2017-2018年度美国数学大联盟杯赛(中国赛区)初赛(含答案)
【精品】2020美国数学大联盟)挑战赛三年级真题(附答案+中文翻译+解题思路)
2017-2018年度美国“数学大联盟杯赛”（中国赛区）题目翻译及解题tips【翻译】：2018与以下哪个数字相加的总和是偶数？The sum of…总和…；the even number偶数【翻译】：约翰和吉尔一共有92美元。
约翰的钱是吉尔的三倍。
问约翰有多少钱？①…has three times（倍数）as many(修饰可数名词)/much(修饰不可数名词)as…A的…是B的几倍②As···as···和什么一样多【翻译】：汤姆是一个篮球热爱者！在他的书中，他写了100次“ILOVENBA”（我爱NBA）。
问他写的第500个字母是什么。
（提示：本题考查周期循环规律题）【翻译】：一个长*宽为8*25的长方形和以下哪个长方形有相同的面积。
【翻译】：前100个正整数（1-100）的和与后50个正整数（51-100）的和之间的差是多少？①Positive difference···与···的差；②positive integers正整数【翻译】：你有一根10英尺长的杆子需要被切成10等份。
若每一份需要10秒去切，完成这份工作一共需要多少秒。
【翻译】：Amy将2018四舍五入约至十位（rounded···to the nearest tens）得到的数字与Ben将2018四舍五入约至百位得到的数字，这两个数字之和是多少？【翻译】：下列哪组数有最小公倍数？【翻译】：Dan每买2支铅笔的同时也会5支钢笔。
如果他买了10支铅笔，那他一共买了几支钢笔？【翻译】：星期四的20天后是星期几？【翻译】：下列哪个角的度数最小？①an obtuse钝角②an acute锐角③a right直角④a stright平角【翻译】：我们班的每位学生都要轮流喊一个整数。
第一个人喊的是1。
2018年美国“数学大联盟杯赛”(中国赛区)初赛四年级试卷(1)
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(四年级)(初赛时间：2017年11月26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。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
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.Which of the following is the smallest?A) 2.018 B) 20.18 C) 0.218 D) 20182.What is the least common multiple of 20 and 18?A) 90 B) 180 C) 240 D) 3603.The sum of the degree-measures of the exterior angles of a triangle is?A) 180 B) 360 C) 540 D) 7204.In the figure on the right, please put the numbers 1 – 11 in the elevencircles so that the three numbers in every straight line add up to 18.What is the number in the middle circle? Note: There are 5 straightlines in total in this figure.A) 6 B) 7 C) 8 D) 95.I am a lovely cat. When I multiply the digits of a whole numberand the product I get is 8, I put that whole number on my list offavorite numbers. Of the whole numbers from 1000 to 9999,how many would I put on my list of favorite numbers?A) 10 B) 12 C) 16 D) 206.Two planes take off at the same time from the same point to race to apoint and back. Place A travels at 180 miles per hour on the way out and240 miles per hour on the return trip. Plane B covers the entire distance at an averagespeed of 210 miles per hour. Which plane wins the race, or is it a tie?A) plane A wins B) plane B winsC) a tie D) non-deterministic 7.52 × 88 = 44 ×?A) 102 B) 96 C) 104 D) 1248.What is the smallest whole number that leaves a remainder of 4, 5, 6 when divided byeach of 5, 6, 7?A) 29 B) 209 C) 210 D) 20099.In △ABC, m∠A + m∠C = m∠B. What is the degree measure of ∠B?A) 80 B) 90 C) 100 D) 18010.I bought a toy for $10, sold it for $20, rebought it for $30, and resold it for $40. My totalprofit on the 4 transactions was ?A) 10 B) 20 C) 30 D) 4011.What is the greatest number of integers I can choose from the first ten positive integers sothat any 3 of the chosen integers could be the lengths of the three sides of a triangle?A) 4 B) 5 C) 6 D) 712.How many whole numbers between 200 and 400 have all their digits increasing in valuewhen read from left to right?A) 30 B) 36 C) 42 D) 4813.What is the value of 1% of 10% of 100?A) 0.01 B) 0.1 C) 1 D) 1014.If three cats can eat three bowls of food in three minutes, how many minutes will it take100 cats to eat 100 bowls of food?A) 1 B) 3C) 100 D) None of the above15.There are three squares. The area of the smallest one is 2. The side-length of the secondsquare is twice the side-length of the smallest one. And the side-length of the third square is three-times the side-length of the smallest one. The total area of the three squares isA) 12 B) 28 C) 36 D) 7216.A man, who had been married for three years, spent25of his yearly income on his family,14on business, and110on personal travel. If he saved $45000 during those three years, what was his annual income?A) $45000 B) $50000C) $65000 D) None of the above17.Given four different integers, at most how many different sums can be formed bychoosing two, three, or four of them and finding each sum?A) 8 B) 9 C) 10 D) 1118. Max places 100 eggs in 10 baskets, with each basket receiving at least1 egg, but no2 baskets receiving the same number of eggs. What is the greatest number of eggs that may be placed in a basket?A) 45 B) 47 C) 55 D) 6519. 2 + 3 × 4 – 5 =A) 0 B) 6 C) 9 D) 15 20. What is the highest power of 2 that divides 2 × 4 × 6 × 8 × 10? A) 25 B) 27 C) 28 D) 215 21. Which of the following is a prime number?A) 2017B) 2018C) 2015D) 201622. What is the greatest possible number of acute angles in a figure consisting of a triangleand a line passing through two sides of the triangle?A) 5B) 6C) 7D) 823. Amy can solve 5 questions every 3 minutes. Kate can solve 3 questions every 5 minutes.How many more questions Amy can solve than Kate in one hour?A) 15B) 32C) 60D) 6424. Using 3 Ts and 2 Js, in how many different orders can the five letters be arranged? Forexample, TTTJJ and TTJJT are two such different orders.A) 2B) 10C) 20D) 6025. Coastal Coconuts can divide all their coconuts evenly among 8, 9, or10 customers, with 1 coconut left over each time. If Coastal Coconuts has more than 1 coconut, what is the least number of coconuts they could have?A) 561 B) 721C) 831 D) None of the above 26. 