2023年12月27日发(作者：九师联盟数学试卷讲解)
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2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛
(七年级)
(初赛时间：2015年11月14日，考试时间90分钟，总分200分)
学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，
我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
如果您同意遵守以上协议请在装订线内签名
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. Of the following, which has the largest value?
A) 2016 B) 20 × 16 C) 201 × 6 D) 20 + 16
2. I have worked for a number of days equal to the product of five consecutive positive
integers. I may have worked for ? days.
A) 64 B) 100 C) 120 D) 360
3. The product of a 3-digit number and a 5-digit number at most has ? digits.
A) 7 B) 8 C) 9 D) 10
4. What is the sum of the greatest common factor of 16 and 20 and the least common
multiple of 16 and 20?
A) 36 B) 76 C) 81 D) 84
5. The volume of a cube is a perfect fourth power. Which of the following could be the
length of an edge of the cube?
A) 4 B) 8 C) 16 D) 32
6. Today, Jerry read part of a book starting on top of page 17 and finishing on the bottom of
page 45. How many pages did he read?
A) 27 B) 28 C) 29 D) 30
7. Using the 24-hour notation, what is the time 72960 seconds after midnight?
A) 08:15 B) 08:16 C) 20:15 D) 20:16
8. How many odd positive primes are less than 30?
A) 8 B) 9 C) 10 D) 11
9. 10(100 + 1) + 10(100 + 2) + 10(100 + 3) + 10(100 + 4) = ?
A) 4100 B) 5000 C) 5100 D) 6100
10. SuperDan has been working efficiently in painting houses. He painted a whole number of
houses on each of three days. If the product of these three numbers is a prime, he could
have painted a total of ? houses.
A) 17 B) 23 C) 26 D) 43
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11. 12 years from now, Joe’s age will be double what it is today. How old was Joe 10 years
ago?
A) 2 B) 12 C) 22 D) 36
12. The measure of ∠A is 50°. If ∠B is complementary to ∠A and supplementary to ∠C, what
is the measure of ∠C?
A) 40° B) 50° C) 100° D) 140°
13. The sum of five consecutive whole numbers is always
A) odd B) even C) prime D) composite
14. At 1 PM, there are 256 apples on a tree. Half of the apples on
the tree fall off each hour until only 1 apple is left on the tree.
At what time will there be exactly 2 apples on the tree?
A) 8 PM B) 9 PM
C) 10 PM D) 11 PM
15. Which of the following is a prime?
A) 91 B) 127 C) 789 D) 1661
16. What is the hundredths digit in the number 2.0152016 × 104?
A) 2 B) 0 C) 1 D) 6
17. The length of one leg of a right triangle is 30. The hypotenuse of this triangle is 34. What
is the area of this triangle?
A) 240 B) 272 C) 480 D) 510
18. What is the maximum number of points of intersection of one circle and three different
lines?
A) 9 B) 10 C) 11 D) 12
19. Which of the following is not the reciprocal of a whole number?
A) 0.125 B) 0.25 C) 0.5 D) 0.75
20. I have some $1, $5, $10, $20, $50, and $100 bills. If my bills have a total value of $999,
what is the minimum number of bills I have?
A) 17 B) 18 C) 19 D) 20
21. Jack and Jill are climbing stairs starting from the first floor at the same time and travelling
at constant speeds. When Jack reaches the 11th floor, Jill reaches the 6th floor. Which
floor will Jill be at when Jack reaches the 15th floor?
A) 7 B) 8 C) 9 D) 10
22. Set A = {10, 20, 30, 40, 50}. The numbers in set B are each 100 more than the
corresponding numbers in set A. What is the range of set B?
A) 40 B) 100 C) 500 D) 540
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23. The product of 12345679 and my number is a number with all its digits the same. My
number could be
A) 37 B) 60 C) 78 D) 81
24. The area of isosceles right triangle T is twice of that of square S. What is the ratio of the
length of a leg of T to the length of a side of S?
