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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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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