2024年3月30日发(作者：小学数学试卷哪里可以免费下载)
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2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛
(五年级)
(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。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. The smallest possible sum of two different prime numbers is
A) 3 B) 4 C) 5 D) 6
2. The greatest common factor of two numbers is 3. The product of these two numbers must
be divisible by
A) 6 B) 9 C) 12 D) 18
3. The sum of 5 consecutive one-digit integers is at most
A) 15 B) 25 C) 35 D) 45
4. How many two-digit multiples of 10 are also multiples of 12?
A) 4 B) 3 C) 2 D) 1
5. I have read exactly
1
3
of the total number of chapters in my 120-page book. If each
chapter has the same whole number of pages, then the total
number of chapters I have left could be
A) 16 B) 24 C) 32 D) 50
6. What is the greatest odd factor of 4
4
× 5
5
× 6
6
?
A) 3
6
B) 5
5
C) 3
5
× 5
5
D) 3
6
× 5
5
7. What is the sum of the factors of the prime number 2017?
A) 2016 B) 2017 C) 2018 D) 2019
8. Lynn ran in 6 times as many races as the number of races
she won. How many of her 126 races did Lynn not win?
A) 21 B) 90 C) 96 D) 105
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9. The least common multiple of 8 and 12 is the greatest common factor of 120 and
A) 80 B) 124 C) 144 D) 180
10. January has the greatest possible number of Saturdays when January 1 occurs on any of
the following days of the week except
A) Thursday B) Friday C) Saturday D) Sunday
11. The number that is 10% of 1000 is 10 more than 10% of
A) 90 B) 100 C) 900 D) 990
12. The sum of 16 fours has the same value as the product of ? fours.
A) 2 B) 3 C) 4 D) 16
13. Of the following, which is the sum of two consecutive integers?
A) 111 111 B) 222 222 C) 444 444 D) 888 888
14. Abe drove for 2 hours at 30 km/hr. and for 3 hours at 50 km/hr. What was Abe’s average
speed over the 5 hours?
A) 35 km/hr. B) 40 km/hr. C) 42 km/hr. D) 45 km/hr.
15. My broken watch runs twice as fast as it should. If my watch first broke at 6:15 P.M.,
what time was displayed on my watch 65 minutes later?
A) 7:20 P.M. B) 7:25 P.M. C) 8:20 P.M. D) 8:25 P.M.
16. (2018 × 2017) + (2018 × 1) =
A) 2017
2
B) 2018
2
C) 2018
3
D) (2018 + 2017)
2
17. A prized bird lays 2, 3, or 4 eggs each day. If the bird laid 17 eggs in 1 week,
on at most how many days that week did the bird lay exactly 2 eggs?
A) 2 B) 3 C) 4 D) 5
18. Of the following, which could be the perimeter of a rectangle whose
side-lengths, in cm, are prime numbers?
A) 10 cm B) 22 cm C) 34 cm D) 58 cm
19. The average of all possible total values of a 4-coin stack of nickels and dimes (containing
at least one of each coin) is
A) 20¢ B) 30¢ C) 40¢ D) 60¢
20. The diameter of Ann’s drum is 40 cm more than the radius.
What is half the circumference of the drum?
A) 120π cm B) 80π cm C) 60π cm D) 40π cm
21. Of the following, which expression has the greatest number of
factors that are multiples of 2018?
A) 2018 × 12 B) 2018
2
C) 2019
2
D) 2019
2019
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22. When the sum of the factors of a prime number is divided by that prime number, the
remainder is
A) 0 B) 1 C) 2 D) 3
23. What is the sum of the digits of the greatest integer that has a square root less than 100?
A) 18 B) 36 C) 99 D) 100
24. My favorite number has 6 different factors. If the product of all 6 factors is 12
3
, what is
the sum of the factors of my favorite number?
A) 24 B) 28 C) 32 D) 36
25. For how many different pairs of unequal positive integers less than 10 is the least common
multiple of the numbers less than their product?
A) 6 B) 7 C) 8 D) 9
26. Exactly
11
2
of the students in my class have at least one brother, and
2
have at least one
sister. If
1
3
have no siblings, what fraction of the students in my class have at least one
brother and at least one sister?
A)
111
6
B)
5
C)
4
D)
1
3
27. Each day, Sal swims a lap 1 second faster than on the day
before. If Sal swims a lap in 60 minutes on the 1st day,
on what day does he swim a lap in 10% less time than
the 1st day?
A) 359th B) 360th C) 361st D) 362nd
28. 2017
2018
× 2017
2019
= 2017
?
× 2017
1009
A) 1010 B) 2010 C) 3028 D) 4038
29. 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
30. For every $5 I earn from my job, I save $2. For every $4 I save from my job, I am given
an additional $1 from my parents to add to my savings. How much must I earn in order to
have $40 in savings?
A) $160 B) $120 C) $100 D) $80
31. 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) 64
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32. 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. A googolplex 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 is
A) 10
100
B)
10
10
100
C)
10
10
10
100
D) None of the above
33. An integral triangle is a triangle with positive integral side-lengths and a positive area.
Such a triangle can have a perimeter as small as 3. What is the next smallest possible
perimeter of an integral triangle?
A) 4 B) 5 C) 6 D) 7
34. 2 liter of 2% fat milk + 3 liter of 3% fat milk = 5 liter of ? fat milk
A) 2.5% B) 2.6% C) 5% D) 6%
35. One day, a motorist came to a hill that was ten-mile drive up one side and a ten-mile drive
down the other. He drove up the hill at an average speed of 30 miles per hour. How fast
will he have to drive down the other side to average 60 miles per hour for the entire
20-mile distance?
A) 30 miles per hour B) 60 miles per hour
C) 90 miles per hour D) None of the above
36. What is the weight of a fish if it weighs ten pounds plus half its weight?
A) 10 B) 15 C) 20 D) 25
37. Without using pennies, how many different combinations of coins (nickels, dimes,
quarters) will make 30 cents?
A) 3 B) 4 C) 5 D) 6
38. A man once bought a fine suit for which he paid $30 more than
1
4
of its price. How
much did he pay for the suit?
A) $30 B) $35 C) $40 D) $45
39. A father is five times as old as his son. In fifteen years he will be only twice as old. How
old is the father at present?
A) 40 B) 35 C) 30 D) 25
40. It takes 30 minutes to completely fill a tank. If, however, a hole allows
1
3
of the water
that is entering the tank to escape, how long will it then take to fill the tank?
A) 40 B) 45 C) 60 D) 90
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