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# 美国数学大联盟杯赛试题

1. Ira is a player. There are 9 of Ira in line, and 20

are in the line? behind him. In all, how many

A) 28

B) 29

C) 30

D) 31

C There are 9 players ahead of Ira in line, and 20 behind him.

players in the line. Ira, there are 9 + 20 + 1 = 30

A) 28

B) 29

C) 30

D) 31

2. (2 × 3 × 4 × 5) ÷ 12 =

A) 6

B) 8

C) 10

D) 12 C

(2 × 12 × 5) ÷ 12 = 2 × 5 = 10.

A) 6

B) 8

C) 10

D) 12

3. Rachel to cut a single 30 m long piece of

are 4 m long. into smaller pieces. She can cut at most ? pieces A) 6 B) 7

C) 8

D) 9

B

Since 30 m ÷ 4 m has a

7 pieces that are 4 m long.

A) 6

B) 7

C) 8

D) 9

4. Sam 4 shells each minute at the beach. How shells does she find in an hour?

A)15

B)20

C)64

D)240

D

Sam hour, she A) 15

B) 20

C) 64

D) 240 4 each minute at the beach. 4 × 60 = 240 in an hour. there are 60 minutes in an 答案: A

5. (32 ÷ 4) + (48 ÷ 6) + (64 ÷ 8) = 8 × ?

A) 3

B) 6

C) 8

D) 12

A

(32 ÷ 4) + (48 ÷ 6) + (64 ÷ 8) = 8 + 8 + 8 = 8 × 3.

A) 3

B) 6

C) 8

D) 12

6. 9 × 9 is

A) 999 ÷ 9

B) 90 + 9

C) 90 ? 9

D) 99

C to

9 × 9 = 81 = 90 ? 9.

A) 999 ÷ 9

B) 90 + 9

C) 90 ? 9

D) 99

7. Tom, Dick, and go to the movies together. Tom pays for all 3

ticket costs the with a \$50 bill. If he gets \$18.50 in change and

same amount, is the cost of ticket?

A) \$10.50

B) \$11.50

C) \$12.50 D) \$18.50 A Tom, Dick, and go to the movies together. Tom pays for all 3 \$50.00 ? \$18.50 with a \$50 bill. If he gets \$18.50 in change, the 3 = \$31.50. The

A) \$10.50

B) \$11.50

C) \$12.50

D) \$18.50

8. Of the

A) 1050

B) 2024

C) 3058

D) 4022

A

1 + 0 + 5 + 0 is

A) 1050

B) 2024

C) 3058

D) 4022

9. If 4 of Tom’s can paint his fence in 12 hours, and all of his

hours would it take for 8 of his work at the same rate, then how

to paint his fence?

A) 4

B) 6

C) 8

D) 24

B When 4 of Tom’s twice as many workers, it

A) 4

B) 6

C) 8

D) 24 his fence, it takes 12 hours to

take half as long, 6 hours. it. With

10. 2:50 P.M. is ? minutes

A) 25

B) 45 3:15 P.M.

C) 65 D) 75 A It’s 10 mins. to 3 P.M. and 15 A) 25

B) 45

C) 65

D) 75

11. The digit of the product 2009 × 2008 × 2007 × 2006 × 2005 × 2004 × 2003 × 2002 is

A) 8

B) 6

C) 4

D) 0

D

The of 2004 and 2005 has a ones digit of 0. Therefore, the entire

has a ones digit of 0.

A) 8

B) 6

C) 4

D) 0

12. The

A) \$7.01

B) \$7.16

C) \$7.51

D) \$8.11

C

The value of 25 quarters, 10 dimes, 5 nickels, and 1 penny is is (25 × 25￠) + (10 × 10￠) + (5 × 5￠) + (1 × 1￠) = (625+ 100 + 25 + 1)￠.

A) \$7.01

B) \$7.16

C) \$7.51

D) \$8.11

13. The

A) 298

B) 296

C) 294 D) 292 B multiple of 8 that is less than 300 is

Since 300 ÷ 8 has a

A) 298

B) 296

C) 294

D) 292

14. Of the

A) 7 × 10

B) 6 × 12

C) 5 × 14

D) 4 × 16

D products, which is 3 less than (2010 ÷ 30)?

2010 ÷ 30 = 67, 67 ? 3 = 64, and 64 = 4 × 16.

A) 7 × 10

B) 6 × 12

C) 5 × 14

D) 4 × 16

15. Rose 180 dentists whether she should chew gum. If 4

out of 5 of them say she should, how many do NOT say she should?

A) 9

B) 36

C) 72

D) 144

B If 4 out of 5 1 out of 5 do not sugarless gum, then it. Since 180

÷

5 =

each, and 1

it. 36, there are 36 of 5 dentist from group does not

A) 9

B) 36

C) 72

D) 144

16. 20

A) 222

B) 2022

C) 2040

D) 2220 D + 20 tens + 20 ones =

20 × 100 + 20 × 10 + 20 = 2000 + 200 + 20 = 2220.

