**How to Pass the Numeracy Skills Section**

**Specific skills you need to know:**

- How to work out ratios & percentages
- What formula you need to know beforehand
- How to re-arrange formulas
- Accurately obtain data from tables and charts

### Overview

The Numerical Skills assessment tests your ability to solve mathematical questions that are presented in situations using; words, diagrams, charts, tables etc.

### Quick Tips

**Write small on your worksheet**A basic online calculator will be provided as well as a sheet of A4 paper to work on. You will be only provide one sheet of paper. You can ask for more, but you will lose time as the attendants are walking around a large room during the exam. Best to write small!**Read questions first**

As always, the clock is working against you. Because the numerical skills questions are visual based, I recommend reading the question first before scanning the information. Why? Some questions present information that isn’t relevant so you lose time reading it. Better to hunt for the information you actually need.**Complete easier calculations first**Some calculations are easier and quicker than others. If you know what you are good at and not good at, ie, I’m slow at working out ratios, I will skip that question to find an easier one and come back to it if I have time.**Have a strategy to answer questions**

Do you have an answering strategy or a method to answer each question? I recommend a simple 3 step process:**Step 1:**Read one question at a time

Before looking at the information presented, read (re-read if necessary) to find out what specific information you’re looking for.**Step 2:**Identify relevant information

Sometimes, much of the info presented is not relevant to your answer so quickly scan the information presented, focusing only on the relevant pieces of information required.**Step 3:**Work out the answer

Work on your calculations. Check the answer twice if uncertain.

### Ratios

Ratios are used to compare different things and are often answered in decimals, fractions or percentages.

Example: Which of the four changes shown below provides the __highest proportion__ of savings?

To work out proportions (ratio):

Savings per year / Initial investment

Coffee = 240 / 450 = 053

Heater = 295 / 2250 = 0.13

LEDs = 25 / 75 = 0.33

Phone = 320 / 650 = 0.49

**Answer: **Coffee provides the highest proportion of savings

### Percentages

You will be asked different types of percentage questions during the numerical skills exam.

**#1 Applying a percentage to a value**

**Q: **How much would it cost to buy 2 pots from Pots Galore?

**Step 1:** Work out cost of 2 plants at original prices

25 x 2 = 50

**Step 2: **Work out value of 25%

50 x 25% (or 25 / 100 = 0.25) = 12.5

**Step 3: **Subtract percentage from original value

50 – 12.5 = **37.5 is the answer**

**#2 Using percentages to work out missing values**

In the ACER practice exam, Q22 is:

*The national gender pay gap in the education and training industry is 11.3%.If women in this industry earn $69061.20 per year, what would the average yearly earnings be for men?*

I found this question to be very difficult to answer as I didn’t know how to answer it. Once you know the steps to take, it becomes a lot easier.

**Answer****Step 1:** Work out percentage of earnings for women compared to men.

100% – 11.3% = 88.7%

**Step 2: **Write out equation*(it can be easier to answer a question once you write out the equation)*88.7% x M = 69061.20 (M = men’s average wage)

**Step 3: **Divide 88.7 by 100

(this turns the percentage into a number)

88.7 / 100 = 0.887

**Step 4: **Re-arrange equation

(find out more about re-arranging equations here)

M = 69061.20 / 0.887 = 77859.3 is the answer

You can double check the answer: 77859.3 x 11.3% = 8798.1

77859.3 – 8798.1 = 69061.2

**Practice question:**The gap between two numbers is 13%. One number is 21.75, what is the other number?

Take a moment and work this out on paper. Cross-check your answer to the explanation below:

**Step 1:** Work out percentage difference.

100% – 13% = 87%

**Step 2: **Write out equation

87% x M = 21.75 (M = missing number)

**Step 3: **Divide 87 by 100

87/ 100 = 0.87

**Step 4: **Re-arrange equation

M = 21.75 / 0.87 = **25 is the answer**

### How to Use & Re-Arrange Formulas / Equations

One formula you should know for the numerical skills exam is **Distance = Speed x Time (D = S x T)**

This formula can be re-arranged 3 ways (shown above). Let’s look at an question that requires this formula to work out the answer.