35 ÷ 32 =A) 3 B) 9 C) 27 D) 81 27. If the sum of three prime numbers is 30, what is the least prime number?A) 2B) 3C) 5D) 728. Juxtaposing two identical squares to form a rectangle, the perimeter of the rectangle is 12less than the sum of the perimeter of the two squares. What is the side-length of the original square?A) 3B) 6C) 9D) 1229. It takes Mike 2 hours to finish a task. It takes 4 hours for Tom to finish the same task.Mike and Tom worked together on this task for one hour before Mike had to leave. How long will it take Tom to finish the rest of the task?A) 1 B) 2 C) 3 D) 4 30. The number of triangles in the figure on the right isA) 9 B) 10 C) 11 D) 12 31. What is the thousands digit of the product 1234560 × 2345670 × 3456780?A) 8B) 6C) 5D) 032. The sum of nine consecutive positive integers is always divisible byA) 2B) 5C) 7D) 933. You can put as many as 96 books in 6 backpacks. How many backpacks are necessary for144 books?A) 7B) 8C) 9D) 1034. The number of nickels I have is twice the number of dimes I have, and together thesecoins are worth more than $1. The least number of dimes that I can have isA) 5B) 6C) 8D) 1035. The ages of four kids are four consecutive positive integers. The product of their ages is3024. How old is the oldest kid?A) 8B) 9C) 10D) 1136. In the Game of Life, you earn 3 points for flipping a coin to “heads”, and 5 points forflipping a coin to “tails”. In all, how many positive whole number scores are IMPOSSIBLE to get after flipping it one or more times?A) 4B) 5C) 7D) 1137. Four monkeys can eat four bags of peanuts in three minutes. How many monkeys will ittake to eat 100 bags of peanuts in one hour?A) 4 B) 5 C) 20 D) 100 38. The tens digit of the product of the first 100 positive integers isA) 2B) 4C) 8D) 039. Someone put three dimes into my pile of quarters. If I add up the value of these coins,including the dimes, the sum could beA) $6.25B) $7.75C) $8.05D) $9.5040. Brooke's empty tub fills in 20 minutes with the drain plugged, andher full tub drains in 10 minutes with the water off. How manyminutes would it take the full tub to drain while the water is on?A) 12B) 15 C) 20 D) 30。
2014-2015年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷
………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………2014-2015 年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)(初赛时间：2015 年 1 月 3 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。
一、选择题(每小题 5 分，答对加 5 分，答错不扣分，共 175 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) 25D) 301. Three cases of 24 cans each is the same number of cans as twelve boxes of ? cans each. ( )A) 6 B) 15 C) 21 D) 96 2. A trapezoid has ? sides. ( )11. Thok has a simple plan. He will spend 50% of the day in the cave, 25% of the rest of the day on the hunt, and the remainder of the day watching films outside. How many hours will Thok spend watching films? ( ) A) 3 B) 6 C) 9 D) 25 12. 2 × 3 × 6 × 36 × 2 × 3 × 6 × 36 = ( )A) 65 B) 66C) 67D) 6813. I have 5 pennies, 4 nickels, 3 quarters, 2 half-dollars, and 1 dollar. The average value of one of my coins is ( )14.Wyatt O’Vine’s sheep weighs twice as much as Wyatt, and Wyatt weights twice as much as his hat. If Wyatt, his sheep, and his hat have a combined weight of 210 kg, how much does Wyatt weigh? ( ) A) 30 kg B) 35 kg C) 60 kg D) 70 kg 15. (12 + 34) × (56 + 78) = 12 × (56 + 78) + ? × (56 + 78) ()A) 12 B) 34 C) 56 D) 78 16. If 2 flocks equal 5 flecks, then 500 flocks equal ? flecks. ( )3. Abby put an X through 7 of the 28 days in this month. Abby put anX through ? of the days. ()17.2= ( )4. 60 ÷ 4 = 3 × ? ( )A) 20 B) 12 C) 6 D) 5 5. 30 × 40 × 50 = 120 × ? ( )A) 50 B) 200 C) 500 D) 6006. If 3 out of 4 of the students in my class have brown eyes, and there are 24 students in my class, then how many have brown eyes? ( ) A) 6 B) 8 C)18 D)217. Four identical squares, each with a perimeter of 36, are put together as shown to make one big square. What is the perimeter of the big square? ()8. 80 + (160 + 240) ÷ 4 = 40 + 80 + (120 ÷ ? ) ( )A) 4 B) 2 C) 1 D) 0 9. In which of the following divisions is the remainder greatest? ()A) 1111 ÷ 8 B) 2222 ÷ 7 C) 3333 ÷ 6 D) 4444 ÷ 5 10. Of the following, which is a factor of 20 × 14 × 20 × 15? ( )A) 13 B) 11 C) 9 D) 718.If the sum of seven consecutive even numbers is 182, the smallest of the seven numbers is ( ) A) 20 B) 23 C) 26 D) 3219. While he was standing on his head, Flip decided to count backward from 777 by eights. Which of the following numbers did Flip count? ( A) 123 B) 125 C) 127 D) 129 20. The cost of five apples is the same as the cost of six pears. If one apple costs 15 cents more than one pear, then what is the total cost of 5 apples and 6 pears? ( ) A) $3 B) $6 C) $9 D) $1821. What is the difference between 27 and the product of all its whole-number factors? ( ) A) 2 B) 27 C) 2 × 27 D) 26 × 27 22. The prime factorization of a whole number less than 100 is the product of at most ? primes (not necessarily different). ( )A) 3 B) 4 C) 5 D) 6 23. A rectangle with sides of integer length is divided into a square regionand a shaded rectangular region as shown. If the area of the shaded)城市区 学校年级性别姓名（正楷）A) 3 B) 4 C) 5 D) 10 A) 0.07 B) 0.25C) 0.28D) 0.35A) 36B) 48C) 72D) 144A) $0.20 B) $0.60 C) $1.50 D) $3.00A) 200 B) 250 C) 1000 D) 1250 A) 16B) 64C) 128D) 256)2 ………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………region is 8, the area of the entire figure is at most ( )A) 24 B) 64 C) 72 D) 8124. Gabriel wrote his name 100 times in the sand. What was the 100th letter hewrote? ( ) A) a B) b C) r D) i 25. I put $100 in a savings account. At the end of each year, I earned 10% interest on the balance of my account at that point. With no deposits or withdrawals, after 5 years I had ? . (Round to the nearest