1、2021 美国大联盟(Math League)国际夏季数学挑战活动2021 Math League International Summer ChallengeGrade 5, Speed Questions1. (2021 5) + (2021 5) + (2021 5) + (2021 5) + (2021 5)=A) 2020B) 2021C) 2022D) 80842. Kirok the dragon has 2021 scales on his neck, 3031 scales on his wings, and 5051 scales on the rest of his bo
2、dy. What is the total number of scales on Kiroks body?A) 1013B) 7073C) 10103D) 1001033. What is the remainder when (7 + 77 + 777 + 7777 ) is divided by 7?A) 0B) 1C) 4D) 12344. Four out of every five dentists recommend HiGlo toothpaste. If I ask 100 dentists whether they would recommend HiGlo toothpa
3、ste, how many of the dentists will recommend it?A) 25B) 30C) 50D) 80115. What is the perimeter of a square that has an area of 64?A) 16B) 24C) 32D) 646. 4 5 101 = 1010 ? A) 2B) 20C) 101D) 10107. Each angle of a rectangle is ? degrees greater than each angle of an equilateral triangle.A) 30B) 60C) 90
4、D) 1208. It is 2021 hours after midnight. What time is it?A) 5 AMB) 7 AMC) 5 PMD) 7 PM9. If 20% of a number is 50, what is 40% of the same number?A) 30B) 60C) 100D) 15010. As he rides, Sir Reginald von Prime is going to plant a flag every time the total distance he has ridden is a prime number of km
5、. How far will he have gone when he plants his 11th flag?A) 23 kmB) 29 kmC) 31 kmD) 37 km11. The greatest common factor of 43 52 and 53 72 isA) 5B) 52C) 53D) 5512. How many 2-digit odd numbers do not have 3 as either digit?A) 32B) 36C) 40D) 4413. My average score on the 3 tests Ive taken so far is 8
6、5. What score do I have to get on the next to raise my average score to 88?A) 94B) 95C) 96D) 9714. Nan knits new tops for newborns. Today she knitted one more top than yesterday. The number of tops she knitted in the two days combined could beA) 12B) 23C) 34D) 10015. 8 dozen socks = ? pairs of socks
7、A) 24B) 36C) 48D) 9616. A boy is in line with 30 people behind him and twice as many ahead of him. How many people are in this line?A) 60B) 61C) 90D) 9117. If the sum of 6 consecutive integers is 255, what is the sum of the greatest and the least of the integers?A) 38B) 43C) 81D) 8518. Paola ran the
8、 300 m from her door to the bus in 20 seconds. What was her speed in km/hr?A) 15B) 20C) 34D) 5419. What is the product of all the positive divisors of 64?A) 64B) 8 642C) 8 643D) 64420. In 30 years my age will double, my sisters age will triple, and my brothers age will quadruple! What is the sum of
9、our ages now?A) 32.5B) 55C) 90D) 100.521. The greatest prime factor of the number of seconds in 2197 hours isA) 11B) 13C) 17D) 1922. In the country of Latka, 6 simkas are worth 25 ibidas and 2 ibidas are worth 15 yatabes, If I pay 12 simkas for a chicken that is priced at 365 yatabes, how many yatab
10、es should I expect in change?A) 10B) 12C) 13D) 1523. A lighthouse can be seen from at most 50 km on a clear night but from at most 20 km during fog. The greatest viewing distance on a clear night is what percent of the greatest during fog?A) 40B) 60C) 150D) 25024. What is the greatest possible numbe
11、r of points of intersections of a circle and a rectangle?A) 2B) 4C) 6D) 825. How many squares of integers have 3 digits?A) 20B) 21C) 22D) 2326. Al writes the first 20% of his report on Monday, then 30% of the remaining report on Tuesday. What percent of the entire report that Al began on Monday rema
12、ins to be written on Wednesday?A) 44%B) 50%C) 54%D) 56%27. 42 44 46 48 =A) 240B) 41024C) 1630D) 643028. Zak shuffled together four decks of cards and started dealing them out. Surprisingly, the suits came out in a pattern that repeated as follows until the 26th club appeared: club, diamond, heart, c
13、lub, heart, diamond, club, diamond, heart, club, heart, diamond, .How many cards must Zak deal in order to have dealt 26 of the club suit?A) 75B) 76C) 78D) 8429. Mylocal ice cream shop offers 15 different flavors of ice cream. If I want two scoops of ice cream, each scoop a different flavor, how man
14、y combinations of two scoops of ice cream are possible?A) 29B) 30C) 105D) 21030. Inez multiplied 21 by the product of 21 21s. Then she subtracted 21 from that product 2121 times. With what number did she end up?A) 0B) 2120C) 2121 + 212D) 2122 21231. What is the greatest number of prime factors (not