A) 1:4 B) 1:2 C) 2:1 D) 4:1
25. How many integers between 1 and 100 have exactly 5 divisors?
A) 0 B) 1 C) 2 D) 3
26. Math books are for sale! If you buy two books, you can get the third one for half price. If
each book costs $6, what is the least that you can pay for 2016 math books at this sale?
A) 9999 B) 10080 C) 11088 D) 12096
27. If p is a prime, what is the product of the positive divisors of p10?
A) p20 B) p40 C) p45 D) p55
28. The sum of the first ? positive integers is 2016.
A) 60 B) 61 C) 62 D) 63
29. 10 students in my class like mathematics, and 15 students in my class like English. If my
class has 21 students, how many students like both mathematics and English?
A) 4 B) 5 C) 6 D) 7
30. A regular polygon with each angle of measure 108° has ? sides.
A) 5 B) 6 C) 7 D) 8
31. How many of the first 100 positive integers are double a prime?
A) 15 B) 20 C) 25 D) 30
32. Cy can build a bridge in 3 years. Di can do the same task in 6 years. Working together, Cy
and Di can build a bridge in ? years.
A) 1 B) 1.5 C) 2 D) 2.5
33. I made a list of 2016 numbers. The first four numbers in order are 2, 0, 1, and 6. I
continued to write these same four numbers in the same order until I have written 2016
numbers. What is the last digit I wrote?
A) 2 B) 0 C) 1 D) 6
34. I am taking 10 tests this year. My average grade of the first 7 tests is 87. If my average
grade on all 10 tests is a 90, what should my average be on the last 3 tests?
A) 90 B) 93 C) 95 D) 97
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35. In the diagram at the right, any two adjacent points in the same column or
same row are the same distance apart. How many different squares may be
drawn whose vertices are 4 of the points in this diagram?
A) 12 B) 14 C) 18 D) 20
36. The sum of ten different natural numbers is 69. The difference between the biggest
number and smallest number is 10. What is the product of the biggest number and the
smallest number?
A) 20 B) 22 C) 24 D) 26
37.
2x9y1 is a five-digit number, and it is a perfect square. What is the value of x2 + 2xy +
y2?
A) 36 B) 49 C) 64 D) 81
38. The first two terms in a number sequence are 1 and 2. Starting from the 3rd term, each
term is the ones digit of the sum of its two preceding terms. What is the 2015th term?
A) 2 B) 3 C) 4 D) 5
39. m and n are two positive integers. Their greatest common divisor is greater than 1.
m3 = 371 – n. What is the value of m2 – n?
A) 19 B) 21 C) 23 D) 25
A40. The area of triangle ABC is 20, figure at the right, not drawn to scale.
E is the midpoint of AC. O is the midpoint of BE. A, O, and D are on
the same line, so are C, O, and F. What is the area of quadrilateral
EOBDOF?
FA)
20
B) 5 C) 4
10BDC3D)
3
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2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛七年级试卷答案
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1
A
11
A
21
B
31
A
2
C
12
D
22
A
32
C
3
B
13
D
23
D
33
D
4
D
14
A
24
C
34
D
5
C
15
B
25
C
35
D
6
C
16
C
26
B
36
C
7
D
17
A
27
D
37
B
8
B
18
A
28
D
38
A
9
A
19
D
29
A
39
B
10
D
20
A
30
A
40
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2016-2017年度美国“数学大联盟杯赛”(中国赛区)初赛
(七年级)
(初赛时间：2016年11月20日，考试时间90分钟，总分200分)
学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，
我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
如果您同意遵守以上协议请在装订线内签名
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. Of the ten digits, how many cannot be the units digit of the product of two prime
numbers?
A) 0 B) 1 C) 2 D) 3
2. Of the following times, at which is the smaller angle formed by the minute and hour hands
of a round clock greatest?
A) 2:00 B) 3:30 C) 9:00 D) 11:10
3. My printer can print 200 pages in 5 minutes. My friend’s printer can print 300 pages in 6
minutes. If we use both printers together at their respective rates, how many minutes will
it take to print 1800 pages?
A) 15 B) 20 C) 24 D) 30
4. The least common multiple of 18, 30, and ? is 180.
A) 10 B) 20 C) 40 D) 90
5. If the sides of a triangle have lengths that are consecutive integers, which of the following
CANNOT be the length of one of the sides?
