2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段四年级试卷及答案

首先感谢胡锐博士从美国引进了“数学大联盟杯赛”这么好的一个活动，它让中国的学生得以领略美国最为普及、最受欢迎的数学竞赛的原貌，同时也为数英双优的培训开辟了新的模式，尤其是目前在北京及全国都缺少这样一种培养方式。

古希腊伟大的哲学家亚里士多德曾说：“虽然数学没有明显提到善和美，但善和美也不能和数学完全分开，因为美的形式，就是‘秩序、匀称和确定性’，这些正是数学研究的原则。

”让孩子们年少时就开始接触数学，感受数学之美，从而培养他们对数学的兴趣，这在国外被称为“天才少年培养计划”。

虽然国内也很早就开始了这样的尝试，但像引进美国“数学大联盟杯赛”这种形式的活动还尚属首次。

美国“数学大联盟杯赛”至今已连续举办了35年，它不仅是美国及北美地区影响力最大的中小学数学赛事，也是一项具有世界影响力的中小学数学赛事。

杯赛每年举办一次，分为初赛(包括复赛)和决赛两个阶段。

初赛(包括复赛)试题灵活、生动，富有趣味性，同时也贴近生活。

让学生理解数学、欣赏数学，激励学生创新，更能激发学生学习数学的兴趣，培养学生主动探索的精神。

初赛的目的是普及数学。

决赛的试题由美国“数学大联盟杯赛”和斯坦福大学联合命题，具有很高的挑战性，着力培养学生创造性地解决问题和创新思维的能力(fun and creative problems that promote critical-thinking and problem-solving skills)，是数学超常少年展现才华的绝佳平台。

2012年伊始，在各方的努力之下美国“数学大联盟杯赛”得以成功登陆中国，中国赛区初赛于2012年2月25日举行，首次举办即得到广大中小学生的积极响应及踊跃参与，同时也涌现出大批数学能力与英语水平俱佳的优秀学生。

而随着2011-2012年度美国“数学大联盟杯赛”颁奖会的圆满结束，决赛的大幕正式拉起，我们也马不停蹄的投入到决赛和数学夏令营的组织工作中。

2011-2012年度美国“数学大联盟杯赛”中学组的决赛和数学夏令营是由美国“数学大联盟杯赛”和斯坦福大学联合举办，试题新颖、灵活、生动，富有趣味性和挑战性，培养学生创造性地解决问题和创新思维的能力。

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(七年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

请在装订线内签名表示你同意遵守以上规定。

考前注意事项：1. 本试卷是七年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、草稿纸。

试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一半题目的学生就应该受到表扬和鼓励。

选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。

1.(4 × 6 × 8 × 10) ÷ (6 × 8 × 10) =A) 3 B) 4 C) 12 D) 3 × 6 × 8 × 102.(2 ÷ 3) rounded to the nearest hundredth isA) 0.33 B) 0.66 C) 0.67 D) 0.703.Baby Amy is one day older than Baby Barry. The product of theirages measured in days could beA) 33 B) 132 C) 245 D) 2464.(The largest even divisor of 200) ÷ (the largest odd divisor of 200) =A) 4 B) 8 C) 20 D) 2005.An equilateral triangle with integer side-lengths has a perimeter that is numerically equalto the area of a square. Which of the following could be the length of a side of the square?A)12 B)10 C) 8 D) 46.I have only nickels, dimes, and quarters to pay for my dinner, which costs $12.60. Thesmallest number of coins I can use to pay isA) 51 B) 52 C) 54 D) 557.The smallest prime factor of 2019 isA) 1 B) 3 C) 19 D) 6738.The product of four consecutive integers must be divisible by each of the following exceptA) 4 B) 6 C) 10 D) 129.There are ? hours in 4 weeks.A) 48 B) 96 C) 336 D) 67210.If I divide my favorite number by its reciprocal, the quotient is 10 times as large as myfavorite number. My favorite number isA)110B)15C)12D) 1011.The height of the smoke from my barbecue is 100 000 cm, which is thesame as ? km.A) 1 B) 10C) 100 D) 100012.If the degree measures of the angles of a triangle are in a 4:5:6 ratio, whatis the difference between the measures of the largest and the smallest angles?A) 12°B) 24°C) 30°D) 36°13.The population of a town started at 1000, then went up 10%, then down 20%, then backup 10%. The population of the town ended atA) 968 B) 972 C) 1000 D) 102414.In my orchard, there are 60 more apples than oranges, and 5times as many apples as oranges. How many apples are there?A) 50 B) 75 C) 100 D) 12515.A polygon in which every pair of angles is supplementary must be aA) triangle B) squareC) rectangle D) hexagon16.Which of the following is smallest in value?A) 2600B) 3500C) 4400D) 530017.(2100 × 450) ÷ 2 =A) 275B) 2100C) 2149D) 219918.What is the remainder when 3333 is divided by 10?A) 1 B) 3 C) 7 D) 919.On a series of tests, Gus got 100 once, 90 twice, and 80 five times. What was his averagescore for all of the tests?A) 80 B) 85 C) 90 D) 9220.The product of the thousands and tenths digits of 1234.5678 isA) 5 B) 10 C) 35 D) 40第1页，共4页第2页，共4页21. The probability of heads then tails then heads on 3 tosses of a coin isA) 0.125B) 0.25C) 0.375D) 0.522. On January 1 last year, Rui got a jar of jellybeans. On each day he ate the same number ofjellybeans. He counted 560 on January 31 before eating any and he counted 380 on March 17 before eating any. There were ? jellybeans in the jar when Rui got it.A) 600 B) 650 C) 680D) 74023. Jake used 120 boxes of tissues in 3 days! There are 144 tissues per box. That’s ? tissues per minute!A) 2B) 3C) 4D) 524. The number 5184 has ? positive odd divisors.A) 1B) 2C) 4D) 525. The sum of 5 consecutive even integers could beA) 120B) 125C) 164D) 21226. Jacques, who paints only smiley faces, signs and numbers each of his paintings. If he started with Smiley #1 and has painted through Smiley #111, how many times has he used the digit 1 in his numbering?A) 12B) 22C) 24D) 3627. How many whole numbers have squares that are between 2 and 200?A) 12B) 13C) 24D) 2628. A baker cuts circular cookies out of a flat rectangle of cookie dough. If the rectangle is2 m by 1 m, and the cookies have radius 10 cm, at most how many cookies can the baker cut from the sheet of dough?A) 50B) 63C) 64D) 20029. 0.02% of 20% of ? = 200% of 2000A) 1000 B) 100 000 C) 1 000 000D) 100 000 00030. A miner combines 1200 kg of ore that is on average 3% gold with 2400 kg of ore that is on average 6% gold. If the 100 kg containing the most gold of the 3600 kg is 40% gold, the remaining ore will be ? gold.A) 2%B) 3%C) 4%D) 5%31. Including face diagonals, the total number of diagonals of a cube isA) 12B) 14C) 16D) 2432. How many odd 3-digit integers greater than 500 are composed of 3 different non-zero digits?A) 154B) 175C) 185D) 20033. If I square all whole-number factors of 36 and multiply the resulting numbers, the product will be equal toA) 362B) 364C) 368D) 36934. When the four members of the Beaverton family carry a log, each has a 0.02 probability of tripping, and each probability is independent of the others. What is theprobability that they will carry the log without any of them tripping?A) 1 – (0.02)4 B) (0.98)4 C) (0.02)4D) 1 – (0.98)435. What is the largest prime factor of the product of all even numbers from 2 through 200?A) 47B) 97C) 199D) 201936. What is the sum of the solutions to |10 – 4x | = 5?A) 1.25 B) 3.75C) 5 D) 1037. If 2x × 42x × 83x = 2y , then y =A) 2x 3B) 6xC) 6x 3D) 14x38. Each time Alan falls asleep, he sleeps for exactly 8m minutes and then is awake for the next 4m minutes. If he falls asleep for the 1st time at 11 P.M. and wakes from his 6th time asleep at 4:06 A.M., then m = A) 4.25 B) 4.5 C) 5.125D) 6.37539. If x is a positive integer, the remainder when 2018x is divided by 10 could NOT beA) 4B) 6C) 8D) 040. If a + b = 8 and114a b+=, then ab = A) 2 B) 6 C) 12 D) 32第3页，共4页 第4页，共4页2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(八、九年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论， 我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

