2021年大联盟(Math League)国际夏季四年级数学挑战活动二（含答案）.docx

2021 美国"大联盟"(Math League)国际夏季数学挑战活动2021 Math League International Summer ChallengeGrade 4, Speed Questions & Answers1. 8000 + 800 + 80 + 8 = 9000 ?A) 2B) 12C) 112D) 1112Answer: C2. If 30 of my 5-dozen pencils were sharp, how many of my pencils were not sharp?A) 10B) 20C) 30D) 50 Answer: C3. (2021 × 1) + (2020 × 0) = 2021 +?A) 0B) 1C) 2020D) 202117Answer: A4. The number of dogs I have is 6 × 5 more than 6 dogs. I have ? dogs.A) 15B) 24C) 36D) 66 Answer: C5. If every digit of my secret code is a different prime number, my secret code has at most ? digits.A) 4B) 5C) 6D) 7 Answer: A6. How many digits does the product of ten 100s have?A) 3B) 4C) 20D) 21 Answer: D7. I am reading a 300-page book in 10 hours, at a constant rate. How many pages have I read in the past 10 minutes?A) 5B) 10C) 15D) 30 Answer: A8. A herd that can be divided into 16 groups of 4 animals can also be divided into ? groups of 8 animals.A) 6B) 8C) 12D) 16 Answer: B9. What is the smallest difference between two whole numbers whose product is 253?A) 2B) 11C) 12D) 252Answer: C10. The perimeter of a square with odd side-lengths could beA) 6B) 8C) 10D) 12 Answer: D11. The time 2 hours and 2 minutes before midnight isA) 2:02 AMB) 10:58 PMC) 9:58 PMD) 11:58 PMAnswer: C12. Which of the following is the product of two prime numbers? A) 100B) 112C) 120D) 142Answer: D13. Fido fetches 3 out of every 54 balls Flo throws. At this rate, how many balls must Flo throw to be sure that Fido fetches 54 balls?A) 18B) 162C) 972D) 2916Answer: C14. How many 2-digit multiples of 15 are also multiples of 2?A) 0B) 3C) 4D) 5 Answer: B15. Al chews half of his gum each day. If Al chews 6 sticks of gum today, how manysticks of gum did he chew 4 days ago?A) 30B) 48C) 96D) 192Answer: C16. How many whole numbers are factors of 2 × 4 × 6?A) 5B) 6C) 8D) 10 Answer: D17. Ava bought more than 1 new book for $6 each, and more than 1 used book for $5 each. The total cost of her books could beA) $22B) $23C) $24D) $25 Answer: A18. I started writing all the multiples of 2 in increasing order, starting with 2. What was the 45th digit I wrote?A) 3B) 5C) 7D) 9Answer: B19. What is the sum of the digits of the greatest 3-digit whole number and the digits of the smallest 4-digit whole number?A) 27B) 28C) 36D) 37 Answer: B20. A square with perimeter 16 is cut into two identical rectangles. The perimeter of one of these two rectangles isA) 8B) 12C) 16D) 24 Answer: B21. Kai makes 4 times as many clocks a day working with a friend as she does working alone. Kai and her friend make 60 clocks a day when they work together. How many clocks can Kai make in 5 days when she works alone?A) 60B) 75C) 100D) 180Answer: B22. My house number does not have 2, 3, or 5 as a factor. Which of the following could be my house number?A) 44B) 55C) 66D) 77 Answer: D23. The average of 5 different whole numbers greater than 0 is 20. What is the greatest possible value of one of the whole numbers?A) 42B) 90C) 96D) 100Answer: B24. Bob bought 36 cups at a cost of 4 cups for $5. He will resell the cups for $2 each. How many cups must Bob sell to earn at least what he paid for all 36 cups?A) 3B) 9C) 22D) 23 Answer: D25. The positive multiples of a whole number were listed from least to greatest. If the 3rd multiple was 39, the 5th multiple wasA) 13B) 42C) 65D) 117Answer: C26. At 65 Flavors Ice Cream shop, every 65th customer wins free ice cream. If the 50th winner was 25 customers before me, what number customer am I?A) 90B) 3225C) 3250D) 3275Answer: D27. Cog counted down from 2021 by subtracting 7 repeatedly. How many positive multiples of 3 did Cog count?A) 94B) 95C) 96D) 97 Answer: C28. There are 8 rows of chairs, with 18 chairs in each row. If we keep all the chairs, what is the smallest number of chairs we must move so that the number of rows equals the number of chairs in each row?A) 8B) 18C) 32D) 48 Answer: D29. Sal added two consecutive integers greater than 10. Adding 2 to the greater integer