A) 1 B) 3 C) 5 D) 7
6. My brother’s age is 2 more than 3 times my sister’s age. My brother’s age CANNOT be
divisible by
A) 4 B) 5 C) 7 D) 9
7. After I left home this morning I ran into a friend who gave me some money he owed me,
and the amount in my wallet increased by 60%. After that, I stopped and bought a new
video game, and the amount in my wallet decreased by 20%. At that point, the amount in
my wallet was what percent greater than it had been when I left home?
A) 12% B) 28% C) 32% D) 40%
8. The ratio of adult men to adult women to children at a play is 2:3:7. If there are 120 adults,
how many children are there?
A) 24 B) 140 C) 144 D) 168
9. How many distinct positive divisors does 720 have?
A) 15 B) 24 C) 28 D) 30
10. The sum of all the multiples of 3 between 100 and 200 is
A) 2017 B) 3300 C) 4950 D) 6660
11. The perimeter of a triangle with each sides of integer length is 90. The greatest possible
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difference between the lengths of two sides is
A) 42 B) 43 C) 86 D) 87
12. I stacked all my books on the floor. If the 15th book from the top of the stack was just
under the 15th book from the bottom of the stack, how many books were in the stack?
A) 27 B) 28 C) 29 D) 30
13. The ratio of students to teachers at my school is 187:5. If I assigned each teacher the same
number of students, there would be 12 students left over. How many teachers are at my
school?
A) 15 B) 18 C) 30 D) 33
14. How many odd numbers between 20 and 2000 are squares of integers?
A) 19 B) 20 C) 38 D) 39
15. If a room in the shape of a rectangular solid has dimensions of 6m by 5m by 4m, what is
the volume of the room in cubic centimeters?
A) 12 000 B) 1 200 000 C) 12 000 000 D) 120 000 000
16. Four identical pumps operating simultaneously at the same rate can fill an empty pool in
33 hours. If two more identical pumps were used in the same situation, how many fewer
hours would it take to fill the pool?
A) 22 B) 16 C) 11 D) 2
17. A company accepted job applications last year. Only 2/5 of the initial applicants were
interviewed, and only 5/6 of those who were interviewed were hired. 4/7 of the workers
that were hired haven’t been given a raise yet, but 60 have been. How many initial
applicants were there?
A) 120 B) 210 C) 360 D) 420
18. At my high school, 60% of the students play sports and 70% of the students play musical
instruments. What percent of the students who play sports also play musical instruments if
there are no students who don’t play sports and don’t play musical instruments?
A) 10 B) 30 C) 50 D) 60
19. The average of 5 integers is 0.2 greater than the least of the five integers. At most how
many of the integers can be odd?
A) 1 B) 2 C) 3 D) 4
20. What are the last two digits in the decimal expansion of 9999?
A) 01 B) 09 C) 91 D) 99
21. What is the ratio of the least common multiple of the first 130 positive integers to the least
common multiple of the first 125 positive integers?
A) 127:1 B) 254:1 C) 16 383:1 D) 32 766:1
22. Of 4000 boys and 1000 girls who applied to Harvard College, 30% of the boys and 60%
of the girls were accepted. Of 4000 girls and 1000 boys who applied to Princeton College,
10% of the girls and 20% of the boys were accepted. In all, what was the ratio of girls to
boys accepted?
A) 5:7 B) 5:12 C) 7:5 D) 12:5
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23. When written as a decimal, the sum of the digits of 10100
– 1050 – 1 is
A) 898 B) 899 C) 900 D) 901
24. What is the largest prime factor of the quotient 1/117! ÷ (1/121!), where n! is the product
of all the positive integers ≤ n? For example, 4! = 4 × 3 × 2 × 1.
A) 59 B) 117 C) 119 D) 121
25. Each letter in the English alphabet is assigned a different integer ≤ 26. What is the greatest
possible value of A + M + E + R + I + C + A?
