Question 6:
How many prime numbers are there between 10 and 40?

Solution:
Prime numbers between 10 and 40
= 11, 13, 17, 19, 23, 29, 31, 37
There are 8 prime numbers between 10 and 40.

Question 7:
Diagram below shows a sequence of prime numbers.
$$\boxed{13,17,x,y,29}$$ Find the value of x + y.

Solution:
Value of x + y
= 19 + 23
= 42

Question 8:
The following data shows a sequence of prime numbers in ascending order.
$$\boxed{5,7,x,13,17,\text{ 19},\text{ 23},29,y,z}$$ Find the value of x, y and of z.

Solution:
x = 11, y = 31, z = 37

Question 9:
The following data shows a sequence of prime numbers in ascending order.
$$\boxed{p,\text{ 6}1,\text{ 6}7,q,\text{ 73},r,\text{ 83 }}$$ Find the value of p, q and of r.

Solution:
p = 59, q = 71, r = 79

Question 10:
Diagram below shows several number cards.
$$\boxed{\begin{array}{l}\boxed{49}\boxed{39}\boxed{29}\\ \boxed{87}\boxed{97}\boxed{77}\\ \boxed{5}\boxed{15}\boxed{\text{2}5}\end{array}}$$ List three prime numbers from the diagram.

Solution:
Prime number card from the diagram = 5, 29 and 97.

Question 1:
Diagram below is part of a number line.
What is the value of P and of Q?

Solution:
Each gradation on the number line represents 4 units. Thus P = –12 and Q = 12.

Question 2:
Diagram below shows a sequence of numbers. K and M represent two numbers.
$$\boxed{\boxed{19}\boxed{13}\boxed{K}\boxed{1}\boxed{M}}$$ What are the values of K and M?

Solution:



K = 13 – 6 = 7
M = 1 – 6 = –5

Question 3:
Diagram below shows five integers.


Find the sum of the largest integer and the smallest integer.

Solution:
The largest integer = 1
The smallest integer = –10
Sum of the largest integer and the smallest integer
= 1 + (–10) 
= –9

Question 16:
State the first two common multiples of 3, 5 and 6.

Solution:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, …
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

The first two common multiples of 3, 5 and 6 are 30 and 60.

Question 17:
Find the lowest common multiple (LCM) of 4, 8 and 24.

Solution:

Question 18:
Find the lowest common multiple (LCM) of 8, 12 and 15.

Solution:

Question 19:
Find the highest common factor (HCF) of 26, 52 and 156.

Solution:

Question 20:
Given that (m + 5) is the highest common factor of 81 and 108, find the value of m.

Solution:

Question 11:
State all the prime factors of 156.

Solution:
$\begin{array}{l}\text{Factors of }156:\\ 1\times \text{ 156}\\ \boxed{2}\times \text{ 78}\\ \boxed{3}\times \text{ 52}\\ \text{4 }\times \text{ 39}\\ \text{6 }\times \text{ 26}\\ \text{12 }\times \boxed{\text{13}}\\ \\ 2,3\text{ and }13\text{ are the prime factors of }156.\end{array}$

Question 12:
State all the prime factors of 182.

Solution:
$\begin{array}{l}\text{Factors of }182:\\ 1\times \text{ 182}\\ \boxed{2}\times \text{ 91}\\ \boxed{\text{7}}\times \text{ 26}\\ \boxed{13}\times \text{ 14}\\ \\ 2,\text{ 7, 13 and 91 are the prime factors of }182.\end{array}$