1. Examples of Math League Influence and Significance a) US Best High Schools Rankings
a) /education/best-highschools/national-rankings/spp+100
2. 美国“数学大联盟杯赛”第一届竞赛于1977年 举行， 至今已经连续举办了35年。
3. 每年有来自全球的超过一百万名中小学生参加。
2021/3/12
4
Math League History
Mr. Steven R. Conrad & Mr. Daniel Flegler: 美国著 名的数学教育家
students.php c) Lectures
a) Brian Conrad, /2012/finals/professor/professor1.php
b) Ravi Vakil, /2012/finals/professor/professor3.php
2. Math League in China
a) Intro of Committee Members b) Comparison c) 2012-2013 Math League in China d) Online Learning System
2021/3/12
2
Math League in North America & The World
b) /jointly/consequence.php
b) Harvard Twins Sisters
a) /jointly/consequence.php#
c) US newspaper coverage

B) Monday
C) Tuesday
D) Friday
12. Rounding a decimal to the nearest whole number yields a number that is at most ? greater than the original decimal.
A) 0.05
B) 0.1
C) 0.5
D) 0.9
13. The perimeter of a rectangle with area 2019 and integral side-lengths is greatest when its length and width diffC) 670
A) 6
B) 9
C) 12
D) 18
3. The number 36 is the product of -6 and
A) -6
B) 6
C) -30
D) 42
4. 20 ×18 = 20 ×19 + 20 × ?
A) -1
B) 0
C) 1
D) 20
5. Angel arrived 3 of an hour early for her noon appointment. At what time did Angel 10
城市
区
考号
所在学校
年级
姓名(签名)
………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………

AMC8（美国数学竞赛）历年真题、答案及中英文解析艾蕾特教育的AMC8 美国数学竞赛考试历年真题、答案及中英文解析：AMC8-2020年：真题 --- 答案---解析（英文解析+中文解析）AMC8 - 2019年：真题----答案----解析（英文解析+中文解析）AMC8 - 2018年：真题----答案----解析（英文解析+中文解析）AMC8 - 2017年：真题----答案----解析（英文解析+中文解析）AMC8 - 2016年：真题----答案----解析（英文解析+中文解析）AMC8 - 2015年：真题----答案----解析（英文解析+中文解析）AMC8 - 2014年：真题----答案----解析（英文解析+中文解析）AMC8 - 2013年：真题----答案----解析（英文解析+中文解析）AMC8 - 2012年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 2010年：真题----答案----解析（英文解析+中文解析）AMC8 - 2009年：真题----答案----解析（英文解析+中文解析）AMC8 - 2008年：真题----答案----解析（英文解析+中文解析）AMC8 - 2007年：真题----答案----解析（英文解析+中文解析）AMC8 - 2006年：真题----答案----解析（英文解析+中文解析）AMC8 - 2005年：真题----答案----解析（英文解析+中文解析）AMC8 - 2004年：真题----答案----解析（英文解析+中文解析）AMC8 - 2003年：真题----答案----解析（英文解析+中文解析）AMC8 - 2002年：真题----答案----解析（英文解析+中文解析）AMC8 - 2001年：真题----答案----解析（英文解析+中文解析）AMC8 - 2000年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1998年：真题----答案----解析（英文解析+中文解析）AMC8 - 1997年：真题----答案----解析（英文解析+中文解析）AMC8 - 1996年：真题----答案----解析（英文解析+中文解析）AMC8 - 1995年：真题----答案----解析（英文解析+中文解析）AMC8 - 1994年：真题----答案----解析（英文解析+中文解析）AMC8 - 1993年：真题----答案----解析（英文解析+中文解析）AMC8 - 1992年：真题----答案----解析（英文解析+中文解析）AMC8 - 1991年：真题----答案----解析（英文解析+中文解析）AMC8 - 1990年：真题----答案----解析（英文解析+中文解析）AMC8 - 1989年：真题----答案----解析（英文解析+中文解析）AMC8 - 1988年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1986年：真题----答案----解析（英文解析+中文解析）AMC8 - 1985年：真题----答案----解析（英文解析+中文解析）◆AMC介绍◆AMC（American Mathematics Competitions) 由美国数学协会（MAA）组织的数学竞赛，分为 AMC8 、 AMC10、 AMC12 。

