Questions involving algebra are the most common type of question in a numerical reasoning test. Algebra questions involve using a whole variety of skills such as basic arithmetic, decimals, fractions and percentages. Don't be discouraged if you haven't learned algebra in school yet – algebra is really just trying to find the unknown amount. A simple example of algebra in action is as follows.

A fruit box contains 10 fruit pieces. There are oranges, apples and pears. We know that there are four apples. The number of oranges is half that of apples. How many are pears?

This is algebra because you are required to find the unknown – that is, how many pears? We know that there are:

• 4 apples and,
• 2 oranges (half of four apples equals two).

Given that the fruit box contains 10 fruits, when we deduct the 4 apples and the 2 oranges we are left with 4 pieces of fruit, which are the pears.

Algebra questions test your ability to visualise a question in terms of different items and to find the connection between them.

So how do you know if you are dealing with a question that involves algebra?

Unlike straight numerical questions, where you would perhaps be are asked to find an item, numerical reasoning questions involving algebra can be quite difficult to identify.

Instead of representing the unknown as an item, it may simply ask you to find a missing piece of information in words. Following this logic, you may consider all numerical reasoning questions to be algebraic because they are always asking you for some unknown number.

However, in a worded question it is up to you to consider the clues and assign items to different information. Basically, use what is available to help you solve a question algebraically.

Now… let's look at a sample practice question.

Tania earns an hourly wage for her job. However, she will also receive a 10% bonus at the end of the day if she performs well. If she has made $200 today from a 6-hour shift including the bonus, what is her hourly wage?

Now… let's look at how we can solve this question in a logical manner.

Steps	Illustrated Workings
Step One	What are the unknowns?There are two – Tania's hourly wage and the amount of her bonus.
Step Two	Let the symbol "x" represent Tania's hourly wage as we don't know what that is yet. Her bonus is 10% of her total daily wage. Tania worked for 6 hours, so her bonus must be 6 multiplied by x (the total daily wage) multiplied by 10%Note that 6 multiplied by x (the total daily wage) multiplied by 10% is also the same as:

• 6 multiplied by x (the total daily wage) multiplied by 1/10; or
• 6 multiplied by x (the total daily wage) multiplied by 0.10 Given this, the formula for the bonus is:
• 6 x x x 0.10, and simplified, it is
• 60 x x, or expressed more simply 0.60x

Step Three	So how much does Tania make in total? We can express in an equation form what makes up the $200 that Tania earns as follows.Daily wage + Bonus = $200 (she made $200 today)Put together in the algebraic equation with x as the unknown hourly wage, the equation is:6x + 0.6x = 200Note that 6x means 6 multiplied by x and 0.6x means 0.6 multiplied by x. This is conventional algebraic expression. The 6x represents what Tania earns a day and the 0.6x is her bonus.
Step Four	Now we'll solve the equation for find the unknown, x – Tania's hourly wage.6x + 0.6x = 200 can be simplified to 6.6x = 200Using the simplified equation, let's solve.

• 6x = 200
• x = 200/6.6
• x = 30.30

Step Five	The solution is that x = 30.30Therefore, Tania's hourly wage is $30.30

Now, let's do some example questions:

Example 1

The sum of two numbers is 63, and one of them is 15 more than the other. What are the two numbers?

A 25 and 40

B 24 and 39

C 38 and 25

D 29 and 34

Example 2 & 3

The next 2 questions are based on the following information.

The combination of a safe contains 4 digits. It is known that:

Zero is not one of the digits. The first digit is larger than the third digit, but smaller than the second digit. The fourth digit is twice as large as the first digit. The third digit is an even number.

It is correct to say that:

(a) The 4th and 2nd digit are equal to each other.

(b) The 1st digit is greater than half of the second digit.

(c) The 1st digit cannot be an even number.

(d) The 1st digit cannot be 2.

(e) None of the above.

What would be a possible combination?

(a) 4,7,2,8

(b) 4,3,6,8

(c) 1,3,6,8

(d) 4,6,7,8

(e) None of the above

Example 4

If the total cost of building a swimming pool is $43,000; water costs $1.25 per cubic metre and construction costs $42,400; what is the capacity of the pool?

(a) 500m3

(b) 490m3

(c) 480m3

(d) 488m3

(e) None of the above

Key Rules to remember:

• Algebra is about finding the unknown – so know exactly what you're looking for!
• Set up your equation to quickly solve the unknown as time is of the essence.

Now it's time to do your assignment.

1. Download the assignment question here.
2. Print it out or if you want to do it electronically, save it.
3. Complete the questions to it.
4. Then check the solutions on the video below.
5. For the answers in text instead of video, download them here.

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