Math League 8th 2021真题

1. 222 x 222 x 222 = 111 x 111 x 111 x  ?  

A) 2    B) 2 x 3     C) 222     D) 23

2. What is the hundredths digit of the product 123456789 x 0.00001?

A) 3   B) 4    C) 5    D) 6

3. A cup that holds 2 of tea can hold  ?  ml of tea.

A) 20    B) 200    C) 2000    D) 20 000

4. The sum of the digits of the greatest 4-digit integer that contains exactly 3 different digits is

A) 30    B) 31    C) 32    D) 33

5. How many positive integers less than 100 are not divisible by 3?

A) 33    B) 34    C) 66     D) 67

6. Jan hiked half of a 36-km long trail in 3 hrs. Her average speed was

A) 6 km/hr.    B) 9 km/hr.    C) 12 km/hr.     D) 18 km/hr.

7. How many multiples of 8 are factors of 82?

A) 3     B) 4     C) 6     D) 8

8. The greatest 3-digit perfect square is  ?  more than the greatest

2-digit perfect square.

A) 870     B) 880     C) 890     D) 900

9. 10% of 100 is 10 less than 10% of

A) 20     B) 110    C) 120     D) 200

10. I wrote consecutive multiples of 2 in increasing order, starting with 2. What was the 10th digit I wrote?

A) 1     B) 2    C) 3     D) 4

11. Today Al bought 36 hats and now has triple the

number of hats he had yesterday. If tomorrow Al

buys triple the number of hats he has today, how

many hats will Al have after tomorrow's purchase?

A) 108   B) 144    C) 162    D) 216

12. The sum of 5 integers is divisible by 20. The average must be divisible by

A) 4    B) 5     C) 20     D) 25

13. Ed is late to work 5 days a month. If he works every day in April,

the probability Ed gets to work on time on a given day in April is

A)     B)     C)     D) 

14. Eight friends split 6 identical pizzas evenly. If

each friend got only whole slices, what was the

lowest possible number of slices in each pizza?

A) 2    B) 3    C) 4    D) 6

15. The reciprocal of 1.25 is

A) 0.125    B) 0.14    C) 0.4    D) 0.8

16. If the difference between 2 prime integers is prime, what is the least possible sum of these integers?

A) 5    B) 7     C) 8    D) 9

17. If the degree measures of the 3 angles of a triangle are consecutive integers, what is the sum of the measures of the 2 smallest angles?

A) 118°    B) 119°    C) 120°    D) 121°

18. May painted 6 pots in 2 days working alone. Elsa and May together painted 10 more pots over the next 3 days. Each paints at a constant rate. How many days would it take Elsa to paint 16 pots by herself?

A) 12    B) 24    C) 36     D) 48

19. Exactly 3 diagonals can be drawn from each vertex of a regular ?.

A) octagon    B) parallelogram    C) hexagon    D) pentagon

20. The difference between the squares of 2 consecutive integers is 25. What is the sum of these squares?

A) 221    B) 265    C) 313    D) 365

21. How many different primes are factors of the product of the first 9

positive integers?

A) 4    B) 5    C) 9     D) 13

22. A circle's diameter is what fraction of the circle's circumference?

A)     B)     C)      D)

23. How many of the 24 smallest integers greater than 26 are divisible by at least one of the 24 smallest integers greater than 1?

A) 17    B) 18    C) 19     D) 20

24. If the length and width of a painter's canvas are in

the ratio 3:2, the ratio of its perimeter to its width is

A) 3:2    B) 5:2    C) 5:1     D) 9:4

25. What is the least possible value of a multiple of 63 that is also a multiple of 83?

A) 2 x 63    B) 23 x 63    C) 2 + 63    D) 26 x 63

26. I have 25 nickels and 15 dimes to divide into 2 or

more stacks of equal total value. What is the least

number of stacks I can make if I use all 40 coins?

A) 3    B) 4    C) 5    D) 10

27. For how many 2-digit positive integers less than 50 is it true that both digits are factors of the integer?

A) 9    B) 13    C) 17    D) 18

28. The sum of 22021 and 22020 has the same value as

A) 2 x 22020   B) 3 x 22020    C) 4 x 22020    D) 22020 x 22020

29. What is the ones digit of 99 + 910 + 911 + 912 + 913 + 914 + 915 + 916 + 917?

A) 9    B) 7    C) 1     D) 49

30. Aida has 4 letter tiles: 2 As, 1 D, and 1 I. If 

Aida chooses the 4 tiles one at a time with-

out looking, what is the probability she chooses

them in the order A-I-D-A?

A)     B)   C)     D)

31. Each of 200 runners ran nonstop for 45 seconds. After the 1st runner, each runner began to run when the previous one had run for

15 seconds. How much time elapsed between the time the 1st runner stopped running and the time the last runner stopped running?

A) 2985 sec.   B) 5970 sec.  C) 8940 sec.  D) 8955 sec.

32. For 3 years in a row on Dec. 31, interest of 10% on all the money in my account was added to the account. If I began on Jan. 1 with

$10 000 and never withdrew, I earned  ?  interest total in 3 years.

A) $3000    B) $3100    C) $3310     D) $3641

33. If 21100 has 1012 positive divisors, how many does 25 x 21100 have?

A) 2 x 1012    B) 3 x 1012   C) 5 x 1012   D) 25 x 1012