act is twice as long as the 3rd, what fraction of the play is the 3rd act?
A) 1/9
B) 2/9
C) 3/9
D) 4/9
15. If I double my speed of 12 000 m/hr., my new speed will be
城市
区
考号
所在学校
年级
姓名(签名)
………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………
won every 6th game we played. If my team qualified for the finals after our
96th game, how many wins did we need?
A) 12
B) 16
C) 18
D) 90
12. What is the greatest common factor of 1 ×3 ×5 ×7 ×9 and 2 ×4 ×6 ×8 ×10?
A) 200 m/min.
B) 400 m/min.
C) 600 m/min.
D) 2400 m/min.
16. Which of the following could be the perimeter of an equilateral triangle with integral side-lengths?

2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛(十、十一、十二年级)(初赛时间：2015年11月14日，考试时间90分钟，总分300分)学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

如果您同意遵守以上协议请在装订线内签名一、选择题(每小题10分，答对加10分，答错不扣分，共100分，请将正确答案A、B、C或者D写在每题后面的圆括号内。

)正确答案填写示例如下：20 − 5 × 2 = 2 ×? ( A )A) 5 B) 15 C) 25 D) 301.If a square has the same area as a circle whose radius is 10, then the side-length of thesquare is ( )A) B) 10πC) D) 100π2.x2–y2 + x + y = ( )A) (x + y– 1)(x–y) B) (x + y)(x–y– 1)C) (x + y + 1)(x–y) D) (x + y)(x–y + 1)3.If x + y = 25 and x2–y2 = 50. What is the value of xy? ( )A) 150.25 B) 155.25 C) 175 D) 12504.Janet picked a number from 1 to 10 and rolled a die. What is the probability that the sumof the number she picked and the outcome on the die is an even number? ( )A) 1/5 B) 1/4 C) 1/3 D) 1/25.Let r be a solution of x2– 7x + 11 = 0. What is the value of (r– 3)(r– 4) + (r– 12)(r + 5)?( )A) -71 B) -70 C) -69 D) 70st month the ratio of males to females in Miss Fox’s company was 3:4. When 9 newmales and 52 new females were employed this month, the new ratio of males to females is now 1/2. How many employees are there now in the company total? ( )A) 68 B) 120 C) 180D) 240第1页，共4页his task, he returned 40 mph from the castle to home. What is his average speed, in mph, of his quest? ( )A) 120/7 B) 240/7 C) 35 D) 70to shoot 3 apples, then when I use up the darts, I will be left with 35apples; if each dart is used to shoot 4 apples, then when I use up the apples,I will be left with 5 darts. I have ? apples at the beginning. ( )A) 51 B) 55 C) 200 D) 2409.x/2 = y/3 = z/4, what is the value of x:y:z? ( )A) 6:4:3 B) 3:4:6 C) 2:3:4 D) 4:3:210.Super Jack and Almighty Jill were doing the 100-mile walk at the same time and samestarting point, at constant speeds. Jack took a 5-minute break at the end of every 10 miles;Jill took a 10-minute break at the end of each 20 miles. Jill’s speed was 5/8 of that of Jack.They finished at the same time. How long, in minutes, does the trip take? ( )A) 53.333 B) 56.667 C) 60.333 D) 60.667二、填空题(每小题10分，答对加10分，答错不扣分，共200分。

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(四年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