A) 165 B) 166 C) 167 D) 182
26. How many integers n < 100 satisfy n < n3?
A) 98 B) 99 C) 100 D) 101
27. If last month, Taylor Slow performed at c concerts, where c is the number of values of n that
satisfy |n
– 8| + |n2
–
64| = 0, then c =
A) 1 B) 2 C) 4 D) 8
28. The number of perfect squares between 200 and 300 is ? more than the number of
perfect squares between 500 and 600?
A) 0 B) 1 C) 2 D) 3
29. If the length of a 60° arc of circle A is the same as the length of a 45° arc of circle B, what is
the ratio of the area of circle A to the area of circle B?
A) 3/4 B) 9/16 C) 4/3 D) 16/9
30. How many digits are in the decimal expansion of n10 if n = 102?
A) 20 B) 21 C) 100 D) 101
31. How many perfect squares are in the infinite sequence 4, 44, 444, . . . ?
A) 1 B) 2 C) 3 D) more than 3
32. Jodie made a list of the first 1000 positive integers. She then erased every number divisible
by 2. Next, she erased every number divisible by 3. Finally, she erased every number
divisible by 5. When she was finished, how many numbers were left on her list?
A) 133 B) 233 C) 266 D) 299
33. If the total number of positive integral divisors of n is 12, what is the greatest possible total
number of positive integral divisors of n2?
A) 23 B) 24 C) 33 D) 45
34. Seven flags of all different colors are placed in a circular display. If the white flag must be
next to the yellow one and the red flag must be next to the blue one, in how many different
orders can these seven flags be displayed?
A) 96 B) 120 C) 480 D) 960
35. Each morning the bagel seller buys his bagels at two cents each then
sets off to make his deliveries. He arrives at Tesla’s lab at midday and
sells his last bagel for one dollar and fifty cents.
“You must be making a fortune,” remarked Tesla.
“Not even close,” said the bagel seller miserably, “you are my one and
only customer.”
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On his way to Tesla’s lab, the bagel seller must travel through the territories of three
notorious street gangs. In each territory, he is forced to pay a tariff of half of the bagels he
is carrying, plus two more, to the gang leader.
How much profit does the bagel seller make after all?
A) $0.76 B) $0.78 C) $0.80 D) $0.82
36. You own a farm and have raised 25 racehorses. Each horse runs at a different but constant
pace. When the horses race they will always run at the same pace no matter how many
times they race. You are trying to find your three fastest horses. You do not have a clock of
any kind to time the horses, and you can only race five horses against each other at a time.
What is the minimum number of races you need to conduct in order to find your three
fastest racehorses?
A) 5 B) 6 C) 7 D) 8
37. Tom has constructed two prototypes for his “Death Ray”
tower. Tower A can fire a beam of energy five times in
five seconds. Tower B can fire ten times in ten seconds.
Beams are fired one at a time, and the intervals between
any two consecutive beams are constant. Assume it
takes Tower A t1 seconds to fire 12 beams, and it takes
Tower B t2 seconds to fire 12 beams. Which of the following is true?
A) t1 < t2 B) t1
= t2 C) t1 > t2 D) Non-deterministic
38. You are a prisoner in a strange land. You have been sentenced to death but are given one
chance to live. The king of the land has decided to let you play a simple game to
determine your fate:
You are presented with two clay jars, one containing 100 white stones, and one containing
100 black stones. You are allowed to redistribute these stones any way that you like, but
when you are finished all stones must be in the jars. After you have finished, both jars will
be shaken up, you will be blindfolded, and you will be presented one of the two jars at
random. You will pick one stone out the jar given to you. If the stone is white, your life
will be spared. If the stone is black, you will be executed immediately.
What is your best chance of survival?
A) 50% B) 65.97% C) 74.87% D) 84.77%
39. Your friend has a coin and asks you if you want to play a game: “I will flip this coin until
the number of heads flipped is equal to the number of tails flipped. Then I will give you a
dollar for each time I flipped the coin.”
What is the chance that you play this game with your friend once and he pays you exactly
eight dollars?