dollar.) ( ) A) $162 B) $161 C) $160 D) $150 26. Mrs. Andrews enjoys feeding the birds her special mix of birdseed. She mixes 1 part sunflower seed with 3 parts sesame seed to make a total of 200 6-kg bags. If sunflower seed comes in 12-kg bags, how many such bags does she need? ( ) A) 25 B) 34 C) 50 D) 6737. There are several apples in a basket. Tony removes half of the apples in the basket and then places 15 additional apples in the basket. Sophie then removes half of the apples in the basket, and then places 10 additional apples in the basket. The number of apples Tony removes from the basket is the same as the number of apples Sophie removes. How many apples are now in the basket?Answer: .38. In this problem as shown on the right, each square represents a digit from 0 to 9. What is the final product? Answer: .39. In triangle ABC on the right, BD :DC = 1:2. If the area of triangle ABP is 7 and the area of triangle ACP is 5, what is the area of triangle ADP ?Answer: .40. 甲、乙、丙三位同学参加运动会，他们的号码都 27. The product of 100 one hundreds is the same as the sum of ? one hundreds. ()A) 100100 B) 10099 C) 10010 D) 1002 不一样。
2018年美国“数学大联盟杯赛”(中国赛区)初赛三年级试卷(1)
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(三年级)(初赛时间：2017年11月26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. 本试卷是三年级试卷，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。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
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. 5 + 6 + 7 + 1825 + 175 =A) 2015 B) 2016 C) 2017 D) 20182.The sum of 2018 and ? is an even number.A) 222 B) 223 C) 225 D) 2273.John and Jill have $92 in total. John has three times as much money as Jill. How muchmoney does John have?A) $60 B) $63 C) $66 D) $694.Tom is a basketball lover! On his book, he wrote the phrase “ILOVENBA” 100 times.What is the 500th letter he wrote?A) L B) B C) V D) N5.An 8 by 25 rectangle has the same area as a rectangle with dimensionsA) 4 by 50 B) 6 by 25 C) 10 by 22 D) 12 by 156.What is the positive difference between the sum of the first 100 positive integers and thesum of the next 50 positive integers?A) 1000 B) 1225 C) 2025 D) 50507.You have a ten-foot pole that needs to be cut into ten equal pieces. If it takes ten secondsto make each cut, how many seconds will the job take?A) 110 B) 100 C) 95 D) 908.Amy rounded 2018 to the nearest tens. Ben rounded 2018 to the nearest hundreds. Thesum of their two numbers isA) 4000 B) 4016 C) 4020 D) 4040 9.Which of the following pairs of numbers has the greatest least common multiple?A) 5,6 B) 6,8 C) 8,12 D) 10,2010.For every 2 pencils Dan bought, he also bought 5 pens. If he bought 10 pencils, how manypens did he buy?A) 25 B) 50 C) 10 D) 1311.Twenty days after Thursday isA) Monday B) Tuesday C) Wednesday D) Thursday12.Of the following, ? angle has the least degree-measure.A) an obtuse B) an acute C) a right D) a straight13.Every student in my class shouted out a whole number in turn. The number the firststudent shouted out was 1. Then each student after the first shouted out a number that is 3 more than the number the previous student did. Which number below is a possible number shouted out by one of the students?A) 101 B) 102 C) 103 D) 10414.A boy bought a baseball and a bat, paying $1.25 for both items. If the ball cost 25 centsmore than the bat, how much did the ball cost?A) $1.00 B) $0.75 C) $0.55 D) $0.5015.2 hours + ? minutes + 40 seconds = 7600 secondsA) 5 B) 6 C) 10 D) 3016.In the figure on the right, please put digits 1-7 in the sevencircles so that the three digits in every straight line add upto 12. What is the digit in the middle circle?A) 3 B) 4 C) 5 D) 617.If 5 adults ate 20 apples each and 3 children ate 12 apples in total, what is the averagenumber of apples that each person ate?A) 12 B) 14 C) 15 D) 1618.What is the perimeter of the figure on the right? Note: Allinterior angles in the figure are right angles or 270°.A) 100 B) 110C) 120 D) 16019.Thirty people are waiting in line to buy pizza. There are 10 peoplein front of Andy. Susan is the last person in the line. How manypeople are between Andy and Susan?A) 18 B) 19C) 20 D) 2120.Thirty-nine hours after 9:00 AM isA) 1:00 AM B) 12:00 PM C) 8:00 PM D) 12:00 AM21.200 + 400 + 600 + 800 = (1 + 2 + 3 + 4) ×?A) 2 B) 20 C) 200 D) 200022.11…11 (the number consisting of 2016 1’s) is not a mult iple ofA) 11 B) 111 C) 1111 D) 1111123.The average of two thousands and two millions isA) 10000 B) 1000000 C) 1001000 D) 111100024.A triangle has the same area as a square. If the length of a base of the triangle is the sameas the side-length of the square, and the height of the triangle to the base is 4, what is thearea of the square?A) 1/2 B) 2 C) 4 D) 825.When V olta found a field in the shape of an isosceles triangle, she was soexcited that she ran a lap around all three sides. Two sides of the field havelengths of 505 m each, and the third side has a whole-number length.What is the greatest possible distance that V olta might have run in one lap?A) 2016 B) 2017 C) 2018 D) 201926.25 ×66 = 75 ×?A) 22 B) 44 C) 16 D) 3327.The number that has an odd number of whole number divisors isA) 15 B) 16 C) 17 D) 1828.In a sequence of 8 numbers, the average of the 8 terms is 15. If the average of the firstthree terms is 16 and the average of the next two terms is 15, what is the average of thelast three terms?A) 12 B) 13 C) 14 D) 1529.All years between 2000 and 2050 that are divisible by 4 are leap