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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) 2017 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) 36 × 58 B) 36 × 59 C) 36 × 512 D) 39 × 512

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) 2016th

12. The

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

got 3’s, and 15%

1/10 of got 5’s, 1/5 of got 4’s, 25% of of got 2’s. How many students got 1’s?

A) 40 B) 60 C) 80 D) 100 13. 22000 × 52017 = 102000 × ? A) 517 B) 51000 C) 52000 D) 52017

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 25 × 35 × 55 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 m2/sec, its

is also

A) 600 cm2/min B) 6000 cm2/min

C) 60000 cm2/min D) 600000 cm2/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