请在装订线内签名表示你同意遵守以上规定。

考前注意事项：1. 本试卷是四年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、草稿纸。

试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一半题目的学生就应该受到表扬和鼓励。

选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。

1.(123 + 456) + 678 = (123 + 678) + ?A) 123 B) 456 C) 579 D) 6782.Bea sharpened 1200 pencils. Half the pencils had erasers, andhalf of all the erasers were pink. How many pencils with pinkerasers did Bea sharpen?A) 200 B) 300C) 400 D) 6003.I have a prime number of pairs of socks. The total number of socks I have could not beA) 26 B) 38 C) 46 D) 544.The product of 500 000 and 200 000 has exactly ? zeros.A) 5 B) 6 C) 10 D) 115.Divide 100 by 10, then multiply the result by 10. The final answer isA)0 B)1 C) 10 D) 1006.At most how many complete 8-minute songs can I sing in 3 hours?A) 22 B) 23 C) 24 D) 1807. 2 × (44 + 44 + 44) = 88 + 88 + ?A) 0 B) 44 C) 66 D) 888. A rectangle has sides of even lengths and perimeter 12. Its area isA) 6 B) 8 C) 9 D) 169.16 × (17 + 1) –? × (15 + 1) = 0A) 15 B) 16 C) 17 D) 1810.The crowd clapped for 840 seconds, stopping at 8:15 P.M. Theystarted clapping at ? P.M.A) 7:59 B) 8:01C) 8:08 D) 8:1411.If each digit of my 5-digit ID code is different, the sum of its digitsis at mostA) 15 B) 25 C) 35 D) 4512.At the museum, adult tickets cost $4 each and child tickets cost $3 each. With $50, I canbuy ? more child tickets than adult tickets.A) 1 B) 4 C) 12 D) 1613.Each day last week I read for a whole number of hours. I read forthe same number of hours each day except Sunday. If I read for 12hours last week, I read for ? hours on Sunday.A) 7 B) 6 C) 5 D) 414.The product 2 × 3 × 4 × 5 × 6 has the same value as the product ? × 3 × 5.A) 12 B) 36 C) 48 D) 6315.The average test grade in my class is a whole number, and the sum of the test grades is2400. Of the following, which could be the total number of test grades?A) 18 B) 21 C) 27 D) 3216.If twice a whole number is 120 less than five times the same whole number, then half thewhole number isA) 10 B) 20 C) 40 D) 6017.The number of bees I have doubles each day. If I had 1024 bees last Friday, the first daythe number of bees was more than 100 was aA) Tuesday B) WednesdayC) Thursday D) Friday18.Each of 6 dogs ate 3 treats from each of 4 bags. If each bag started with 30 treats, the 4bags together ended with ? treats.A) 36 B) 48 C) 72 D) 9619.What is the greatest possible product of two different even whole numbers whose sum is100?A) 196 B) 625 C) 2496 D) 250020. Ed built 3 times as many houses as Bob, who built half as many houses as Ally. If the 3 of them built 96 houses in all, Ed and Ally built a combined total of ? houses.A) 16 B) 32 C) 48D) 8021. How many factors of 2 × 4 × 8 × 16 are multiples of 4?A) 3B) 4C) 8D) 922. When I divide a certain number by 3 or 5, I get a remainder of 2. The sum of the digits ofthe least number for which this is true isA) 1B) 3C) 7D) 823. My 144 fish are split between 2 tanks so that 1 tank has twice as many fish as the other. How many fish must I move from one tank to the other so that both tanks have the same number of fish?A) 24 B) 48 C) 60D) 7224. A 3-digit number is the product of at most ? whole numbers greater than 1.A) 2B) 3C) 9D) 1025. Abby earns $2 for every clam she finds and $3 for every oyster. If Abby finds 5 times asmany oysters as clams, which of the following could be her total earnings?A) $150B) $160C) $170D) $18026. (The average value of the 10 smallest even whole numbers greater than 0) – (the average value of the 10 smallest odd whole numbers) =A) 0B) 1C) 10D) 1127. Ana planted seeds in rows. If the total number of rowsequaled the number of seeds in each row, the number of seeds planted could have beenA) 194B) 216C) 250D) 28928. What is the greatest possible sum of five 2-digit whole numbers if all 10 digits of the fivenumbers are different?A) 270B) 315C) 360D) 48529. I thought I wrote every whole number between 1 and 500 in order from least to greatest, but actually I skipped 3 numbers in a row. If I left out a total of 8 digits, what is the sum of the numbers I skipped?A) 100B) 150C) 300D) 39030. Written backwards, 123 becomes 321. How many whole numbers between 100 and 200 have a larger value when written backwards?A) 70B) 80C) 90D) 9831. The average of four different numbers is 18. And the least of the four numbers is 3. What is the least possible value of the biggest of the four numbers?A) 21B) 23C) 24D) 6032. 3 tigers can eat 36 Big Macs in 6 minutes. How many Big Macs can 12 tigers eat in 3 minutes?A) 18B) 36C) 72D) 28833. In the followi ng sequence, 2, 0, 1, 8, 2, 0, 1, 8, … (repeating), what is its 2018th term?A) 2B) 0C) 1D) 834. 2018a b c is a multiple of 9. What is the least possible value of abc ? (Note: abc is a three-digit number, which means a is not 0.)A) 7B) 100C) 106D) 99735. What is the least common multiple of 84 and 112?A) 28B) 196C) 336D) 940836. In triangle ABC , ∠C = 90°, ∠A = 15°, AB = 20. What is the area of this triangle?A) 20B) 50C) 100D) 20037. ABCD is a rectangle and its perimeter is 22, as shown at the right. EFGH is a square. AH = 6. CF = ?A) 4 B) 5 C) 6D) 838. How many leap years are there between 2018 and 2081?A) 16B) 17C) 18D) 1939. My class was lined up on the gym floor in 8 rows, with 2 students in each row. If our coach rearranged us so that the number of rows was the same as the number of students in each row, how many rows were there after we were rearranged? A) 4B) 6C) 10D) 1640. Of the 100 numbers from 1 to 100, how many of them don’t contain 7 as its digit?A) 65 B) 75C) 80 D) none of the above。

Math League in China
裘宗沪先生，美国“数学大联盟杯赛”(中国赛 区)组委会主任。自1985年起，组织我国中学生 参加国际数学奥林匹克竞赛(IMO)，至今，15次 获得总分第一，共荣获107枚金牌和31枚银牌、 铜牌。 曾任中国数学会理事、中国数学会普及
工作委员会主任、中国数学会奥林匹克委员会 副主席、中国青少年科技辅导协会常务理事。 1993年被国家数学竞赛世界联盟授予艾尔多斯 奖(Erdos Award)，以表彰他通过数学竞赛等活 动对中国数学课外教育的杰出贡献。 1994年被 国务院妇女儿童工作委员会评为全国对少年儿 童工作有突出贡献的工作者，同时授予“荣誉 奖章”。 著作有《趣味数学三百题》、《你能 解吗？》、套书《数学奥林匹克教程》等。
Math League in North America
"What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?"
Math League History
1. 美国“数学大联盟杯赛” (Math League) 是美 国及北美地区影响力最大的中小学数学赛事， 也是一项具有全球影响力的中小学生数学赛事。
2. 美国“数学大联盟杯赛”第一届竞赛于1977年 举行， 至今已经连续举办了38年。
3. 每年有来自全球的超过一百万名中小学生参加。
- Benjamin Franklin
“有什么样的科学比数学更崇 高、更完美、对人类更有用 和更加令人敬仰呢？”
本杰明·富兰克林

