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Math3 Olympiad

Total questions: 60

Worksheet time: 5hrs 52mins

Name
Class
Date
1.

Students are lining up for the flag ceremony. If the ratio of the students in front of John to the students at his back is 3:1, how many students are there on the line if the number of students behind him is 20?

(a)  

2.

Mum gave 20 apples to John and Marsha. If Marsha’s number of apples is 3 times the number of John, how many apples does Marsha have?

(a)  

3.

Refer to the following sequence below.

1 3 3 9 27 A B

What is the value of B – A?

(a)  

4.

Find the value of 3 x 5 x 7 x 9.

(a)  

5.

Elise and Tommy have 14 marbles altogether. If Samantha combines her candies to Elise’s and Tommy’s, then divide it to the three of them equally, they will have 8 candies each. How many candies does Samantha have?

(a)  

6.

It takes 2 hours for a carabao to plow a field with an area of 20m x 20m. How many hours would it take for the carabao to plow a field with an area of 100m x 100m?

(a)  

7.

A 3-digit number was divided by 4 and got a remainder of 2. What is the largest possible value for this number?

(a)  

8.

Find the value of 1122 + 2233 + 3344 + 4455.

(a)  

9.

How many 2-digit numbers between 40 and 100 contains odd digits only?

(a)  

10.

Find the value of 304 + 257 + 696 + 743.

(a)  

11.

Today is a Saturday. What day of the week will 104 days after tomorrow be?

(a)  

12.

What is the sum of all even numbers less than 50 that are divisible by 4?

(a)  

13.

It requires 4 minutes to cut a piece of woold into 5 sections. If the time required to cut into each section is the same, how many minutes are required to cut it into 8 sections?

(a)  

14.

If “MATH” is 13012008, what is “VTAMPS”?

(a)  

15.

What is the smallest 3-digit number that can be divided by 3, 7, and 2?

(a)  

16.

How many 2-digit numbers are there between 67 and 104?

(a)  

17.

There are 11 chickens more than cows in the farm. If there are 21 chickens, what is the total number of legs in the farm?

(a)  

18.

Find the value of 18 x 3 + 12 x 6 + 24.

(a)  

19.

Calculate the square of the sum of 1-digit numbers A and B if

8 + 8 + 8 + 8 = A x B

(a)  

20.

Given aⴲb = (2a + 2b) – (a – b) x 10, find the value of 15ⴲ10.

(a)  

21.

Numbers are drawn from 20 integers 1 to 20. At least how many draws must be done to make sure that the draw is greater than 5?

(a)  

22.

What is 10 x 9 – 9 x 8 + 8 x 7 – 7 x 6 + 6 x 5 – 5 x 4 + 4 x 3 – 3 x 2 + 2 x 1?

(a)  

23.

Find the smallest 3-digit number that is divisible by both 3 and 7.

(a)  

24.

The sum of 5 consecutive even numbers is 520. What is the largest number minus the smallest?

(a)  

25.

What are the chances of getting a 5 or a 6 from a deck of cards? Answer in simplest form.

(a)  

26.

4 different points are placed on the same line labeled A, B, C, D.

AB = 4, BC = 6, BD = 10. What will be the product of AC and CD?

(a)  

27.

How many numbers between 50 and 99 are there such that when we add its digits, we will get a sum of at least 14?

(a)  

28.

X and Y are numbers where X < 40 < Y. What is the smallest possible product of X and Y if both of them should be divisible by 2 and 3?

(a)  

29.

Sherry tossed a die and 2 coins. How many possible combinations of outcomes are there?

(a)  

30.

How many prime numbers are there from 1 to 50 such that the sum of the digits is greater than 7?

(a)  

31.

According to the pattern below, what is the number in the blank?

2, 5, 9, 14, 20, 27, (a)  

32.

If August 17 is a Friday, which day of the week was June 12 of the same year?

(a)  

33.

A track is 800 meters long. Now we plant a tree every 40 meters. How many trees can be planted starting from the 0-meter line?

(a)  

34.

According to the pattern, what is the missing number?

(a)  

35.

Fill the missing blank with the correct answer.

(a)  

36.

According to the pattern below, how many ‘*’ are there in the 7th figure?

(a)  

37.

Find the value of 115 + 347 + 562 + 385 + 153 + 38.

(a)  

38.

Find the value of 360 ÷ 3 + 360 ÷ 4 + 360 ÷ 5 + 360 ÷ 6.

(a)  

39.

Fill the blank with the correct number to make the equation below correct.

(32 ÷ (a)   ) + 22 × 2 = 48

40.

Find the value of 57 × 14 + 74 × 14 – 31 × 14.

(a)  

41.

Find the value of 11 ÷ 8 + 45 ÷ 8 + 48 ÷ 16.

(a)  

42.

Find the result of 36 + 40 + 44 + 48 + 52 + 56 + … + 120.

(a)  

43.

Define the operation symbol a∞b = a × 5 + b × 6 – a × b. Find the value of 5 ∞ 6.

(a)  

44.

Fill in the lines with × and + to make the equation below correct.

4___5___7___8 = 47

(a)  

45.

The numbers below follow an arithmetic sequence. Find the sum of the 16th and 21st terms.

15, 22, 29, …

(a)  

46.

What is the difference between the largest and the smallest 3-digit multiple of 27?

(a)  

47.

Five consecutive even numbers have a sum of 250. Find the product of the smallest and the biggest numbers among these numbers.

(a)  

48.

What is 11 less than the quotient of the largest 3-digit number and the second smallest prime number?

(a)  

49.

How many squares are there in the figure below?

(a)  

50.

At least how many squares are there in the figure below if viewing from the top?

(a)  

51.

A pyramid has 38 faces, how many edges does this pyramid have?

(a)  

52.

A square who side-length is 28 is cut into 49 identical smaller squares. Determine the perimeter of one small square.

(a)  

53.

How many squares are there in the figure below?

(a)  

54.

How many rectangles from the figure below contains the symbol ‘*’?

(a)  

55.

How many 3-digit numbers are there less than 400 that has no repeating digits?

(a)  

56.

After Amy gives 11 apples to James and took 4 from Christine, they all have the same number of apples. What is the difference between the number of apples of Amy and Christine originally

(a)  

57.

Numbers are drawn from integers 11 to 29. At least how many draws should be made to make sure that you have 2 numbers whose product is divisible by 3?

(a)  

58.

Choose 3-digits from 2, 5, 6, 7, and 9. How many 3-digit numbers that are divisible by 2 can be formed? Repetition of digits is allowed.

(a)  

59.

34 students are wearing either S, M, or L size of uniforms. At least how many of them are wearing the same size?

(a)  

60.

The sum of two numbers is 29. What is their largest possible product?

(a)