A) 222

B) 2022

C) 2040

D) 2220

17. When 161 616 169 is

A) 1

B) 3

C) 5 D) 7 A

161 616 169 ÷ 8 = 20 202 021

A) 1

B) 3

C) 5

D) 7

18. Each of the 300 5th at Einstein School got a score of 10 on

School scored a 6 on contest. Each of the 300 students at

this same contest.

A) 10 was the average score of all 600 students?

B) 8

C) 7 D) 6 B Since the number of students took the contest at school, the score is the of 10 and 6. The of 10 and 6 is (10 + 6) ÷ 2 = 16 ÷ 2 = 8.

A) 10

B) 8

C) 7

D) 6

19. The 7 hours before 7 P.M. is the same as the 7 hours after

A) 5 A.M.

B) 7 A.M.

C) 2 P.M.

D) 7 P.M.

A

7 before 7 P.M. is noon, and 7

A) 5 A.M.

B) 7 A.M.

C) 2 P.M.

D) 7 P.M.

20. If 1

A) 16

B) 24

C) 48

D) 60

D

2 × 2

× 10 blaps.

A) 16

B) 24

C) 48

D) 60 = 4 blurps, and 2 blurps = 5 blaps, then 6 = ? blaps. = 2 × 5 blaps, so 1 blorp = 10 blaps and 6 × 1 = 6

21. Gavin is a

than 3 and Hal is his owner. Hal’s age is 7 years greater between Gavin’s age. If Gavin is 11, what is the

Gavin’s age and Hal’s age?

A) 15

B) 18

C) 29

D) 51

C Gavin is a

and Hal is his owner. Hal’s age is 7 years greater than 3

Gavin’s age. If Gavin is 11, then Hal is 3 × 11 + 7 = 40. The

between their ages is 40 ? 11 = 29.

A) 15

B) 18

C) 29

D) 51

22. The sum of two

A) 1

B) 9

C) 2009

D) 2010

A

The whole numbers is 4019. What is the between those two numbers? are each about half of 4019; are 2009 and 2010. The

whole is always 1. difference between any pair of

A) 1

B) 9

C) 2009

D) 2010

23. Of the

A)

B) polygons, all have the same number of except a

C)

D)

A A A) B) C) D)

24. Alice and Bob write 20 letters.

A) 18

B) 16

C) 15

D) 12 write 10 letters. Charlie, Dan, and Evelyn people write? is the average number of letters these

B

Together, 5 = 16.

A) 18 and Bob 20 letters. Together, Charlie, Dan, and Evelyn number of letters these five people is 80 ÷ 60 letters. The

B) 16

C) 15 D) 12

25. There are

A) 0 and 6

B) 6 and 12

C) 12 and 18

D) 18 and 24

A 3 prime numbers between

From 0 to 6, 2, 3, and 5 are

A) 0 and 6

B) 6 and 12

C) 12 and 18

D) 18 and 24

26. Jesse and each had \$10 to spend on school supplies. spent his \$10 on pens that cost \$0.50 each. spent his \$10 on pencils that cost \$0.20 each. The between the number of pencils that bought and the number of pens that bought is

A) 10

B) 25

C) 30

D) 50 C Jesse and each had \$10 to spend on school supplies. spent his \$10 on pens that cost \$0.50 each. spent his \$10 on pencils that cost \$0.20 each. bought \$10

÷

\$0.50 = 20 pens and

is 50 ? 20 = 30. bought \$10 ÷ \$0.20 = 50 pencils. The

A) 10

B) 25

C) 30

D) 50

27. As shown,

the area of

A) 10

B) 12

C) 20

D) 24 R? R of 6 squares of perimeter 8. is

D

Each

24.

A) 10

B) 12

C) 20

D) 24 of a small square is 8 ÷ 4 = 2. The area of R is 6 × 4 =

28. I 123 by 4 and got the quotient and the remainder. This quotient by this remainder equals

A) 5

B) 10

C) 15 D) 23 B When you 123 by 4, the quotient is 30 and the remainder is 3. Now 30 by 3 to get a quotient of 10. A) 5 B) 10

C) 15

D) 23

29. Of the numbers less than ten thousand, how many contain of the digits 1, 2, 3, and 4?

A) 6

B) 12

C) 18

D) 24

D

The beginning with 1 are 1234, 1243, 1324, 1342, 1423, and 1432. There are 6 beginning with 2 or 3 or 4.

A) 6

B) 12

C) 18

D) 24

30. A of paper four 5-digit written on it got wet. The

middle digit has been numbers’ middle digits now cannot be read.

replaced

A) 24■58 a ■. of the is divisible by 4?

B) 53■49

C) 25■74

D) 67■92

D Any of 100 is divisible by 4. If the 2-digit formed by the

2 digits of each is divisible by 4, then so is the

divisible by 4. number. Since 92 is divisible by 4, 67■92 is

A) 24■58

B) 53■49

C) 25■74

D) 67■92