美国数学大联盟一等奖
美国数学大联盟一等奖
美国数学大联盟（MAA）奖项是为识别杰出的美国年轻数学家和研究者而设立
的荣誉。

MAA管理着多项奖项，其中包括一等奖。

MAA一等奖被认为是回馈美国数学界最早、最重要的奖项，旨在鼓励和奖励杰出的美国数学学者。

获得MAA一等奖的学者将获得一笔现金奖励，以及MAA一等奖证书。

获奖的个
人将被视为MAA的特殊会员，并享有参加年度MAA会议的机会，以及参与组织活动的资格。

此外，获奖者还可以获得贴近数学界的一些机会，包括参与招聘会、参加职业
发展会议、报名参加其他数学联盟的项目以及访问MAA会员学校所提供的数学研究机会，这些都将为其他有志于从事数学研究的研究者提供更多的积极机会和激励。

MAA一等奖的获得者都具有卓越的学术成就和杰出的研究能力，他们为美国数
学社区的发展做出了杰出的贡献。

获得MAA一等奖是全国范围内数学界获得荣誉的一个重要标志，被认为是改善学生对数学和科学的认识是一个终身成就。

2018-2019年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)(初赛时间：2018年11月14日,考试时间90分钟,总分200分)学生诚信协议：考试期间,我确定没有就所涉及的问题或结论,与任何人、用任何方式交流或讨论,我确定以下的答案均为我个人独立完成的成果,否则愿接受本次成绩无效的处罚。

如果您同意遵守以上协议请在装订线内签名选择题：每小题5分,答对加5分,答错不扣分,共200分,答案请填涂在答题卡上。

1. A 6 by 6 square has the same area as a 4 by ? rectangle.A) 3 B) 6 C) 8 D) 92.Every prime has exactly ? positive divisors.A) 1 B) 2 C) 3 D) 4 or more3.If I answered 34 out of 40 questions on my math test correctly, I answered ? % of thequestions correctly.A) 75 B) 80 C) 85 D) 904.120 ÷ 3 ÷ 4 × 12 =A) 1 B) 10 C) 12 D) 1205.10 × 20 × 30 × 40 = 24 ×?A) 1000 B) 10 000 C) 100 000 D) 1000 0006.One of my boxes contains 1 pencil and the others each contain 5 pencils. If there are 101pencils in my boxes, how many boxes do I have?A) 19 B) 20 C) 21 D) 227.An electrical company imports 2016 light bulbs. Unfortunately, 25%of those are damaged. How many light bulbs are not damaged?A) 25 B) 504 C) 1512 D) 20168.50 × (16 + 24) is the square ofA) -40 B) -4 C) 4 D) 809.Which of the following numbers has exactly 3 positive divisors?A) 49 B) 56 C) 69 D) 10010.Ten people stand in a line. Counting from the left, Jerry stands at the 5th position.Counting from the right, which position is he at?A) 4 B) 5 C) 6 D) 7 11.On a teamwork project, Jack contributed 2/7 of the total amount of work, Jill contributed1/4 of the work, Pat contributed 1/5 of the work, and Matt contributed the rest. Whocontributed the most toward this project?A) Jack B) Jill C) Pat D) Matt12.Which of the following numbers is a factor of 2016?A) 5 B) 11 C) 48 D) 9913.2 × 4 × 8 × 16 × 32 × 64 =A) 210B) 215C) 221D) 212014.On a game show, Al won four times as much as Bob, and Bob won four times as much asCy. If Al won $1536, how much did Al, Bob, and Cy win together?A) $96 B) $384 C) $1920 D) $201615.The sum of two composites cannot beA) odd B) even C) 11 D) 1716.If a and b are positive integers such that a/b = 5/7, then a + b isA) 12 B) 24 C) 36 D) not able to be determined17.What is the greatest odd factor of the number of hours in all the days of the year 2015?A) 3 B) 365 C) 1095 D) 328518.If the current month is February, what month will it be 1 199 999 months from now?A) January B) February C) March D) April19.Two angles are complementary. One of these angles is 36° less than the other. What is themeasure of the larger angle?A) 36°B) 54°C) 63°D) 72°20.(The square root of 16) + (the cube root of 64) + (the 4th root of 256) =A) 12 B) 24 C) 32 D) 6421.In ∆ABC, m∠A–m∠B = m∠B–m∠C. What is the degree measure of ∠B?A) 30 B) 60 C) 90 D) 12022.For every 3 math books I bought, I bought 2 biology books. I bought 55 books in all. Howmany of those are math books?A) 11 B) 22 C) 33 D) 4423.John wrote a number whose digits consists entirely of 1s. This number was a compositenumber. His number could contain exactly ? 1s.A) 17 B) 19 C) 29 D) 3224.Weird Town uses three types of currencies: Cons, Flegs, and Sels. If 3 Sels = 9 Cons and 2Cons = 4 Flegs, then 5 Sels = ? Flegs.A) 12 B) 24 C) 30 D) 36第1页,共4页25.If the length of a rectangular prism with volume V is doubled while the width and theheight are halved, the volume of the new prism will beA) 4V B) V/2 C) V D) 2V26.Rick and Roy each stands at different ends of a straight road that is 64 m long. They runtoward each other. Rick’s speed is 3 m/s and Roy’s speed is 5 m/s. They will meet in? seconds.A) 1 B) 2 C) 4 D) 827.If the area of a certain circle is 2016, its radius isA) sqrt(2016/π) B) sqrt(4032/π)C) 2016/πD) 1008/π28.In a toy shop, the cost of a Teddy Bear is 200% as much as that of a toy train. The cost ofa toy train is 6/5 the cost of a pack of the wooden blocks. The cost of a pack of woodenblocks is $50. What is the cost, in dollars, of the Teddy Bear?A) 60 B) 100 C) 120 D) 20029.In the sequence 2016, 225, 141, 66, 432, 99, 1458 …, each term after the first term is thesum of the cubes of the digits of the previous term. What is the 100th term of thissequence?A) 153 B) 351 C) 370 D) 37130.What is the sum of all the positive divisors of 210?A) 210 – 1 B) 211 – 1 C) 212 – 1 D) 213 – 131.It takes 4 hours for Mike and Lucy to finish a task. It takes Lucy and Jerry 5 hours tofinish the same task. And it takes 6 hours for Mike and Jerry to finish the same task. Lucy and Jerry first work on the task for 1 hour and 45 minutes. Then Mike takes over the task on his own. How many more hours does it take for Mike to finish the task?A) 3 B) 4 C) 5 D) 632.If you sell a cloth at its current price, you get $40 profit. The total profit you get selling 10clothes at 70% of its current price is equal to the total profit you get selling 20 clothes at $82 per cloth. What is the current price of a cloth?A) 80 B) 100 C) 120 D) 12533.There are 6 identical squares in the figure on the right. The side length of eachsquare is 1. Of all the triangles constructed by connecting three of the 18vertices in the figure, how many of them are triangles whose area is 2 andwhich has at least one vertical or horizontal side?A) 12 B) 16 C) 24 D) 2834.Pick up N numbers from 1 to 2015 inclusively, such that the sum of any three of the Nnumbers is divisible by 24. What is the maximum value of N?A) 83 B) 84 C) 168 D) 252 35.汤姆有一件花了64美金买来的衬衫,他打算以比原价高出25%的价格出售,他会卖出多少钱？A) $16 B) $32 C) $48 D) $8036.满足以下条件的最小整数是多少：“除以3余2,除以5余4,除以7余6。

