2022年大联盟(Math League)国际夏季四年级数学挑战活动二（含答案）

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1、Speed Questions, Grade 42022 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. 21 22=A) 43B) 442C) 462D) 2122Answer: C2. What is t

2、he average of 1, 2, 3, 4, 5, 6, and 7?A) 1B) 4C) 7D) 10 Answer: B3. I have 1 penny, 5 nickels, and 10 dimes. How much money do I have? A) $1.25B) $1.26C) $1.50D) $1.51Answer: B4. The digital sum for the year 2022 is 2 + 0 + 2 + 2 or 6. How many years from 2023 to 2500 have a digital sum of 6?A) 10B)

3、 12C) 13D) 14 Answer: B155. 100% of 50 = 200% of ?A) 25B) 75C) 100D) 150Answer: A6. Of the following, which fraction does not equal 2?3A) 22 33B) 4 6C) 18 27D) 40 90Answer: D7. The sum of two whole numbers is 36. Their greatest possible product isA) 35B) 260C) 320D) 324Answer: D8. How many different

4、 rectangles does this diagram contain? (Count all rectangles, including squares.)A) 18B) 24C) 36D) 64 Answer: C9. How many positive prime numbers have ones digit of 5?A) 0B) 1C) 5D) 25 Answer: B10. If I start with $100, increase this by 50%, then decrease the new amount by 50%, how much money will I

5、 have?A) $50B) $66C) $75D) $100 Answer: C11. Bob earned $33 in 6 days. At the same rate, Bobs total earnings should be $88 in how many more days?A) 10B) 14C) 16D) 22 Answer: A12. Of the following whole numbers, which has the fewest number of factors?A) 6B) 8C) 10D) 11Answer:D13. 111111 + 222222 + 33

6、3333 + 444444 = 222222 ?A) 1B) 4C) 5D) 10 Answer: C14. Round 0.999 to the nearest tenth. A) 0.1B) 0.9C) 0.99D) 1.0Answer: D15. Ozzie hid his head in the sand 98 hours after 11 P.M. Sunday. Ozzie hid his head on aA) TuesdayB) WednesdayC) ThursdayD) Friday Answer: D16. The ones digit of the product 9

7、9 9 9 9 9 9 9 isA) 1B) 2C) 9D) 0 Answer: A17. The number of zero-digits in 80500 is 3. If the product 1 2 3 4 5 6 7 8 9 10 = 3628800, how many zero-digits are in the product 10 20 30 40 50 60 70 80 90 100?A) 10B) 11C) 12D) 13 Answer: C18. (200 + 199 + 198 + + 101) (100 + 99 + + 1) = 100 ?A) 99B) 100

8、C) 199D) 200Answer: B19. If I made a list of every seven-digit whole number greater than 1 million which has exactly six of its digits equal to 9, how many different numbers would be on my list?A) 7B) 9C) 62D) 63 Answer: C20. If the sum of two whole numbers equals twice their difference, this sum ca

9、nnot be A) 222B) 444C) 888D) 1000Answer: A21. All the following have 2, 3, 5, 6, 10, 15, and 30 as factors exceptA) 543420B) 85030C) 72630D) 53430Answer: B22. In a class of 30 students, exactly 7 have smart phones, exactly 15 have pocket calculators, and exactly 2 have both. How many of the 30 stude

10、nts have neither?A) 10B) 8C) 6D) 4 Answer: A23. (2 m)- (1000 mm) =A) 10 cmB) 100 cmC) 20 cmD) 200 cm Answer: B24. A prime number multiplied by its reciprocal will always beA) primeB) 0C) evenD) odd Answer: D25. Which of the following fractions is less than one-third?A) 5 14B) 15 46C) 31 90D) 104309A

11、nswer: B26. In a class, the ratio of the number of boys to the number of girls is 2 to 3. The number of boys is what percent of the number of students in the entire class?A) 20%B) 40%C) 60%D) 66 2 %3Answer: B27. Joan bought a painting for $10, sold it for $20, repurchased it for $30, then resold it

12、for $40. JoanA) broke evenB) made $20C) lost $10D) lost $20Answer: B28. How much less is the area of a rectangular field 60 meters by 40 meters than that of a square field with the same perimeter?A) 10 square metersB) 100 square metersC) 1000 square metersD) theyre equal Answer: B29. Choice ?has mor

13、e different prime factors than the other choices. A) 1997B) 1998C) 1999D) 2000Answer: B30. A clock is set correctly at 2 P.M. It loses 3 minutes every hour. What is the correct time when the clock reads 9 A.M. the next day?A) 8 A.M.B) 8:03 A.M.C) 9:57 A.M.D) 10 A.M. Answer: D31. Find the largest pri

14、me factor of 30 40 50.A) 3B) 5C) 10D) 50 Answer: B32. In the rectangle below, the area of triangle ABC is 12. What is the area of triangle ABE? (E is the midpoint of line segment CD.)A) 18B) 15C) 12D) 10 Answer: C33. All the whole numbers with a first digit of 2 are written in increasing order. The

