2017年美国“数学大联盟杯赛”初赛四年级试卷

2016-2017年度美国“数学大联盟杯赛”(中国赛区)初赛

(四年级)

(初赛时间：2016年11月20日，考试时间90分钟，总分200分)

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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 greatest?

A) 2.017 B) 20.17 C) 201.7 D) 2017

2.The sum of the degree-measures of the interior angles of a triangle is

A) 180 B) 360 C) 540 D) 720

3.100 + 200 + 300 + 400 + 500 = 300 ×?

A) 3 B) 4 C) 5 D) 6

4.100 ÷ 4 = 200 ÷?

A) 2 B) 4 C) 8 D) 16

5.In tonight’s talent show, Jack sang 3 songs. The number of songs that Jill sang is 8 less

than 4 times the number of songs Jack sang. How many songs did Jill sing?

A) 3 B) 4 C) 6 D) 7

6.Doubling a certain number is the same as adding that number and 36. What is that

number?

A) 18 B) 36 C) 54 D) 72

7.The side-lengths of three square farms are 1 km, 2 km, and 3 km respectively. The sum of

the areas of these three farms is ? km2.

A) 6 B) 12 C) 13 D) 14

8.What is the greatest common factor of 2017 and 20 × 17?

A) 1 B) 2 C) 3 D) 5

9.If a computer can download 2% of the files in 2 seconds, how many seconds does it take

to download all the files?

A) 100 B) 200 C) 300 D) 400

10.In yesterday’s giant-pie eating, all pies were the same size. Al ate 3/4 of a giant pie, Barb

ate 4/5 of a giant pie, Cy ate 5/6 of a giant pie, and Di ate 6/7 of a giant pie. Who ate the largest portion?

A) Al B) Barb C) Cy D) Di 11.The product of two consecutive positive integers is always

A) odd B) even

C) prime D) composite

12.In a 5-term sequence, the first term is 2. The value of each term after the first is twice that

of its previous term. What is the product of the 5 terms?

A) 24B) 210C) 215D) 245

13.Ace, Bo, and Cat performed in a talent show. Bo’s total score was twice that of Ace, and

Cat’s total score was three times that of Bo. If the sum of all three total scores was 900, what was Cat’s total score?

A) 100 B) 200

C) 300 D) 600

14.The length of each side of triangle T is an integer. If two sides of T have lengths of 2016

and 2017, what is the least possible value for the length of the third side?

A) 1 B) 2 C) 4032 D) 4033

15.If the sum of three consecutive whole numbers is 2016, what is the sum of the next three

consecutive whole numbers?

A) 2032 B) 2025 C) 2020 D) 2017

16.If the sum of a prime and a composite is 2017, what is the least possible value for the

product of the two numbers?

A) 3000 B) 4030 C) 6042 D) 9120

17.What is the smallest whole number that leaves a remainder of 2 when divided by each of 3,

4, 5, and 6?

A) 58 B) 60 C) 62 D) 64

18.What is the highest power of 2 that divides 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9?

A) 25B) 26C) 27D) 28

19.The product of the digits of 23 is 6. How many different whole numbers between 100 and

999 have a product of 6?

A) 12 B) 9 C) 6 D) 3

20.What is the value of 1% of 10% of 100%?

A) 0.001 B) 0.01 C) 0.1 D) 1

21.In a box that contains only balls that are red, yellow, or green, 10% of the balls are red, 1/5

of the balls are yellow, and 49 balls are green. How many balls are in the box?

A) 70 B) 80 C) 90 D) 100

22.Of the following, which has the greatest number of positive whole number divisors?

A) 24 B) 26 C) 51 D) 2017

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23.If you subtract the sum of the digits of a whole number greater than 9 from the number

itself, the result must be divisible by

A) 5 B) 6 C) 9 D) 12

24.I bought a painting for $40, sold it for $50, rebought it for $60, and resold it for $70. My

total profit on the 4 transactions was

A) $10 B) $20 C) $30 D) $40

25.What is the minimum number of whole number divisors of the product of two different

composite numbers?

A) 5 B) 6 C) 8 D) 9

26.For each whole number from 1000 to 9999, inclusive, I write the product of its digits.

How many of the products I write are even?

A) 625 B) 3125 C) 5775 D) 8375

27.Lisa baked some cookies and cakes. Baking one cookie requires 4 cups of sugar and 3

cups of flour, and baking one cake requires 7 cups of sugar and 5 cups of flour. At the end she used 83 cups of sugar and 61 cups of flour. How many cookies did she bake?

A) 11 B) 12 C) 13 D) 14

28.Working by oneself, Al can build a bridge in 3 years, Barb can build a bridge in 4 years,

and Cy can build a bridge in 5 years. Working together, how long, in years, does it take them to build the bridge?

A) 1

2

B)

60

47

C)

60

53

D) 1

29.Jack is a gifted athlete who has trained hard

for the Olympic marathon. In the last

hundred yards he finds the inner strength to

increase his pace and overtakes the runner in

the second place.

But then, with the finishing line just feet

away, he is overt aken by two other runners…

What medal will Jack receive?

A) Gold B) Silver

C) Bronze D) None

30.If we juxtapose three congruent squares, we get a rectangle with perimeter 64. What is the

area of one of the squares?

A) 36 B) 49 C) 64 D) 81

31.In a four-digit perfect square, the digits in the hundreds and thousands places are equal,

and the digits in the tens and ones places are equal. What is this number?

A) 6644 B) 7744 C) 8844 D) 9944 32.For how many of the integers from 100 to 999 inclusive is the product of its digits equal to

9?

A) 6 B) 7 C) 8 D) 9

33.What is the smallest positive integer x for which (x + 8) is divisible by 5 and (x + 17) is

divisible by 7?

A) 30 B) 31 C) 32 D) 33

34.Tom’s new tower was completed. The total value of

the project, the sum of the cost of the construction and

the cost of the land, was one million dollars. The cost of the

construction was $900,000 more than the cost of the

land. So what did Tom pay for the land?

A) $25,000 B) $50,000

C) $75,000 D) $90,000

35.五个连续正整数的和总是可以被下面哪个数整除？

A) 2 B) 3 C) 5 D) 7

36.从1开始，鲍勃一共喊了2017个数，从第一个数之后的每个数都比前一个数大4。

请问以下哪一个数是鲍勃喊过的？

A) 137 B) 138 C) 139 D) 140

37.以下哪个数是质数？

A) 2013 B) 2015 C) 2017 D) 2019

38.202 × 404 × 505 × 606 × 808的最后两位数是多少？

A) 10 B) 20 C) 40 D) 80

39.一共有四种硬币，penny (一美分)，nickel (五美分)，dime(十美分)，quarter (二十五美

分)，每种硬币你可以取任意多个(也可以是0个)放在你的袋子里(在放这些硬币之前，你的袋子是空的)，规则是你袋子里的硬币无法凑成一美元(一美元= 100美分)。你的袋子里最多可以有多少钱？

A) $0.90 B) $0.99 C) $1.19 D) $1.29

40.一群5至12岁的孩子去看电影。这些孩子的年龄的乘积是3080。请问这些孩子的年

龄的和是多少？

A) 30 B) 31 C) 32 D) 33

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