2018 年 ARML 数学竞赛 …………………………………………… 57 2018 年美国数学邀请赛(AIME) I …………………………………… 66 2018 年美国数学邀请赛(AIME) II ………………………………… 69 2018 年美国数学奥林匹克 …………………………………………… 72 2018 年美国初中数学奥林匹克 ……………………………………… 73 2018 年美国 IMO 代表队选拔考试 ………………………………… 74 2018 年美国 TSTST …………………………………………………… 76 2018 年美国第 20 届 ELMO ………………………………………… 78 2018 年美国第 20 届 ELMO 预选题 ………………………………… 80 2018 年第 20 届美国旧金山湾区数学奥林匹克 …………………… 83 2017-2018 年度 USAMTS …………………………………………… 86 2018 年美国女子数学奖学金竞赛(决赛) …………………………… 91 2017-2018 年度威斯康星数学、科学与工程学人才选拔 ………………… 92 2018 年奥地利数学奥林匹克 ………………………………………… 96 2018 年澳大利亚数学奥林匹克 ……………………………………… 99 2018 年澳大利亚、英国 IMO 国家队联合训练考试 ………………… 89 2018 年白罗斯数学奥林匹克 ………………………………………… 101 2018 年波黑数学奥林匹克(地区级) ………………………………… 105 2018 年波黑 EGMO 代表队选拔考试 ……………………………… 107 2018 年波黑 JBMO 代表队选拔考试 ………………………………… 108 2018 年巴西数学奥林匹克 …………………………………………… 109 2018 年巴西 IMO 代表队选拔考试 ………………………………… 111

美国大联盟数学竞赛铜奖小升初美国“大联盟”(Math League)思维探索研学活动是美国及北美地区具有卓越影响力的中小学数学思维探索研学活动，也是一项具有全球影响力的中小学数学思维探索研学活动。

第一届探索活动于1977年举行，至今已经连续举办了43届。

美国“大联盟”(Math League)思维探索研学活动每年举办一次，分为第一阶段、第二阶段、和研学嘉年华三个阶段。

第一阶段活动试题灵活、生动，富有趣味性，同时也贴近生活。

让学生理解数学、欣赏数学，激励学生创新，更能激发学生学习数学的兴趣，培养学生主动探索的精神。

第二阶段活动的目的是为了让中国学生体验美国数学教学的优点和特点，即美国启发式、重视应用、轻松、有趣、与实际生活紧密相关、研究、探索式的教学方式，启发学生如何thinking mathematically，培养学生creative thinking, critical thinking, and problem solving skills，即探索如何用数学解决实际生活中的问题，培养学生创造性思维、批判性思维、和实际解决问题的能力。

第二阶段活动还考察学生的英语能力(listening, speaking, communication, writing, and comprehension)。

研学嘉年华的决赛试题由美国"大联盟"(Math League)思维探索研学活动和普林斯顿大学(Princeton University)、哥伦比亚大学(Columbia University)、威廉姆斯学院(Williams College)联合命题，具有很高的挑战性，是数学超常少年展现才华的绝佳平台。

美国"大联盟"(Math League)思维探索研学活动会在其美方官网公布每年优胜者的成绩并颁发荣誉证书。

优异的成绩更是美国乃至世界各地学生申请北美重点高中和重点大学的重要参考依据。

contribute 贡献 cookie 饼干 coordinate 坐标 coordinate axes 坐标轴 corner 角 cost 花费 count 数；计算；计数；计算 couple 夫妻 cousin 堂[表]兄弟；堂[表]姐妹 cover 盖；覆盖 crack: 裂缝 crate 箱子 create 创建；创造；造成；创作 cross 交叉；穿越；越过 cube 立方体；立方 cubic 立方体的；立方的 customer 顾客；客户 cycle 循环；周期；自行车；骑自 行车 cylindrical 圆柱的
D
dance 跳舞 darken 变黑 dart 飞镖 December 十二月 decimal 十进制的；小数的；小数 define 定义 degree 度数 degree-measure (角的)角度 denominator 分母 dessert 甜点 determine 确定 diagonal 对角线的；对角线 diagram 图表 diameter 直径 diamond 菱形 dice 骰子 die 死亡 difference 差额；差异 different 不同的 digit 数字；阿拉伯数字 digit sum In mathematics, the digit sum of a given integer is the
sum of all its digits (e.g. the digit sum of 84001 is calculated as 8+4+0+0+1 = 13). dime (美元)十美分 dimension 尺寸 dine 就餐；聚餐 dinner 晚餐 display 展览 distance 距离 distinct 不同的 distribute 分发；分配 divide 除；划分；分开；等分 divisible 可除尽的 division 除法 divisor 除数；约数 divorce 离婚 dodecahedron 十二面体 dollar (符号为＄)美元 double 两倍；使加倍 dough (用于制面包和糕点的)生 面团 download 下载