years.No other years between 2000 and 2050 are leap years. How many daysare there all together in the 17 years from 2010 to 2026?A) 6029 B) 6030 C) 5018 D) 501930.The sum of the hundreds digit and the tens digit of 2357 isA) 5 B) 8 C) 10 D) 1231.Which of the expressions below has the greatest value of (quotient × remainder)?A) 27 ÷ 4 B) 47 ÷ 6C) 57 ÷ 8 D) 87 ÷ 1232.I have some dimes and nickels, and together these coins are worth $3. If I replace everynickel with a quarter, I will have $5. How many dimes do I have?A) 10 B) 15 C) 20 D) 2533.I am a lovely cat. When I multiply the digits of a whole numberand the product I get is 9, I put that whole number on my list offavorite numbers. Of the whole numbers from 1000 to 9999, howmany would I put on my list of favorite numbers?A) 5 B) 10 C) 15 D) 2034.The sum of the tens digit and the units digit of the sum 1 + 12 + 123 + 12345+ … + 123456789 isA) 4 B) 5 C) 6 D) 735.The product of all prime numbers between 1 and 10 isA) 210 B) 105C) 1890 D) none of the above36.What is the average of 12, 14, 16, and 18?A) 13 B) 14 C) 15 D) 1637.When Jon shouts out a whole number, Al shouts out the product ofits digits, Barb shouts out the product of the digits of the number Alshouted out, and Cy shouts out the product of the digits of thenumber Barb shouted out. When Cy shouts out 18, what numbermight Jon have shouted out?A) 789 B) 799 C) 899 D) 99938.Each big box contains 3 medium boxes, each medium box contains2 small boxes, and each small box contains 5 apples. How many bigboxes are necessary for 1200 apples?A) 30 B) 40 C) 50 D) 6039.Eighteen years from now, my age will be 4 more than twice my currentage. My age now isA) 12 B) 14 C) 16 D) 1840.Each time Wanda waved her wand, 4 more stars appeared on herdress (which started with no stars). After several waves, Wandamultiplied the total number of stars then on her dress by thenumber of times she had waved her wand. This product cannot beA) 144 B) 256 C) 364 D) 676。
数学思维(高中)：2015-2016年度美国“数学大联盟”思维探索十至十二年级试卷(含参考答案)
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。
2015年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷
2014-2015 年度美国“数学大联盟杯赛”(中国赛区)初赛
(五年级) (初赛时间：2015 年 1 月 3 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。
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城市
22. The prime factorization of a whole number less than 100 is the product of at most ? primes (not necessarily different). ( ) A) 3 B) 4 C) 5 D) 6 23. A rectangle with sides of integer length is divided into a square region and a shaded rectangular region as shown. If the area of the shaded
11. Thok has a simple plan. He will spend 50% of the day in the cave, 25% of the rest of the day on the hunt, and the remainder of the day watching films outside. How many hours will Thok spend watching films? ( ) A) 3 B) 6 C) 9 D) 25 12. 2 × 3 × 6 × 36 × 2 × 3 × 6 × 36 = A) 65 B) 66 ( C) 67 ) D) 68
20162017年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级).doc
2016-2017年度美国“数学大联盟杯赛”（中国赛区）初赛（五年级）1.Which of the has the greatest value?A) 2017 B) 2017C) 20 × 17 D) 20 + 172.Which of the leaves a remainder of 2 when divided by 4?A) 2014 B) 2015 C) 2016 D) 20173.Which of the is a product of two consecutive primes?A) 30 B) 72 C) 77 D) 1874.A Bizz-Number is a integer that either contains the 3 or is a multiple of 3. What is the of the 10th Bizz-Number?A) 24 B) 27 C) 30 D) 315.The of an isosceles triangle with side-lengths 1 and 1008 isA) 1010 B) 1012 C) 2017 D) 20186.How integers less than 2017 are divisible by 16 but not by 4?A) 0 B) 126 C) 378 D) 5047.Jon has a number of pens. If he distributed them evenly among 4 students,he have 3 left. If he distributed them evenly among 5 students, he have 4 left. The minimum number of pens that Jon have isA) 14 B) 17 C) 19 D) 248.Which of the numbers is not divisible by 8?A) 123168 B) 234236 C) 345424 D) 4566249.Which of the is both a square and a cube?A) 36 × 58B) 36 × 59C) 36 × 512D) 39 × 51210.The of two prime numbers cannot beA) odd B) even C) prime D) composite11.At the end of day, the amount of water in a cup is twice what it was atthe beginning of the day. If the cup is at the end of 2017th day, then it was1/4 at the end of the ? day.A) 504th B) 505th C) 2015th D) 2016th12.The grades on an exam are 5, 4, 3, 2, or 1. In a class of 200 students, 1/10of got 5’s, 1/5 of got 4’s, 25% of got 3’s, and 15% of got 2’s. How many students got 1’s?A) 40 B) 60 C) 80 D) 10013.22000 × 52017 = 102000 × ?A) 517B) 51000C) 52000D) 5201714.1% of 1/10 of 10000 is ? percent than 10A) 0 B) 9 C) 90 D) 90015.What is the of the of Circle C to the of Square S if the of adiameter of C and a of S are equal?A) π:1 B) π:2 C) π:3 D) π:416.Which of the is not a prime?A) 2003 B) 2011 C) 2017 D) 201917.If the sum of prime numbers is 30, what is the possible value of any of the primes?A) 19 B) 23 C) 27 D) 2918.For $3 I spend on books, I spend $4 on and $5 on toys. If I spent $20 on food, how much, in dollars, did I spend in total?A) 60 B) 90 C) 120 D) 15019.How positive odd factors does 25 × 35 × 55 have?A) 25 B) 36 C) 125 D) 21620.The of scalene triangles with perimeter 15 and side-lengths isA) 3 B) 5 C) 6 D) 721.Which of the when rounding to the nearest thousands, hundreds, and tens, 3000, 3500, and 3460, respectively?A) 3210 B) 3333 C) 3456 D) 351722.Which of the below has exactly 5 positive divisors?A) 16 B) 49 C) 64 D) 10023.Each after the 1st in the sequence 1, 5, 