Math Olympiad Grade 6

Multiple Choice

1. 1. How many squares are there in the 9^th figure?

• 29

• 28

• 27

• 26

• 25

Multiple Choice

2. 2. There are 8 points on the circumference of a circle. 

3. How many pentagons can be formed by using any five points as their vertices?

• 48

• 50

• 56

• 68

• None of them

Multiple Choice

3. 3. The product of three prime numbers is 627. What is the sum of these three prime numbers?

• 11

• 19

• 29

• 23

• 33

Multiple Choice

4. 4. How many pairs of twin prime numbers are there between 1 and 70?

• 5

• 6

• 7

• 8

• 9

Multiple Select

5. 5.      Only 2 out of the 4 figures below will form a 3 by 3 cube as shown on the right.

6. Which 2 figures can form a 3 by 3 cube?

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6. 6. Evaluate: 10 × 234 + 10 × 342 + 10 × 423

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7. 7. The numbers 541𝐴3, 541𝐵3, and 541𝐶3 are all different multiples of 3.

8. The letters 𝐴, 𝐵, and 𝐶 represent digits within the numbers.

9. What is the product 𝐴 × 𝐵 × 𝐶?

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8. A flight of stairs has 10 steps. David can go up for 1 step, 2 steps or 3 steps each time. The 4^th and the 7^th step cannot be stepped on as it is destroyed. How many way(s) is/ are there for David to go up the stairs?

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6. 9. Given A and B are two non-zero digits and the 2-digit numbers formed by these two digits have the following properties:

          1.       BA is a prime number greater than 30;

          2.       AB only has 1 prime factor and is not prime;

          Find the 2-digit number BA.

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7. 10. ABCD is a rectangle with CD = 24. E lies on the side AB such that ED = 7 and EC = 24. Find the area of ABCD.

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11. 11. Two 13 × 17 rectangles overlap as shown to form a 13 × 31 rectangle.

12. What is the area of the overlap region?

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12. 12. Find the least counting number which when divided by 5 gives a remainder of 1 and when divided by 12 gives a remainder of 3.