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(五年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论， 我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

请在装订线内签名表示你同意遵守以上规定。

考前注意事项：1. 本试卷是五年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、 草稿纸。

试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一半题目的学生就应该受到表扬和鼓励。

选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。

1. 2018 + 2019 = 20 + 18 + 20 + 19 + ?A) 0B) 2000C) 3960D) 40002. If 1/3 of my hats are red, and 36 are not red, I have ? hats.A) 18B) 54C) 72D) 1083. The sum of the measures of the 2 smallest angles of a triangle could beA) 151 degrees B) 135 degrees C) 121 degreesD) 61 degrees4. 2018 = 20 × ? + 18 × 1A) 1B) 10C) 18D) 1005. Every English letter appears in my 2018-letter password at least once. The letter A appears at most ? times.A) 77B) 78C) 1992D) 19936. Which of the following is the product of 2 consecutive integers?A) 182B) 195C) 208D) 2217. The least integer with a prime number of different prime factors isA) 6B) 8C) 12D) 158. I have 5 coins consisting of pennies, nickels, and dimes. If I have at least 1 of each type of coin, the least possible value of my 5 coins isA) 5¢B) 15¢C) 16¢D) 18¢9. Exactly ? different 3-digit area codes can be made using only 2s and 3s, with at leastone 2 and one 3 in each area code.A) 4B) 6C) 9D) 1210. How many multiples of 10 are factors of 102?A) 1B) 2C) 3D) 411. My team had to win a certain number of games to make it to the finals, and we won every 6th game we played. If my team qualified for the finals after our 96th game, how many wins did we need?A) 12 B) 16 C) 18D) 9012. What is the greatest common factor of 1 × 3 × 5 × 7 × 9 and 2 × 4 × 6 × 8 × 10?A) 1B) 3C) 5D) 1513. The expression 2400 is the product of exactly ? sixteens.A) 25B) 50C) 100D) 20014. The 2nd act of a 3-act play is 1/3 the length of the entire play. If the 1st act is twice as long as the 3rd, what fraction of the play is the 3rd act?A) 1/9 B) 2/9 C) 3/9 D) 4/9 15. If I double my speed of 12 000 m/hr., my new speed will beA) 200 m/min. B) 400 m/min. C) 600 m/min.D) 2400 m/min.16. Which of the following could be the perimeter of an equilateral triangle with integralside-lengths?A) 2017B) 2018C) 2019D) 202017. The greatest of 10 consecutive positive integers is a prime number. What is the least possible sum of these integers?A) 65B) 77C) 127D) 12918. One-fourth of Ed’s balloons popped, with 2 balloons popping every3 minutes for an hour. How many balloons did not pop?A) 40 B) 80 C) 120 D) 160 19. What is the greatest common factor of 68 and 86?A) 22B) 44C) 66D) 8820. The expression 1002018 can be written as the product of exactly ? prime numbers.A) 5 × 2018B) 4 × 2018C) 2 × 2018D) 201821. How many integers have a square root greater than 15 and less than 16?A) 0B) 1C) 29D) 3022.=A) 0B) 54C) 90D) 14423. Each day for a month, Sully wakes up 5 minutes earlier than he did the day before. IfSully woke up at 6:50 a.m. on a Monday, on what day did he wake up at 6:20 a.m.?A) Sunday B) Monday C) TuesdayD) Wednesday24. The product of all factors of 21 equals 21 × ? .A) 1B) 2C) 3D) 2125. (1234 + 0 + 1234 + 1 + 1234 + 2 + 1234 + 3 + 1234 + 4) ÷ 5 =A) 1234B) 1234 + 1C) 1234 + 2D) 1234 + 326. On a number line, two different integers are each the same distance from my favorite integer and have a sum of 144. What is my favorite integer?A) 31B) 36C) 48D) 7227. Last year I spent $180 for 80 pairs of shades. This year I spent $180for 5 fewer pairs of the same shades. How much did the price per pair increase since I bought them last year?A) 15¢B) 72¢C) 96¢D) 120¢28. I drove at a constant speed of 60 km/hr. without stopping. At exactly 5:00 p.m. I had traveled 318 km. At what time did I start driving?A) 10:42 a.m. B) 11:42 a.m. C) 12:42 p.m.D) 1:42 p.m.29. I added 3 of the numbers 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, and 99999. My sum was one of these 9 numbers. When my sum was divided by 11, the remainder could not have beenA) 5B) 6C) 7D) 830. I wrote the 101 integers from 1 to 101 in order on paper. If I wrote 101 digits per line, what was the sum of the last 4 digits on the first line?A) 11B) 17C) 19D) 2131. The product of all the factors of an integer greater than 1 equals the cube of that integer.What is the least integer for which this is true?A) 24B) 18C) 12D) 832. On our last history test, at least one student scored each of the grades A, B, C, D, and F. If 8 got an A, 15 got a C or higher, 10 got a B or lower, and only one student got a D, how many students got an F?A) 1B) 2 C) 3 D) 5 33. (22 × 24 × 26 × … × 298 × 2100) ÷ (21 × 23 × 25 × … × 297 × 299) =A) 2B) 249C) 250D) 210034. Starting at 1:00 p.m., a ball was rolled in each of two lanes. A ballwas rolled once every 15 seconds in one lane and once every 18 seconds in the other. By 1:44 p.m., how many times had balls been rolled at the same time in both lanes?A) 29B) 30C) 40D) 4435. I counted backwards out loud from 2018 by ones. When I said my 50th multiple of 8, howmany numbers had I counted?A) 252B) 395C) 400D) 161836. If 30% of a number is 42, the 50% of the number is?A) 60B) 70C) 84D) 10837. The perimeter of a square is 12. The area of the square is?A) 3B) 6C) 9D) 1238. A year is called a lucky year if the sum of its digits is 18. For example, 1917 is alucky year since 1 + 9 + 1 + 7 = 18. How many lucky years are there between 2018 and 2108? A) 2B) 3C) 4D) 539. I ran 1 km in 6.0 minutes. Rabbit ran 50% faster and finished inA) 3.0 minutes B) 4.0 minutes C) 4.5 minutesD) 9.0 minutes40. If the pattern of the first 5 letters of ABCDEABCDEABCDE … continues to the right, the 2018th letter in the pattern would beA) A B) BC) CD) D or E。