9, … is 4 than the previousterm. The greatest in sequence that is < 1000 and that leaves a of1 when divided by 6 isA) 991 B) 995 C) 997 D) 99924.For integer from 100 to 999 I the of the integer’s digits. Howmany of the products I are prime?A) 4 B) 8 C) 12 D) 1625.If a machine paints at a of 1 m2/sec, its is alsoA) 600 cm2/min B) 6000 cm2/minC) 60000 cm2/min D) 600000 cm2/min26.The of Square A is 1. The of Square B is times ofSquare A. The of Square C is times of Square B. The of Square C is ? times of Square A.A) 3 B) 6 C) 36 D) 8127.If the 17 minutes ago was 19:43, what will be the 17 minutes from now?A) 20:00 B) 20:17 C) 20:34 D) 20:1528.Pick any greater than 100 and subtract the sum of its from theinteger. The largest that must the result isA) 1 B) 3 C) 9 D) 2729.The number of needed in a room so there are always atleast five in the room born in the same month isA) 48 B) 49 C) 60 D) 6130.If M, A, T, and H are digits such that MATH + HTAM = 12221, is the value of M + A + T + H?A) 8 B) 20 C) 22 D) 2431.If 10 forks, 20 knives, and 30 $360, and 30 forks, 20 knives, and10 $240, what is the of 5 forks, 5 knives, and 5 spoons?A) 15 B) 75 C) 150 D) 22532.Write, in reduced form, the value ofA) 0.5 B) 1 C) 1.5 D) 233.Al, Barb, Cal, Di, Ed, Fred, and participated in a chess tournament. Eachplayer play each of his six opponents exactly once. So far, Al has 1match. Barb has 2 matches. Cal has 3 matches. Di has 4matches. Ed has 5 matches, and has 6 matches. How manymatches has at this point?A) 1 B) 3 C) 5 D) 734.What is the number of different integers I can choose from the 100positive integers so that no of these integers could be the of the sides of the same triangle?A) 8 B) 9 C) 10 D) 1135.What is the value of change that you can have in US (pennies, nickels, dimes, and quarters) without being able to someone exact change for a one-dollar bill?A) $0.90 B) $0.99 C) $1.19 D) $1.2936.小罗星期一工作了2个小时。
2016-2017年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)名师制作优质教学资料
2016-2017年度美国“数学大联盟杯赛”（中国赛区）初赛（五年级）1.Which of the has the greatest value?A)2017B)2017C)20×17D)20+172.Which of the leaves a remainder of2when divided by4?A)2014B)2015C)2016D)20173.Which of the is a pr oduct of two consecutive primes?A)30B)72C)77D)1874.A Bizz-Number is a integer that either contains the3or is a multiple of3.What is the of the10th Bizz-Number?A)24B)27C)30D)315.The of an isosceles triangle with side-lengths1and1008isA)1010B)1012C)2017D)20186.How integers less than2017are divisible by16bu t not by4?A)0B)126C)378D)5047.Jon has a n u mbe r of pens.If he distributed them evenly among4students, he have3left.If he distributed them evenly among5students,he have 4left.The minimum n u mbe r of pens that Jon have isA)14B)17C)19D)248.Which of the numbers is not divisible by8?A)123168B)234236C)345424D)4566249.Which of the is both a square and a cube?A)36×58B)36×59C)36×512D)39×51210.The of two prime numbers cannot beA)odd B)even C)prime D)composite11.At the end of day,the amount of water in a cup is twice what it was at the beginning of the day.If the cup is at the end of2017th day,then it was1/4at the end of the?day.A)504th B)505th C)2015th D)2016th12.The grades on an exam are5,4,3,2,or1.In a class of200students,1/10of got5’s,1/5of got4’s,25%ofgot3’s,and15%of got2’s.How many students got1’s?A)40B)60C)80D)10013.22000×52017=102000×?A)517B)51000C)52000D)5201714.1%of1/10of10000is?percent than10A)0B)9C)90D)90015.What is the of the of Circle C t o the of Square S if the ofa diameter of C and a of S are equal?A)π:1B)π:2C)π:3D)π:416.Which of the is not a prime?A)2003B)2011C)2017D)201917.If the su m of prime numbers is30,what is the possible value of any of the primes?A)19B)23C)27D)2918.For$3I s pe n d on books,I s pe n d$4on and$5on toys.If I spent$20 on food,how much,in dollars,did I s pen d in total?A)60B)90C)120D)15019.How positive odd factors do e s25×35×55have?A)25B)36C)125D)21620.The of scalene triangles with perimeter15and side-lengths isA)3B)5C)6D)721.Which of the when rounding t o the nearest thousands,hundreds,and tens,3000,3500,and3460,respectively?A)3210B)3333C)3456D)351722.Which of the below has exactly5positive divisors?A)16B)49C)64D)10023.Each after the1st in the sequence1,5,9,…is4than the previous term.The gr eatest in sequence that is<1000and that leavesa of1when divided by6isA)991B)995C)997D)99924.For integer from100t o999I the of the integer’s digits.How many of the products I are prime?A)4B)8C)12D)1625.If a machine paints at a of1m2/sec,its is alsoA)600cm2/min B)6000cm2/minof Square C is timesC)60000cm2/min D)600000cm2/min26.The of Square A is1.The of Square B is times of Square A.The of Square B.The of Square C is?times of Square A.A)3B)6C)36D)8127.If the17minutes ago was19:43,what will be the17minutes from now?A)20:00B)20:17C)20:34D)20:1528.Pick any greater than100and subtract the su m of its from the integer.The largest that must the result isA)1B)3C)9D)2729.The n u mbe r of needed in a room so there are always at least five in the room born in the s ame month isA)48B)49C)60D)6130.If M,A,T,and H are digits such that MA TH+HT AM=12221,is the value of M+A+T+H?A)8B)20C)22D)2431.If10forks,20knives,and30$360,and30forks,20knives,and10$240,what is the of5forks,5knives,and5spoons?A)15B)75C)150D)22532.Write,in r educed form,the value ofA)0.5B)1C)1.5D)233.Al,Barb,Cal,Di,Ed,Fred,and participated in a chess tournament.Each player play each of his six o ppo n en t s exactly once.So far,Al has1 match.Barb has2matches.Cal has3matches.Di has4 matches.Ed hasmatches has5matches,andat this point?has6matches.How many A)1B)3C)5D)7of these integers could be the34. What is the n u mber of different integers I can choose from the100positive integers so that noof the sides ofthe s a me triangle? A) 8 B) 9 C) 10 D) 1135. What is thevalue of change that you can have in US(pennies,nickels, dimes, and quarters) without being able t o someone exact change for aone-dollar bill? A) $0.90 B) $0.99 C) $1.19 D) $1.2936. 小罗星期一工作了 2 个小时。
