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