Session 8

Whole Numbers

2

Evaluate 7 × 17 + 34 × 7 + 49 × 7

700

3

Evaluate (2 × 99 × 7) ÷ (63 × 44)

0.5 or 1/2

5

Calculate 57329 × 150 - 57329 × 350 + 57329 × 200

0

7

Compute 499 × 501 (Hint: create a variable and set it to 500)

249 999

11

Compute (2763 × 2763 - 2762 × 2764)²⁷⁶³

1

Algebra

2

3 times a number z plus 6 equals the product of 5 and z. Find z.

3

3

Alvin has 3 times as much money as Clifton. After spending $60 each, Alvin has 4 times as much money as Clifton. How much money did Alvin have at first?

$540

5

The average weights of Naren and Morgan is 42 kg. Morgan is 4 kg heavier than Naren. Find the weights of Naren and Morgan respectively.

40 kg, 44 kg

7

The total mass of a rectangle, triangle, and circle is 20 kg. The rectangle weighs 2 kg more than the triangle, while the circle weighs 3 kg less than the triangle. What is the product of the masses of the three shapes?

252

11

Joel's score was twice Louis' score. Kathlyn scored 5 points less than Louis. Marion scored 10 points more than Joel. Marion's score was 6 times Kathlyn's. Who scored 10 points?

Louis

Indices

2

Find the missing number in this pattern: 4, 9, 16, __, 36, 49

25

3

Find the last digit of 6⁴⁵⁴⁸¹.

6

5

Find the ones digit of 3⁷⁴ + 4²¹.

3

7

Find the last digit of 1⁷⁴⁶ × 2⁹⁴ × 3¹⁹¹ × 4⁶²⁵ × 5⁵⁹⁸⁶⁹ × 6²⁶⁰⁴¹² × 7²⁹⁶⁹ × 8^6413291 × 9³²⁵⁶⁸⁹ × 10^{346013489662590}.

0

11

What is the remainder when 2⁴ + 3⁵ + 4⁶ + 5⁷ + 6⁸ + 7⁹ + 8¹⁰ is divided by 5?

2

Divisibility

2

If the five-digit number 2345N is divisible by 6, find N.

4

3

If 457Q is divisible by 12, find Q.

2

5

Find the value of a + b + c if 173a is divisible by 9, 173b is divisible by 8, and 173c is divisible by 6.

17

7

Naomi uses the digits 1, 3, 4, 5, 7, and 8 to form a four-digit multiple of 4. She may only use each digit once. What is the greatest number she can form?

7584

11

Given a 7-digit number 1997abc that is divisible by 3, 4, and 5, find the lowest possible value of the 3-digit number abc. (a is allowed to be 0.)

40 (or 040)

Prime Numbers

2

What do the five point levels of this Jeopardy all have in common?

They're all prime numbers

3

Find the prime factorisation of 2070.

2 × 3² × 5 × 23

5

The product of 3 boys' ages is 210, and the sum of their ages is 18. Find their ages.

5, 6, and 7

7

What are the side lengths of a rectangle that:

1. has an area of 72 cm²,

2. has a perimeter of 34 cm

8 cm and 9 cm

11

Given that 7! is 7 × 6 × 5 × 4 × 3 × 2 × 1, find the number of consecutive zeroes at the end of 20!

4