2022-2023年度美国Math League思维探索第一阶段活动(三年级)(答题时间：75分钟，总分：175分)学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。

选择题：每小题5分，答对加5分，答错不扣分，共175分。

1.2–0+2–1+2–2+2–3=A)2B)3C)4D)52.Sandy the Snail ran6cm in an hour!At that rate,how many cm could she runin4hours?A)10B)12C)24D)303.2022+2023=4044+?A)0B)1C)2D)44.The names of how many months begin with a vowel?A)0B)1C)2D)35.Tyson eats only chicken2days a week,only sausages3days a week,and onlyhamburgers the rest of the week.Tyson eats hamburgers?days a week.A)1B)2C)4D)56.When?is divided by6,the remainder is4.A)20B)22C)24D)267.I began with20hats9years ago.For the first5years after that,each year I doubled the number of hats Ihad.For the next4years,each year I gave away half of my hats.How many hats do I have now?A)10B)20C)30D)408.(60+40+20)–(50+30+10)=A)10B)20C)30D)609.Turbo Turtles are toys that can run one-half of1km in2minutes.The average hourly speed of a TurboTurtle isA)15km/hr.B)20km/hr.C)30km/hr.D)60km/hr.10.The sum of the hundreds and ones digits of the product of12and34isA)9B)10C)11D)1211.How many different possible perimeters could a rectangle that has area100cm2and side-lengths that areall whole numbers have?A)4B)5C)6D)712.20+31+42=23+34+?A)36B)39C)45D)4813.Five days ago my birthday was exactly three weeks away.Today my birthday is?days away.A)16B)18C)25D)2614.Sophia Squirrel started with44acorns and found4more,then divided all of heracorns equally among her4friends.How many acorns did each friend get?A)4B)7C)11D)1215.If my motorcycle travels135km on9L of gas,how far can it travel on2L at that same rate?A)20km B)25km C)30km D)35km16.I have an odd number of nickels and an odd number of quarters.What could be the total value of all mynickels and quarters?A)$0.75B)$1.20C)$2.55D)$5.2517.Two train cars are placed end-to-end,and one car is twice as long as the other.If the total length is48m,the longer car has lengthA)16m B)20m C)28m D)32m18.200+200+200+200=40×?A)5B)10C)16D)2019.Franny Farmer has an empty bucket that can hold up to30oranges.Each morninghe puts5oranges in it,and each evening he eats3oranges.In how many dayswill he need a2nd bucket to hold his oranges?A)13B)14C)15D)1620.10×100×1000×10000=100000×1000000÷?A)10B)100C)1000D)1000021.Victor has100same-sized Rubik’s Cubes,and boxes that hold8Cubes each.How many boxes must hehave to hold all the Cubes?A)12B)13C)14D)1522.Stevie counted even numbers backwards,and the22nd number he counted was22.At what number didhe start counting?A)64B)66C)68D)7023.The product of two whole numbers,each of which is less than1000,can have at most?digits.A)5B)6C)7D)824.Rhonda the Racehorse runs70km in1hour.Sammy the Sloth runs1km in4hours.At these rates,Rhonda runs?km farther than Sammy in8hours.A)552B)556C)558D)55925.Jonah found the difference between a two-digit number and the number formed by reversing the digits inthe two-digit number.This difference could beA)72B)74C)76D)7826.A square and a rectangle have equal perimeters.If the length of a side of the square is6cm and thelength of one side of the rectangle is2cm,the length of the longer side of the rectangle is?cm.A)10B)12C)18D)2027.The time on Noelle’s digital clock was5:55PM.How many minutes later didNoelle next see all identical digits?A)71B)316C)376D)43628.Between which numbers listed do the greatest number of primes fall?A)20and30B)30and40C)40and50D)50and6029.If a line segment divides a certain polygon into a square and a triangle with the square and the trianglesharing a common side,the greatest number of sides this polygon could have isA)5B)6C)7D)830.When talking about a number,Marcia said,“It is an odd number,”and Jan said,“Both of the digits aredifferent.”If only one of them is telling the truth,what could the number be?A)20B)21C)22D)2331.It cost me$30to buy2balls and2bats.At the same unit prices,it cost mysister$65for5balls and4bats.The cost of1bat isA)$5B)$10C)$15D)$2032.What is the sum of all the positive divisors of18?A)20B)28C)30D)3933.The number of orangutans living in my tree increases by a constant numbereach year.If there are40orangutans now and there were24two years ago,how many orangutans will be in my tree in six years?A)64B)72C)88D)13634.The ratio of game stands to food stands at the beach boardwalk is currently3:1.There are80food stands.How many game stands must be converted to food stands to make the ratio1:1?A)40B)80C)120D)16035.The product of three whole numbers is36.What could not be the sum of the three?A)10B)11C)12D)13。