33D) 55:21Answer: C60. If my rocketcar goes 30 km at an average speed of 30 km/hr, what average speed must it maintain over the next 30 km for it to achieve an average speed of 50 km/hr for the entire 60 km?A) 70 km/hrB) 80 km/hrC) 100 km/hrD) 150 km/hr Answer: D