15、necessarily all different) that a three-digit number can have?A) 5B) 6C) 8D) 932. How many of the first 2021 even positive integers are divisible by 6?A) 336B) 337C) 673D) 67433. Maestro must be able to divide the birds in his all-bird choir into 6, 7, and 8 equal groups. He wants a 3-digit total nu
16、mber of birds. In all, how many such 3-digit numbers are possible?A) 2B) 3C) 4D) 534. If 25 people take 27 hours to catch all the birds, at that rate how long would it take 45 people to catch all the birds?A) 9 hrsB) 15 hrsC) 18 hrsD) 21 hrs35. What is the least number of consecutive positive intege
17、rs starting with 1 that must be multiplied together to get a multiple of 2021?A) 22B) 80C) 90D) 10536. (2 + 4 + 8)2 =A) (3 + 4 + 5)2B) (4 + 5 + 6) 2C) (1 + 2 + 4)2 4D) 22 + 42 + 8237. Each equilateral triangle shown has a perimeter of 9. What is the perimeter of the figure?A) 6B) 8C) 10D) 1238. The
18、base of an isosceles triangle with integral sides is 12. What could be the perimeter?A) 20B) 22C) 24D) 2639. Emma counted up from 0 by 1s every second for 5 minutes, and then down by 1s every second for 2 minutes. What number did she end on?A) 180B) 240C) 360D) 48040. What is the 200th number in the
19、 sequence 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, .?A) 1B) 100C) 101D) 20041. 2020 is divisible by ? different prime numbers.A) 2B) 3C) 4D) 542. The larger angle between the minute hand and the hour hand of a circular clock at 1:10 PM measuresA) 300B) 315C) 330D) 33543. How many prime numbers less than 50 hav
20、e reciprocals that are terminating decimals?A) 1B) 2C) 3D) 444. Red pens are sold at 3 for $1 and black pens are sold at 4 for $1.50. Alice bought 12 red pens and 24 black pens. She paid for them with a $20 bill. How much change did she receive?A) $7B) $9C) $13D) $1645. The number 1000 has only 16 p
21、ositive whole number factors. The product of all 16 of these factors isA) 108B) 1016C) 1024D) 103246. The average of 21 consecutive integers is 31. The largest of these integers must beA) 40B) 41C) 51D) 5247. (221 1000) + (221 100) + (221 10) + (221 1) is divisible byA) 2B) 3C) 4D) 1148. 314159272 3
22、14159262 = 31415926 + ? A) 0B) 31415927C) 31415928D) 3141592549. Each km of a 5 km race, my horses average speed decreased 1 km/hr. If I averaged 5 km/hr at first, it took me ? minutes to finish.A) 120B) 137C) 216D) 68550. I make a straight cut through a rectangular piece of paper and get two pieces
23、. When I make a straight cut through one of these two pieces, I then have three pieces. Altogether, the number of edges on these three pieces cannot beA) 8B) 9C) 10D) 1151. 51.12 +13 +1is equivalent to4 + 15A)68B)15729C)12617D) none of these1541 25 25 452.=A) 4B) 25C) 50D) 10053. If the total value
24、of an equal number of pennies, nickels, and dimes is $3.20, what is the value of the nickels alone?A) 40 centsB) 60 centsC) 80 centsD) 100 cents54. What is the ones digit of 22021?A) 2B) 4C) 6D) 855. The sum of 50 consecutive whole numbers equals the sum of 25 other consecutive whole numbers. If the
25、 smallest of the 50 numbers is 2021, the smallest of the 25 numbers isA) 4079B) 4103C) 2021D) 207056. If B is the midpoint of AC , and if C is the midpoint of BD , then what percent ofCD is AC?A) 25%B) 50%C) 100%D) 200%57. If 1 10010= 0.00.1, then the total number of times that a 0 appears to the ri
26、ght ofthe decimal point and left of the 1 isA) 98B) 99C) 100D) 10158. I plan to give a total of 3 (identical) slices of pizza to Ali, Bob, and Carl. Each person will get 0, 1, 2, or 3 slices. In how many different ways can I distribute these 3 slices of pizza?A) 8B) 9C) 10D) 1259. All the whole numb
27、ers with a first digit of 2 are written in increasing order. The list begins 2, 20, 21, 22,Find the 1000th digit thus written.A) 6B) 7C) 8D) 960. A perfect square is the square of an integer. Of the integers from 2 through 99 inclusive, how many have at least one perfect square factor 1 ?A) 36B) 38C) 40D) 44