A) 1.5% B) 2.3% C) 3.1% D) 3.9%
40. You have in front of you a standard balance scale. What is the fewest number of weights
that you would need to be able to accurately weigh any object that weighs between one
and one hundred pounds (rounded up to the nearest pound), inclusive?
A) 5 B) 6 C) 7 D) 8
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2016-2017年度美国“数学大联盟杯赛”(中国赛区)初赛七年级试卷答案
题号
答案
题号
答案
题号
答案
题号
答案
1
A
11
A
21
B
31
A
2
C
12
B
22
A
32
C
3
B
13
C
23
B
33
D
4
B
14
B
24
A
34
A
5
A
15
D
25
C
35
B
6
D
16
C
26
A
36
C
7
B
17
D
27
A
37
C
8
D
18
B
28
B
38
C
9
D
19
D
29
B
39
D
10
C
20
D
30
B
40
A
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„„
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„„
„„
„„
„„)名„„签„„(„„名„„姓„„
„„
„题
„„
„„
„„
级„„年„„„„
„„
线答
„„
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„„
„„
„不
„„
„„
„„
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„„
校„„学„„„内在„„所订„
„„
„„
„„
„„
„„
„线
„„
„„
„„
„
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„„
„„
„
号„订„„证„„考装„„准„
„„
„„
„„装
„
„„
„„„
区„„„
„„„
„
„„
„„„
„
„„
市„„城„„„„„
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛
(七年级)
(初赛时间：2017年11月26日，考试时间90分钟，总分200分)
学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，
我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
请在装订线内签名表示你同意遵守以上规定。
考前注意事项：
1. 本试卷是七年级试卷，请确保和你的参赛年级一致；
2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；
3. 请确保你已经拿到以下材料：
本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、
草稿纸。考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、
及如何参加复赛的说明。其他材料均不能带走，请留在原地。
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. Drawing the diagonals of a rectangle creates exactly ? triangles.
A) 2 B) 4 C) 6 D) 8
2. The least possible average of 2017 different positive integers is
A) 1008 B) 1009 C) 2017 D) 2018
3. There were seven friends who decide that they would all dine together every evening if
they could sit in a different arrangement each time. They would use the same table, always
with seven chairs in the same spots. (Two arrangements are considered identical if and
only if everyone of the seven friends sits on the same chair.) How many dinners could the
seven of them eat before exhausting all possible arrangements?
A) 2520 B) 5040
C) 720 D) 1440
4. Increasing a number by 20% is the same as multiplying it by
A) 20% B) 80% C) 120% D) 200%
5. $100 in nickels is ? more coins than $100 in dimes.
A) 100 B) 200 C) 1000 D) 2000
6. What is the range of any 2018 consecutive integers?
A) 1009 B) 2017 C) 2018 D) 2019
7. Written as a decimal,
0 has exactly ? non-zero digits to the right of the
decimal point.
A) 2 B) 3 C) 6 D) 7
第1页，共4页
8. Each choir member sang 1 song alone and 2 songs with the entire choir.
If 24 songs were sung in all, the choir must have ? members.
A) 8 B) 11 C) 12 D) 22
9. A multiple of 2017 is divided by a multiple of 2018. What is the least
remainder possible?
A) 0 B) 1 C) 2017 D) 2018
10. My armful of identical gumballs weighs 4% less since I dropped one
gumball. How many gumballs are in my arms now?
A) 23 B) 24 C) 25 D) 26
11. The digits of the least 2-digit integer that is a perfect square and a
perfect cube have the sum
A) 7 B) 8 C) 9 D) 10
12. The year in which my grandfather was born, a perfect square, when subtracted from the
year in which my daughter was born, another perfect square, gives my grandfather’s age
when he died. If my grandfather had lived, I would have been exactly half his age in 1943.
How old was I in 1943?
A) 42 B) 44 C) 46 D) None of the above
13. A man had two horses. He sold one of them on Tuesday for $198 and made a profit of ten
percent. On Wednesday, he sold the other one for $198 and took a loss of ten percent.
Tallying up his two deals, did he show a net profit or a loss?
