度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)

2024年3月30日发(作者：2010年河南中考数学试卷)

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) 20

17

C) 20 × 17 D) 20 + 17

2.

Which of the leaves a remainder of 2 when divided by 4?

A) 2014 B) 2015 C) 2016 D) 2017

3.

Which of the is a product of two consecutive primes?

A) 30 B) 72 C) 77 D) 187

4.

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) 31

5.

The of an isosceles triangle with side-lengths 1 and 1008 is

A) 1010 B) 1012 C) 2017 D) 2018

6.

How integers less than 2017 are divisible by 16 but not by 4?

A) 0 B) 126 C) 378 D) 504

7.

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 is

A) 14 B) 17 C) 19 D) 24

8.

Which of the numbers is not divisible by 8?

A) 123168 B) 234236 C) 345424 D) 456624

9.

Which of the is both a square and a cube?

A) 3

6

× 5

8

B) 3

6

× 5

9

C) 3

6

× 5

12

D) 3

9

× 5

12

10.

The of two prime numbers cannot be

A) odd B) even C) prime D) composite

11.

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 of 2017th day, then it was

1/4 at the end of the ? day.

A) 504th B) 505th C) 2015th D) 2016

th

12.

The grades on an exam are 5, 4, 3, 2, or 1. In a class of 200 students, 1/10

got 3’s, and 15% of got 2’s. of got 5’s, 1/5 of got 4’s, 25% of

How many students got 1’s?

A) 40 B) 60 C) 80 D) 100

13.

2

2000

× 5

2017

= 10

2000

× ?

A) 5

17

B) 5

1000

C) 5

2000

D) 5

2017

14.

1% of 1/10 of 10000 is ? percent than 10

A) 0 B) 9 C) 90 D) 900

15.

What is the of the of Circle C to the of Square S if the of a

diameter of C and a of S are equal?

A) π:1 B) π:2 C) π:3 D) π:4

16.

Which of the is not a prime?

A) 2003 B) 2011 C) 2017 D) 2019

17.

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) 29

18.

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) 150

19.

How positive odd factors does 2

5

× 3

5

× 5

5

have?

A) 25 B) 36 C) 125 D) 216

20.

The of scalene triangles with perimeter 15 and side-lengths is

A) 3 B) 5 C) 6 D) 7

21.

Which of the when rounding to the nearest thousands, hundreds, and

tens, 3000, 3500, and 3460, respectively?

A) 3210 B) 3333 C) 3456 D) 3517

22.

Which of the below has exactly 5 positive divisors?

A) 16 B) 49 C) 64 D) 100

23.

Each after the 1st in the sequence 1, 5, 9, … is 4 than the previous

term. The greatest in sequence that is < 1000 and that leaves a of

1 when divided by 6 is

A) 991 B) 995 C) 997 D) 999

24.

For integer from 100 to 999 I the of the integer’s digits. How

many of the products I are prime?

A) 4 B) 8 C) 12 D) 16

25.

If a machine paints at a of 1 m

2

/sec, its is also

A) 600 cm

2

/min B) 6000 cm

2

/min

C) 60000 cm

2

/min D) 600000 cm

2

/min

26.

The of Square A is 1. The

of Square C is

of Square B is

times

times of

of Square A. The of Square B. The

Square C is ? times of Square A.

A) 3 B) 6 C) 36 D) 81

27.

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) 20:15

28.

Pick any greater than 100 and subtract the sum of its

that must the result is

from the

integer. The largest

A) 1 B) 3 C) 9 D) 27

29.

The number of needed in a room so there are always at

least five in the room born in the same month is

A) 48 B) 49 C) 60 D) 61

30.

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) 24

31.

If 10 forks, 20 knives, and 30 $360, and 30 forks, 20 knives, and

10 $240, what is the of 5 forks, 5 knives, and 5 spoons?

A) 15 B) 75 C) 150 D) 225

32.

Write, in reduced form, the value of

A) 0.5 B) 1 C) 1.5 D) 2

33.

Al, Barb, Cal, Di, Ed, Fred, and participated in a chess tournament. Each

1

4

player play each of his six opponents exactly once. So far, Al has

2 matches. Cal has

5 matches, and

at this point?

has

3 matches. Di has match. Barb has

matches. Ed has

matches has

6 matches. How many

A) 1 B) 3 C) 5 D) 7

34.

What is the number of different integers I can choose from the

of these integers could be the

100

positive integers so that no of the sides of

the same triangle?

A) 8 B) 9 C) 10 D) 11

35.

What is the value of change that you can have in US

nickels, dimes, and quarters) without being able to

(pennies,

someone exact change for a

one-dollar bill?

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

36.

小罗星期一工作了2个小时。在那之后的每一天，他的工作时间是前一天的

两倍。请问他从星期一到星期四总共工作了多少个小时？

A) 14 B) 16 C) 28 D) 30

37.

苏珊花了一天中的的时间做英语作业，的时间做数学作业，请问她这一天

还剩余多少个小时？

A) 4 B) 6 C) 8 D) 12

38.

下面哪个数是11,111,111和111,111,111,111的公约数？

A) 111 B) 1111 C) 11111 D) 111111

39.

设 n 是一任意自然数。若将 n 的各位数字反向排列所得自然数 n

1

与 n 相等，

则称 n 为一回文数。例如，若 n = 1234321，则称 n 为一回文数；但若 n = 1234567，

则 n 不是回文数。请问在10000和100000之间有多少个回文数？

A) 900 B) 1000 C) 1100 D) 1200

40.

汤姆建了两个塔。塔A发射5次能量波需要正好5秒。塔B发射10次能量波

需要正好10秒。能量波是间隔发送的，并且任何两个连续的能量波之间的时间

间隔是相同的。假设塔A发射12次能量波需要t

1

秒，塔B发射12次能量波需

要t

2

秒。那么下面哪个是正确的?

A) t

1

< t

2

B) t

1

= t

2

C) t

1

> t

2

D) 无法判断