would increase the tens digit of their sum. What is the smallest possible value of the smaller integer?A) 11B) 14C) 44D) 98 Answer: B30. The product of 5 different primes can be written as the product of at most ? different non-prime whole numbers.A) 2B) 3C) 4D) 5 Answer: B31. The average of 2018, 2020, 2021, 2022, and 2024 isA) 5B) 2019C) 2021D) 2022Answer: C32. The difference between any two odd multiples of 3 is alwaysA) evenB) oddC) 3D) 6 Answer: A33. What is the probability that, in its spelling, a randomly chosen day of the week uses the letter “s” or “S”?A) 2 7B) 3 7C) 5 7D) 6 7Answer: C34. 60 × 60 seconds =A) 36 minutesB) 600 minutesC) 6 hoursD) 1 hour Answer: D35. Starting with January, number the months from 1 to 12. How many of the odd-numbered months have an odd number of days?A) 1B) 2C) 3D) 4 Answer: D36. Five years ago, Al was as old as Bob is now. In how many years from now will Bob be as old as Al is now?A) 5B) 10C) 15D) 20 Answer: A37. When Bucky gave me 8 coins worth 25¢ to help him build a dam, he gave me exactlyA) 1 nickelB) 2 dimesC) 3 nickelsD) 5 pennies Answer: D38. A rectangle has area 48 and integral sides. Its perimeter cannot beA) 38B) 42C) 52D) 98 Answer: B39. The sum of 10 different whole numbers can be ? , but never less.A) 11B) 45C) 55D) 66 Answer: B40. The perimeter of a triangle is 36cm. Its longest side could beA) 11 cmB) 17 cmC) 18 cmD) 19 cm Answer: B41. I said “no stone shall go unturned” in my search for different whole-number factors of 36. Just how many such factors are there?A) 6B) 8C) 9D) 18 Answer: C42. Points A, B, C, and D lie on a line, but not in that order. If AB = 9, BC = 4, and CD = 2, the least possible value of AD isA) 2B) 3C) 4D) 7 Answer: B43. If the symbol hh:mm:ss means hours:minutes:seconds, how much time passes from 5:55:55 P.M. until midnight?A) 6:04:05B) 6:05:05C) 7:04:05D) 7:05:05Answer: A44. Multiply the largest 2-digit prime by the smallest 3-digit prime. A) 1111B) 9191C) 9797D) 9991Answer: C45. If a 卐 b means a × ( a b) , what is the value of 4 卐 3?A) -4B) 4C) 12D) -12Answer: B46. 6 quarters + 2 dimes = 20 pennies + ? nickels.A) 25B) 30C) 33D) 35 Answer: B47. Huck is twice as old as Becky and 2 years older than Tom. If Becky is 13, how old is Tom?A) 14B) 20C) 22D) 24 Answer: D48. The difference between two primes, each greater than 100, is alwaysA) evenB) oddC) compositeD) prime Answer: A49. How many different positive primes are factors of 2021?A) 2B) 3C) 4D) 5 Answer: A50. If the sum of 4 consecutive odd numbers is 4 more than the sum of 4 consecutive even numbers, then the least of the odd numbers is ? more than the least of the even numbers.A) 1B) 2C) 3D) 4 Answer: A51. The largest 4-digit integral multiple of 9 equals the largest 4-digit integral multiple of all of the following exceptA) 3B) 11C) 17D) 101Answer: C52. (the least positive integer) (the largest negative integer) =A) 2B) 1C) 0D) -1 Answer: A53. The greatest common factor of 2 × 4 × 6 × 8 × 10 and 1 × 2 × 3 × 4 × 5 isA) 2B) 4C) 8D) 120Answer: D54. What month will it be 1000 days after February 14?A) OctoberB) NovemberC) DecemberD) January Answer: B55. Each side of a triangle has a different positive integer as its length. What is the least possible perimeter of this triangle?A) 3B) 6C) 9D) 12 Answer: C56. If today is Tuesday, what day will it be in 2022 days?A) MondayB) WednesdayC) ThursdayD) Saturday Answer: A57. The sum of two angles in an equilateral triangle is ? . A) 180B) 120C) 90D) 60 Answer: B58. What is the remainder when the product of all the prime numbers between 1 and 100 is divided by 4?A) 3B) 2C) 1D) 0 Answer: B59. Each month, Dad gives me $1 on the 1st day, $2 on the 2nd day, $3 on the 3rd day,and, in general, $n on the nth day of the month. During 1992, Dad gave me a total of ? .A) $5395B) $5738C) $5767D) $5797Answer: C60. If 10 + 20 + 30 + . + 990 + 1000 = 50500, then what is the value of (10 1) +(20 2) + (30 3) + . + (990 99) + (1000 100)?A) 40400B) 45000C) 45450D) 50000Answer: C