A) Even B) A net profit of $6
C) A net profit of $4 D) A net loss of $4
14. The sum of the lengths of all the edges of a cube is 144 cm. What is the area of one face of
the cube?
A) 144 cm2 B) 196 cm2 C) 256 cm2 D) 324 cm2
15. The time 815 minutes after 8:15 P.M. is
A) 3:15 A.M. B) 9:50 A.M.
C) 3:15 P.M. D) 9:50 P.M.
16. The number 180 has ? more divisors than the number 120 has.
A) 0 B) 2 C) 30 D) 60
17. The 8 houses on my street have consecutive integer addresses that add up to 1500. The
address with the greatest numerical value is
A) 184 B) 187 C) 188 D) 191
18. Which of these fractions is the sum of an integer and its reciprocal?
A)
73 B)
89103 C)
3 D)
3
第2页，共4页
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19. The mixed number
214 is equivalent to many improper fractions that have integer
numerators and denominators. The numerator of such a fraction could be any of the
following except
A) 24 B) 27 C) 36 D) 45
20. At my store, $1 of every $5 in sales is profit. If I split 10%
of all profits equally among 10 people, each gets ? % of
the total sales.
A) 0.2 B) 2 C) 5 D) 20
21. If Mary is twice as old as Ann was when Mary was as old as Ann is now, and Mary is 32,
how old is Ann?
A) 20 B) 24 C) 32 D) None of the above
22. Of the following, which expression has the least value?
A)
31004
B)
31004
C)
34 D)
34100
23. I randomly select a positive integer less than 100. The probability that it is the product of
exactly 3 different primes is
A)
199 B)
499 C)
599 D)
899
24. If the average of 3 consecutive ticket numbers is odd, then the sum
of the least and greatest ticket numbers could be
A) 18 B) 20 C) 24 D) 28
25. Eve counted to 460
by consecutive powers of 2, starting with 21, 22,
23, . . . . How many powers of 2 did Eve count?
A) 30 B) 120 C) 240 D) 3600
26. How many even integers between 1 and 1 000 000 have digits that are all primes?
A) 1365 B) 3906 C) 5400 D) 19 530
27. If 6 identical machines can fill 80 bottles of soda in 12 seconds, how many seconds would
it take 36 of the same machines to fill 240 bottles of soda?
A) 6 B) 12 C) 18 D) 24
28. Of my 100 favorite released songs , 42% were released after the year
2015 and 76% were released before the year 2017. What percent of my
favorite songs were released in 2016?
A) 18% B) 24% C) 34% D) 58%
29. (The number of positive even integers less than 106 that are perfect
squares) : (the number of positive odd integers less than 106 that are
perfect squares) =
A) 1:1 B) 2:1 C) 499:500 D) 999:1000
第3页，共4页
30. Of the following, which is a multiple of 4?
A) 20172018 + 1 B) 20172018
+ 3 C) 20172018 + 5 D) 20182017 + 1
31. If the sum of the measures of two angles of a parallelogram is 108 degrees, the sum of the
measures of three of its angles could be
A) 72 degrees B) 162 degrees C) 234 degrees D) 252 degrees
32. Mr. Einstein hates repetition. He eats at a restaurant near his house once everyday. On the
menu of this restaurant, there are 11 appetizers, 26 entrees, and 12 kinds of desserts. In
addition, there are 12 wine selections offered. Mr. Einstein insists that everyday he eats a
different meal combination that has never been served to him before. Each meal
combination consists of one item from each of the four categories. For how many years
can Mr. Einstein eat at this restaurant?
A) 5 B) 20 C) 25 D) Over 100
33. In the complete expansion of (x + 1)4, what is the sum of the coefficients of the odd
powers of x?
A) 4 B) 6 C) 8 D) 10
34. A man starts with $10000 and increases his wealth by 50 percent every three years. How
much will he have in 12 years?
A) $30000 B) $50625 C) $70000 D) None of the above
35. What is the sum of all positive two-digit integers which are divisible by both the sum and
product of their digits?