15、list begins 2, 20, 21, 22, Find the 1000th digit thus written.A) 6B) 7C) 8D) 9 Answer: A34. My bicycle has a rear wheel whose diameter is 1.2 times as big as the diameter of the front wheel. As I ride my bicycle, if the front wheel turns 120 times, the rear wheel will turnA) 96 timesB) 100 timesC) 1

16、20 timesD) 144 times Answer: B35. For any number N, let #(N) be the number of prime numbers less than or equal to N. What is #(8620) - #(8614)?A) 0B) 1C) 2D) 3 Answer: A36. I multiplied one whole number by 18. I multiplied a second whole number by 21. I then added the two products. Of the following,

17、 which could have been the resulting sum?A) 2020B) 2021C) 2022D) 2023Answer: C37. The lengths of the sides of a triangle are 6, 8, and 10. The area of this triangle isA) 24B) 30C) 40D) 48 Answer: A38. In a 10-team league, each team plays every other team exactly twice. Find the total number of games

18、 played in the league.A) 45B) 81C) 90D) 180Answer: C39. A man has 2 pennies, 3 nickels, 1 dime, and 2 quarters. How many different sums of money can he make using one or more of these 8 coins?A) 8B) 12C) 47D) 77 Answer: C40. A pilot flew 80 km. He flew the first 4 minutes at half speed and the secon

19、d 4 minutes at full speed. The full speed of the plane isA) 400 km/hrB) 600 km/hrC) 800 km/hrD) 1000 km/hr Answer: C41. A whole number is called an increasing number if each digit in the number is greater than the digit to its left. For example, 2359 is an increasing number. How many increasing numb

20、ers are there between 5000 and 10000?A) 3B) 4C) 5D) 6 Answer: C91642.+=5A)7B)C) 5D) 7 Answer: D43. How many different three-digit numbers can be made using any three of the following five digits: 1, 2, 2, 3, and 3?A) 12B) 16C) 18D) 20 Answer: C44. If B is the midpoint of AC , and if C is the midpoin

21、t of BD , then what percent of CD is AC?A) 25%B) 50%C) 100%D) 200%Answer: D45. At 3:30, the hands of an accurate school clock make an angle ofA) 90 degreesB) 75 degreesC) 65 degreesD) 60 degrees Answer: B46. For what value of x will the sum of the numbers in each row, each column, and both major dia

22、gonals be equal in the “magic square” shown below?134810175612x9A) 14B) 15C) 16D) 18 Answer: C47. What is the 200th number in the sequence 1, 1, 1, 2, 1, 3, 1, 4, 1, 5,?A) 1B) 100C) 101D) 200Answer: B48. What is the remainder whenA) 0B) 1C) 2D) 3 Answer: B1099is divided by 9?49. A square can be divi

23、ded into 9 smaller congruent squares, as shown. By drawing different lines, it would be possible to divide this square into ?smaller congruent squares.A) 70B) 80C) 90D) 100Answer: D50. A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour

24、. Find his average rate for the round trip in miles per hour.A) 50B) 48C) 47D) 46 Answer: B51. How many whole numbers between 1 and 500 are divisible by 6 but are not divisible by 8?A) 83B) 73C) 63D) 53 Answer: C52. What is the missing length in the diagram (which is not drawn to scale)?AB = 9, BC =

25、 18, BD = 6, CE= ?A) 12B) 15C) 18D) 21 Answer: C53. Ann says “I never lie.” Bob says “Ann is not lying.” Carol says “Bob is lying.” Dan says “Carol is not lying.” If Bob is lying, how many of the other three must be lying?A) 0B) 1C) 2D) 3 Answer: B54. What is the probability that, in its spelling (u

26、sing all lowercase letters except the first one), a randomly chosen day of the week uses the letter “u”?A) 2 7B) 3 7C) 4 7D) 5 7Answer: C55. If the average of21999and22001is equal to the number of pirates who everlived on Treasure Island, then how many pirates ever lived on Treasure Island?A) 5 2199

27、8B) 3 21998C) 3 21999D) 22000Answer: A56. After 5 tests, a students average was 80. After taking an examination which counted as two test grades, his average dropped to 76. What was his grade on that examination?A) 52B) 66C) 72D) 76 Answer: B57. A 12-hour clock loses 10 minutes each day. The clock w

28、ill first return to the correct time inA) 36 daysB) 72 daysC) 120 daysD) 144 days Answer: B58. In the correct addition below, A, B, and C are 3 different non-zero digits. Find the value of C.AB+ CC AAAA) 1B) 9C) 8D) 7 Answer: B59. Two cars are traveling in the same direction, one at 40 km/hr and the

29、 other at 50 km/hr. If the slower car is 15 km ahead of the faster car, how long will it take the faster car to catch up with the slower car?A) 60 minutesB) 75 minutesC) 80 minutesD) 90 minutes Answer: D60. A man has a 10 m 10 m square garden. In the center is a 2 m 2 m square patch which he can not use. He divides his usable space into four congruent rectangular patches, each of which measuresA) 3 m 3 mB) 8 m 3 mC) 4 m 6 mD) 2 m 12 m Answer: C