2017-2018年美国“数学大联盟杯赛”(中国赛区)初赛高中年级试卷及答案
2017-2018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：2017年11月26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. 本试卷是十、十一、十二年级试卷，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)、答题纸、英文词汇手册、草稿纸。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
填空题(每小题10分，答对加10分，答错不扣分，共300分。
)1.Each pirate wants his own treasure chest, but there is 1 more pirate than thereare treasure chests. If the pirates would agree to pair up so each pirateshares a treasure chest with another pirate, then 1 treasure chest wouldnot be assigned to any pirate. How many treasure chests are there?Answer: ________________.2.If m and nare positive integers that satisfy 10=, what is the greatest possiblevalue of m + n?Answer: ________________.3.There are an infinite number of points with positive coordinates(x,y) the sum of whose coordinates is the square of an integer.Among all such points (x,y), which one satisfies y = 2x and hasx as small as possible?Answer: ________________.4.As shown, a small square is inscribed in one of the triangles formed whenboth diagonals of a larger square are drawn. If the area of the larger squareis 144, what is the area of the smaller square?Answer: ________________.5.Trisection points on opposite sides of a rectangle are joined, as shown. Ifthe area of the shaded region is 2018, what is the area of the rectangle?Answer: ________________.6. A unit fraction is a fraction whose numerator is 1 and whosedenominator is a positive integer. What is the largest rationalnumber that can be written as the sum of 3 different unitfractions?Answer: ________________.7.What is the greatest possible perimeter of a rectangle whose length and width are differentprime numbers, each less than 120?Answer: ________________.8.Mom, Dad, and I each write a positive integer. My number is leastand Dad's is greatest. The average of all 3 numbers is 20. Theaverage of the 2 smallest numbers is 8. If Dad's number is d andif my number is m, what is the greatest possible value of d–m?Answer: ________________.9.If 8 different integers are chosen at random from the first 15 positive integers, what is theprobability that an additional number chosen at random from the remaining 7 positiveintegers is smaller than every one of the 8 originally chosen positive integers?Answer: ________________.10.What sequence of 5 positive integers has these three properties:1) All but one of the numbers is a multiple of 5.2) Every number after the first is 1 more than the sum of all the preceding numbers.3) The first number is as small as possible.Answer: ________________.11.Three beavers (one not shown) take turns biting a tree until it falls. Thesecond beaver is twice as likely as the first to make the tree fall. Thethird is twice as likely as the second to make the tree fall. What isthe probability that a bite taken by the third beaver causes thetree to fall?Answer: ________________.12.What is the ratio, larger to smaller, of a rectangle's dimensions if halfof the rectangle is similar to the original rectangle?Answer: ________________.第1页，共4页第2页，共4页A rectangle is partitioned into 9 different squares, as shown at the right. The area of the smallest square, shown fully darkened, is 1. Two other squares have areas of 196 and 324, as shown. What is the area of the shaded square? Answer: ________________.When the square of an eight-digit integer is subtracted from the square of a differenteight-digit integer, the difference will sometimes have eight identical even digits. What are both possible values of the repeated digit in such a situation? Answer: ________________.If the perimeter of an isosceles triangle with integral sides is 2017, how many different lengthsare possible for the legs? Answer: ________________.What are all ordered triples of positive primes (p ,q ,r ) which satisfy p q + 1 = r ? Answer: ________________.The reflection of (6,3) across the line x = 4 is (2,3). If m ≠ 4, what is the reflection of (m ,n )across the line x = 4? Answer: ________________.The vertices of a triangle are (8,7), (0,1), and (8,1). What are thecoordinates of all points inside this triangle that have integralcoordinates and lie on the bisector of the smallest angle of the triangle? Answer: ________________.In a regular 10-sided polygon, two pairs of different vertices (four different verticesaltogether) are chosen at random, so that all points chosen are distinct from each other. What is the probability that the line segments determined by each pair of points do not intersect? Answer: ________________.A line segment is drawn from the upper right vertex of aparallelogram, as shown, dividing the opposite side into segments with lengths in a 2:1 ratio. If the area of the parallelogram is 90, what is the area of the shaded region?Answer: ________________.21. If 0 < a ≤ b ≤ 1, what is the maximum value of ab 2 – a 