A) 36 B) 54 C) 72 D) None of the above
36. If n is the smallest positive integer such that 99n is the cube of an integer, and d is the sum
of the digits of n, then d is
A) 27 B) 18 C) 12 D) 9
37. The area of my rectangle is 480. If my rectangle\'s length is 14 greater than its width, then
its perimeter is
A) 88 B) 92 C) 116 D) 172
38. If
4x12, which of the following must always be true?
A) x > 3
B)
x11113 C)
x3 D)
x3
39. If x + y = a and xy = b, then what is the value of x3 + y3 in terms of a and b?
A) a3 + 3ab B) a3 – 3ab C) a3 + b3 D) a3 – b3
40. If I subtract the square of one integer from the square of another integer, then the
difference could be
A) 386 B) 558 C) 768 D) 970
第4页，共4页
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛七年级试卷答案
题号
答案
题号
答案
题号
答案
题号
答案
1
D
11
D
21
B
31
C
2
B
12
D
22
D
32
D
3
B
13
D
23
C
33
C
4
C
14
A
24
A
34
B
5
C
15
B
25
B
35
C
6
B
16
B
26
A
36
C
7
A
17
D
27
A
37
B
8
D
18
D
28
A
38
C
9
A
19
A
29
C
39
B
10
B
20
A
30
B
40
C
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2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段
(七年级)
(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)
学生诚信协议：答题期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，
我确定我所填写的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
请在装订线内签名表示你同意遵守以上规定。
考前注意事项：
1. 本试卷是七年级试卷，请确保和你的参赛年级一致；
2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；
3. 请确保你已经拿到以下材料：
本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、
草稿纸。试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。
4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一
半题目的学生就应该受到表扬和鼓励。
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. (4 × 6 × 8 × 10) ÷ (6 × 8 × 10) =
A) 3 B) 4 C) 12 D) 3 × 6 × 8 × 10
2. (2 ÷ 3) rounded to the nearest hundredth is
A) 0.33 B) 0.66 C) 0.67 D) 0.70
3. Baby Amy is one day older than Baby Barry. The product of their
ages measured in days could be
A) 33 B) 132 C) 245 D) 246
4. (The largest even divisor of 200) ÷ (the largest odd divisor of 200) =
A) 4 B) 8 C) 20 D) 200
5. An equilateral triangle with integer side-lengths has a perimeter that is numerically equal
to the area of a square. Which of the following could be the length of a side of the square?
A) 12 B) 10 C) 8 D) 4
6. I have only nickels, dimes, and quarters to pay for my dinner, which costs $12.60. The
smallest number of coins I can use to pay is
A) 51 B) 52 C) 54 D) 55
7. The smallest prime factor of 2019 is
A) 1 B) 3 C) 19 D) 673
8. The product of four consecutive integers must be divisible by each of the following except
A) 4 B) 6 C) 10 D) 12
第1页，共4页
9. There are ? hours in 4 weeks.
A) 48 B) 96 C) 336 D) 672
10. If I divide my favorite number by its reciprocal, the quotient is 10 times as large as my
favorite number. My favorite number is
A)
11110 B)
5 C)
2
D) 10
11. The height of the smoke from my barbecue is 100 000 cm, which is the
same as ? km.
A) 1 B) 10
C) 100 D) 1000
12. If the degree measures of the angles of a triangle are in a 4:5:6 ratio, what
is the difference between the measures of the largest and the smallest angles?
A) 12° B) 24° C) 30° D) 36°
13. The population of a town started at 1000, then went up 10%, then down 20%, then back
up 10%. The population of the town ended at
A) 968 B) 972 C) 1000 D) 1024
14. In my orchard, there are 60 more apples than oranges, and 5
times as many apples as oranges. How many apples are there?
A) 50 B) 75 C) 100 D) 125
15. A polygon in which every pair of angles is supplementary must be a
A) triangle B) square
C) rectangle D) hexagon
16. Which of the following is smallest in value?
A) 2600 B) 3500 C) 4400 D) 5300
17. (2100 × 450) ÷ 2 =
A) 275 B) 2100 C) 2149 D) 2199
18. What is the remainder when 3333 is divided by 10?
A) 1 B) 3 C) 7 D) 9
19. On a series of tests, Gus got 100 once, 90 twice, and 80 five times. What was his average
score for all of the tests?