**Q: **Sonya cycles 30km to work each day. She usually cycles at an average speed of 40 kilometres per hour (km/h). One day, she rides into heavy wind and her average speed is 20km/h.

*What is the difference in time between the two average speeds? *

**Answer**

**Step 1:**Workout average time for Sonya on a normal day

Distance / Speed = Time

30km / 40km/hr = 0.75

0.75 of an hour = 45mins

**Step 2:** Workout average time for Sonya riding into heavy wind

Time = Distance / Speed

30km / 20km/h = 1.5

1.5 hours = 1 hours 30 mins

The difference between the two times 1h 30mins – 45mins**45mins is the answer**** **

**How to convert units used in formulas**

Often, numerical questions using the D = S x T formula will provide values in different units of measurement. Example, distance will be in metres and speed in kilometres. You cannot use the formula when this is the case.

You may be required to convert time, distance and speed values into numbers before using in a formula.

Let’s look how you can quickly convert these values:

**Time**

Time values, such as 3 hours and 22 minutes need to be converted to a whole number. How?

3 hours = 3

22 minutes = 22 / 60 = 0.37 (60 is the number of minutes in an hour)

Final number: 3.37

Easier time values converted include

15 mins = 0.25

30 mins = 0.5

45 mins = 0.75

**Distance**

Remember 1000m = 1km

**Speed**

If speed is in km/hr, then distance needs to be in km’s and time needs to be in the value outlined above.

*Q: Sandy takes 1 hour and 50 minutes to run the first half of the marathon. What was his running speed for the first half of the marathon compared (Provide your answer in km/hr with one decimal place)*

Answer**Formula to use: **Speed = distance / time

**Step 1: **Work out distance & time values

Distance: first half of marathon = 21.1km

Time: 1hr 50mins needs to be converted to decimal number

1 hour = 1

50 mins = 50 / 60 = 0.83

Total = 1.83

**Step 2:** Insert values into formula

Speed: 21.1 / 1.83 = **11.5 km/hr is the answer.**

### Accurately Reading Charts / Tables

In the Numerical Skills exam, you will be presented with tables and charts that contain the info you need to answer questions.

The faster and more accurately you can obtain this data, the better.

Let’s look at some sample questions

**Q: **What was the highest value for VAS from 2000-2019?

**AnswerStep 1: **identify VAS line = solid black

**Step 2:**Identify highest value = 2015

**Step 3:**Work out value

The mark is two lines from the top. Looking at the investment returns on the left, two lines from the top = 70.

Don’t forget the (‘000) in brackets needs to be added.

70,000 is the answer.

**Q:** Are the following statements True or False based on the information in the graph:*2015-2016 was the largest loss of value for VAS in a single year*

**Answer**

Quickly scan the chart for steep falls. 2008-09 & 2015-16 are the obvious possible answers.

You could spend time working out the drop of value for each, but time is important, so I would recommend making a decision based on the visual information.**True is the answer.**

*Q: **VTS had greater overall returns compared to VAS from 2000-2019*

**Answer****Step 1:** Work out VTS gains

2000: 44,000

2019: 64,000

Total Gain = 64,000 – 44,000 = 20000

**Step 2:** Work out VAS gains

2000: 22,000

2019: 58,000

Total Gain = 58,000 – 22,000 = 36000

VAS has larger gains**False is the answer**.

*Q: **The value of VTS increased over 50% from 2002-2019?*

**Answer**

Value of VTS in 2002 = 38,000

Value of VTS in 2019 = 64,000

There are 2 methods to work out the percentage increase:**#1: Quick method but not accurate**

50% of 38,000 = 19000.

19000 + 38000 = 57000

Because 64000 is more than 57000, we can say VTS has increase over 50%**True is the answer.**

**#2: Accurate but slower**To work out percentage increase:

New number – original number / original number

(64000 – 38000) / 38000 = 0.68

Convert to percentage = 0.68 x 100 = 68%

**True is the answer**.

### If you want more practice...

Check out the 3 full-size Numerical Skills exams that can be completed online or printed off. Each exam contains the same type of questions found in the entrance exam with full explanations for each question provided. If you are worried about this section, the best way to improve is to practice. Start today.

Good luck with the prep!

If you would like extra help on a question, drop me an email.

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