2b ? Answer: ________________.22. What are all ordered pairs of integers (x ,y ) that satisfy 5x 3 + 2xy – 23 = 0? Answer: ________________.23. If two altitudes of a triangle have lengths 10 and 15, what is the smallest integer that couldbe the length of the third altitude?Answer: ________________.24. If h is the number of heads obtained when 4 fair coins are each tossed once, what is theexpected (average) value of h 2? Answer: ________________.25. What is the largest integer N for which 7x + 11y = N has no solution in non-negativeintegers (x ,y )? Answer: ________________.26. There are only two six-digit integers n greater than 100 000 for which n 2 has n as its finalsix digits (or, equivalently, for which n 2 – n is divisible by 106). One of the integers is 890 625. What is the other?Answer: ________________.27. A hexagon is inscribed in a circle as shown. If lengths of three sidesof the hexagon are each 1 and the lengths of the other three sides are each 2, what is the area of this hexagon? Write your answer in its exact format or round to the nearest tenth. Answer: ________________.28. If x is a number chosen uniformly at random between 0 and 1, what is the probability thatthe greatest integer ≤ 21log x ⎛⎫⎪⎝⎭ is odd?Answer: ________________.29. In the interval -1 < x < 1, sin θ is one root of x 4 – 4x 3 + 2x 2 – 4x + 1 = 0. In that sameinterval, for what ordered pair of integers (a ,b ) is cos 2θ one root of x 2 + ax + b = 0? Answer: ________________.30. Let P (x ) = 2x 10 + 3x 9 + 4x + 9. If z is a non-real solution of z 3 = 1, what is the numericalvalue of 23111P P P z z z ⎛⎫⎛⎫⎛⎫++ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭?Answer: ________________.第3页，共4页第4页，共4页。
(参考资料)2014年美国“数学大联盟杯赛”(中国赛区)初赛五、六年级试卷
A) 100
B) 160
C) 200
D) 250
二、填空题(每小题 5 分，答对加 5 分，答错不扣分，共 50 分，答案请填涂在答题卡上)
31. The sum of the digits of 2014 is 2 + 0 + 1 + 4 = 7. Let n be a natural number.
m = n + 2014. The sum of the digits of m is half the sum of the digits of n.
What is the minimum value of n?
Answer: ______.
32. The sum of 5 different prime numbers is 200. Each of the 5 prime
1
2
26. If 5 of the 200 stripes on Frank’s giant shell are blue, 5 of the remaining
stripes are brown, and the rest are white, there are ? more white stripes
D) 110
22. The average of 2014 sixes is equal to the average of 4028 ? .
A) threes
B) sixes
C) nines
D) twelves
23. What is 0.625% of 8% of 500?
A) 0.25
B) 2.5
数字为三个连续的偶数，个位数字为三个连续的奇数。如果将四位数的
2018年美国“数学大联盟杯赛”(中国赛区)初赛六年级试卷及答案
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(六年级)(初赛时间：2017年11月26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. 本试卷是六年级试卷，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。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、 及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
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. Pick any integer greater than 1. Double it twice, then triple the result. The final outcomeis ? of your starting integer.A) 700%B) 1100%C) 1200%D) 1300%2. Barry listened to the radio for 3 hours and 36 minutes. Rounded to thenearest 10 minutes, for how many minutes was Barry listening? A) 210 B) 220 C) 330 D) 340 3. Divide 99 by 22 to get a quotient and remainder. Divide that remainder by that quotient, and the new remainder is A) 4 B) 3 C) 2 D) 14. A man had five pieces of chain, each made up of three links, figure below. He wanted to join the five pieces together to make a big chain of fifteen links and went to a blacksmith to see how much it would cost. “Well,” said the blacksmith, “I will charge you 50 cents for cutting a link and $1.00 for welding a link. Any bending that is required is free.” Given those prices, what is the smallest amount of money for which the job could be done? Note: In a chain, each link is connected to one or two other links. A) $4.50 B) $5.00 C) $5.50 D) $6.00 5. A bee sat on the head of a horse rider whose horse was trotting eastbound at a steady five miles per hour. Some distance ahead on the same path, another horse and rider were approaching westbound, also at five miles per hour. When the two horses were 20 miles apart, the bee left the first horse rider and flew toward the second horse at a rate of ten miles per hour. Upon reaching the second horse, the bee immediately turned around and flew back at the same rate to the first horse. If the bee kept up this performance until the two riders met, how far (in miles) did he travel from the moment he left the first horse rider?A) 10B) 20C) 30D) None of the above6. Which of the following is the sum of the prime factors of 2018?A) 11 B) 219 C) 1011 D) 20197. If the length of the longest side of a triangle is 18, which of the following could not be the length of its second-longest side? A) 9 B) 10 C) 12 D) 17 8. My final score in a competition is the average of my scores on 5 rounds. To get a final score of 88 after getting 84, 80, and 92 on the first 3 rounds, what must be my average score for the last 2 rounds? A) 88 B) 90 C) 92 D) 96 9. Mr. Rice had breakfast one day at a restaurant with Mr. Wheat. When it came time to pay the bill, it was found that Mr. Rice had as many one-dollar bills as Mr. Wheat had quarters. (Mr. Rice had one-dollar bills only, and Mr. Wheat had quarters only.) Rather than each man paying separately, Mr. Rice paid his share of the bill, $6, to Mr. Wheat. At that point, Mr. Wheat had four times as much money as Mr. Rice. How much money did Mr. Rice have at the beginning? A) $6 B) $8 C) $9 D) $12 10. Professor Peach teaches chemistry to clever kids. The ratio of freshmen to other students in his class is 3:8. The total number of students in Professor Peach’s class could be A) 42 B) 45 C) 56 D) 77 11. 