A) 80 B) 85 C) 90 D) 92
20. The product of the thousands and tenths digits of 1234.5678 is
A) 5 B) 10 C) 35 D) 40
第2页，共4页
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21. The probability of heads then tails then heads on 3 tosses of a coin is
A) 0.125 B) 0.25 C) 0.375 D) 0.5
22. On January 1 last year, Rui got a jar of jellybeans. On each day he ate the same number of
jellybeans. He counted 560 on January 31 before eating any and he counted 380 on March
17 before eating any. There were ? jellybeans in the jar when Rui got it.
A) 600 B) 650
C) 680 D) 740
23. Jake used 120 boxes of tissues in 3 days! There are 144 tissues per box.
That’s ? tissues per minute!
A) 2 B) 3 C) 4 D) 5
24. The number 5184 has ? positive odd divisors.
A) 1 B) 2 C) 4 D) 5
25. The sum of 5 consecutive even integers could be
A) 120 B) 125 C) 164 D) 212
26. Jacques, who paints only smiley faces, signs and numbers each of his
paintings. If he started with Smiley #1 and has painted through Smiley
#111, how many times has he used the digit 1 in his numbering?
A) 12 B) 22 C) 24 D) 36
27. How many whole numbers have squares that are between 2 and 200?
A) 12 B) 13 C) 24 D) 26
28. A baker cuts circular cookies out of a flat rectangle of cookie dough. If the rectangle is
2 m by 1 m, and the cookies have radius 10 cm, at most how many cookies can the baker
cut from the sheet of dough?
A) 50 B) 63 C) 64 D) 200
29. 0.02% of 20% of ? = 200% of 2000
A) 1000 B) 100 000
C) 1 000 000 D) 100 000 000
30. A miner combines 1200 kg of ore that is on average 3% gold with 2400 kg of ore that is
on average 6% gold. If the 100 kg containing the most gold of the 3600 kg is 40% gold,
the remaining ore will be ? gold.
A) 2% B) 3% C) 4% D) 5%
31. Including face diagonals, the total number of diagonals of a cube is
A) 12 B) 14 C) 16 D) 24
第3页，共4页
32. How many odd 3-digit integers greater than 500 are composed of 3 different non-zero
digits?
A) 154 B) 175 C) 185 D) 200
33. If I square all whole-number factors of 36 and multiply the resulting numbers, the product
will be equal to
A) 362 B) 364 C) 368 D) 369
34. When the four members of the Beaverton family carry
a log, each has a 0.02 probability of tripping, and each
probability is independent of the others. What is the
probability that they will carry the log without any of them tripping?
A) 1 – (0.02)4 B) (0.98)4
C) (0.02)4 D) 1 – (0.98)4
35. What is the largest prime factor of the product of all even numbers from 2 through 200?
A) 47 B) 97 C) 199 D) 2019
36. What is the sum of the solutions to |10 – 4x| = 5?
A) 1.25 B) 3.75 C) 5 D) 10
37. If 2x × 42x × 83x = 2y, then y =
A) 2x3 B) 6x C) 6x3 D) 14x
38. Each time Alan falls asleep, he sleeps for exactly 8m
minutes and then is awake for the next 4m minutes.
If he falls asleep for the 1st time at 11 P.M. and wakes
from his 6th time asleep at 4:06 A.M., then m =
A) 4.25 B) 4.5
C) 5.125 D) 6.375
39. If x is a positive integer, the remainder when 2018x is divided by 10 could NOT be
A) 4 B) 6 C) 8 D) 0
40. If a + b = 8 and
1a1b4, then ab =
A) 2 B) 6 C) 12 D) 32
第4页，共4页
2018-2019年度美国“大联盟”(MathLeague)思维探索活动第一阶段七年级试卷答案题号答案题号答案题号答案题号答案1B11A21A31C2C12B22C32A3B13A23C33D4B14B24D34B5A15C25A35B6A16A26D36C7B17D27B37D8C18B28A38B9D19B29D39D10D20A30C40A
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