440 ÷ 220 = A) 22B) 24C) 220D) 26012. Mr. Bogsworth once left a will which read:To Bob, twice as much as to Betty. To Brian, twice as much as to Bob. To Bill, twice as much as to Brian.If his estate was valued at $45000, how much money did Betty, one of his four heirs, receive? A) $1000 B) $2000 C) $3000 D) $6000 13. I paid $5 and got 5 quarters, 5 dimes, and 5 nickels in change. I spent A) $3.00 B) $3.25 C) $3.45 D) $3.75 14. One side of Todd ’s truck is a perfect rectangle with an area of 12 m 2. If its length is 3 times its width, then its perimeter is A) 8 m B) 12 m C) 16 m D) 20 m15. If a bird in the hand is worth two in the bush, and a bird in the bush is worth four in the sky, then 4 birds in the hand are worth ? birds in the sky.A) 1B) 4C) 16D) 3216. On each of the four shelves of my bookcase is a different prime number of books. Therecould be a total of ? books on my shelves.A) 15B) 21C) 22D) 24第1页，共4页 第2页，共4页Seven years ago I realized that my age would be tripled twelve years from then. How old am I now? A) 11 B) 13 C) 16 D) 18How many fractions with a numerator of 1 and a whole-number denominator are greater than 0.01 and less than 1? A) 98 B) 99 C) 100 D) 101If I write the letters R-E-P-E-A-T repeatedly, stopping when I have written exactly 100 letters, how many times do I write the letter E? A) 16 B) 18 C) 32 D) 34On my map, 1 cm represents 100 km. If a park shown on the map is a rectangle that is2.5 cm by 4 cm, the area of the actual park is ? km 2. A) 100 B) 1000 C) 10 000 D) 100 000Gloomy Gus’s Tu esday rain cloud shows up every Tuesday at 8:30 A.M.and every 50 minutes after that. Its last appearance on Tuesday is at ? P.M.A) 11:00 B) 11:10 C) 11:30 D) 11:50If my lucky number divided by its reciprocal is 100, then the square ofmy lucky number isA) 100 B) 10 C) 1D) 1100A boy and his sister were walking down the street one afternoon when they met a kind old man. When the old man asked them about the size of their family, the boy quicklyanswered. “I have as many brothers as I have sisters,” he proudly stated. Not to be left out, the girl added, “I have three times as many brothers as I have sisters.” Can you tell how many boys and girls in total there were in their family? A) 5 B) 6 C) 7 D) 8A farmer was asked how many pigs he had. “Well,” he said, “if I had just as m any more again, plus half as many more, plus another 1.5 times more, I would have three dozen.” How many pigs did he have?A) 6 B) 9 C) 12 D) 15 15% of 80 is 40% ofA) 30B) 55C) 105D) 210It took me 90 minutes to cycle 45 km to the beach. Later I got a ride from the beach tothe park at twice my cycling speed. If the ride to the park took 15 minutes, what distance did I travel from the beach to the park?A) 15 kmB) 30 kmC) 45 kmD) 135 kmTed, Rick, and Sam painted a wall together. Ted painted 80% more ofthe wall than Sam painted. Sam painted 40% less than Rick. Ted painted ? of the amount that Rick painted. A) 102% B) 108% C) 120% D) 140% The greatest integer power of 20 that is a divisor of 5050 isA) 2020B) 2025C) 2050D) 2012529. The ones digit of the sum of all even integers from 2 to 1492 is A) 2B) 4 C) 8 D) 030. The median of 12, 13, 14, 15, 16, and 17isA) 18 B) 223840 C) 514 D) 94031. The average of all positive even integers from 2 to 2018 is A) 1000 B) 1009 C) 1010 D) 1014 32. Pirate Percy has 300 coins in his chest. Of the Spanish coins,20% are gold. If 100 of the coins are gold but not Spanish and 70 of the coins are neither gold nor Spanish, how many Spanish gold coins are in Percy’s chest?A) 20 B) 26 C) 30 D) 3433. When I divided the population of my city by the number of streets in the city, I got a remainder of 18. If the exact quotient on my calculator was 123.06, how many streets are there in my city? A) 60 B) 120 C) 186 D) 30034. What is the greatest number of 3-by-7 rectangles that can be placed inside an 80-by-90 rectangle with no overlapping?A) 312B) 330C) 334D) 34235. How many four-digit whole numbers have four different even digitsand a ones digit greater than its thousands digit?A) 36B) 54C) 60D) 9036. Both arcs AB and AD are quarter circles of radius 5, figure on the right.Arc BCD is a semi-circle of radius 5. What is the area of the region ABCD ? A) 25 B) 10 + 5π C) 50 D) 50 + 5π 37. In the figure on the right, the side-length of the smaller square is 4. The four arcs are four semi-circles. Each side of square ABCD is tangent to one of the semi-circles. The area of ABCD is A) 32 B) 36 C) 48 D) 6438. A million is a large number, a “1” followed by 6 zeros. A googol is a large number, a “1” followed by one hundred zeros. Agoogo lplex is a large number, a “1” followed by a googol of zeros. A googolplexian is a large number, a “1” followed by a googolplex of zeros. A googolplexian isA) 1010 B) 1001010 C) 100101010 D) none of the above 39. If the total number of positive integral divisors of n is 12, what is the greatest possibletotal number of positive integral divisors of n 2? A) 23 B) 24 C) 33 D) 4540. Of all the isosceles triangles whose perimeter is 20 and whose side-lengths are integers, what is the length of the base of the triangle with the largest area? A) 2 B) 5 C) 6 D) 8第3页，共4页第4页，共4页。