Beginner’s Guide To The EPSO Numerical Reasoning Test

Beginner’s Guide To The EPSO Numerical Reasoning Test

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EPSO Numerical Reasoning Tests:

Today’s Hosts

2

Today’s Trainer Robin Bott

EPSO Numerical Reasoning Tests:

Starter Session Overview

30-minute introduction (recorded)Theory-focused – no full questions to work outOverview of numericalHow to tackle questionsNot “maths basics”Tips and tricksFollowed by a 1 hr “Pro Tips” session with - practice questions and Q&A opportunity.

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4

EPSO Numerical Tests 10

20

Questions

Minutes

Minutes per question

2≈

Small Whiteboar

d

Maximum Score

• You cannot take anything into the exam room with you. • Everything you need will be provided.

Calculator Skill-based – not knowledge!

10Pass mark 5/10

Example Question

As a percentage of total population, how many cars were sold in 2015 across France and Germany combined?

a. 3.51%b. 4.11%c. 32.54%d. 39.23%e. 43.21%

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National Populations in 1000s2005 2010 2015

France 61444 63230 64982Germany

83836 83017 82562

Italy 58671 60508 61142UK 60291 62066 63843

2005 2010 201510000

15000

20000

25000

30000

35000

Cars Bought (in 1000s) in various European Countries

France Germany Italy UK

Year

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Solving Numerical Questions:Skills required

Interpretation of the information

Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning

Calculation

Estimation

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Interpretation of Information

What does the data tell you?What does the question ask you?What is the scale? What units are used?How do different elements interact?Any other important features?You don’t need to fully interpret the whole table/chart!Sometimes the question will introduce additional information!

What parts of the data are relevant to the question?

ExampleAs a percentage of total population, how many cars were sold in 2015 across France and Germany combined?

a. 3.51%b. 4.11%c. 32.54 %d. 39.23%e. 43.21%

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2005 2010 201510000

15000

20000

25000

30000

35000

Cars Bought (in 1000s) in various European Countries

France Germany Italy UK

Year

National Populations in 1000s2005 2010 2015

France 61444 63230 64982Germany

83836 83017 82562

Italy 58671 60508 61142UK 60291 62066 63843

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1. What is the average temperature across all 4 quarters in Belgium?

2. What is the total rainfall across all 3 countries for Quarter 2?

3. What is the difference between total rainfall in Austria and Belgium?

4. The total rainfall in Poland is 18% lower than Czech Republic. What is the total rainfall in Poland across the whole year?

Some Potential questions:

Example

Q1 Q2 Q3 Q4

AustriaAverage

Temperature (degrees Celsius)

2.2 13.6 17.9 3.4Total Rainfall

(mm) 102 159 232 148

Belgium

Average Temperature

(degrees Celsius)5.1 14.2 17.2 6.2

Total Rainfall (mm) 198 179 201 256

Czech Republi

c

Average Temperature

(degrees Celsius)1.9 15 14.2 4.5


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Example

Q1 Q2 Q3 Q4

AustriaAverage



(mm) 102 159 232 148

Belgium

Average Temperature



Czech Republi

c

Average Temperature



12







Example

Q1 Q2 Q3 Q4

AustriaAverage



(mm) 102 159 232 148

Belgium

Average Temperature



Czech Republi

c

Average Temperature



13







Example

Q1 Q2 Q3 Q4

AustriaAverage



(mm) 102 159 232 148

Belgium

Average Temperature



Czech Republi

c

Average Temperature



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Example

Q1 Q2 Q3 Q4

AustriaAverage



(mm) 102 159 232 148

Belgium

Average Temperature



Czech Republi

c

Average Temperature



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Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning Addition

SubtractionMultiplicationDivisionPercentages and Percentage PointRatios

Key skills: Things you shouldn’t be asked:Complex financial termsMultiplication tablesAlgebra, geometry, trigonometryLong divisionYou shouldn’t be given fancy infographicsThere should not be a strong verbal component

How do I use the data in the tables/charts to figure out the answer?

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Example

Employment Figures in Various Countries, 2006

CountryPopulation (thousand persons)

Proportion of Population (%) Employment Rate of Population (%)

Aged 15 to 64 Aged 55 to 64 Aged 15 to 64 Aged 55 to 64

Bulgaria 5328 69.2 13.4 58.6 39.6

Croatia 2961 67.3 12.6 55.6 34.3Greece 7459 67.2 11.7 61 42.3

What is the total population of Bulgaria, Croatia and Greece?

Addition

Numerical Reasoning

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Example





Bulgaria 5328 69.2 13.4 58.6 39.6

Croatia 2961 67.3 12.6 55.6 34.3Greece 7459 67.2 11.7 61 42.3

What is the difference between the population of Bulgaria and Croatia?

Subtraction

Numerical Reasoning

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Example





Bulgaria 5328 69.2 13.4 58.6 39.6

Croatia 2961 67.3 12.6 55.6 34.3Greece 7459 67.2 11.7 61 42.3

Based on the above table, how many people between the ages of 15 and 64 are employed in Croatia? Multiplication and

more multiplication (using percentages)

Numerical Reasoning

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Example





Bulgaria 5328 69.2 13.4 58.6 39.6

Croatia 2961 67.3 12.6 55.6 34.3Greece 7459 67.2 11.7 61 42.3

How many times more 15-64 year olds are there in Greece than in Croatia?Multiplication (to find out the number of 15-64 year olds in Greece and the number in Croatia)Division (to compare these two numbers)Subtraction (would answer ‘How many more 15-64 year olds are there in Greece than in Croatia’)

Numerical Reasoning

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Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning

Calculation

Estimation

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CalculationUse a calculator

Write down answers

Double check answer and/or use estimation to check

answers

Check units

There may be multiple steps, so take notes

There could be multiple routes to an answer

Take care with percentages

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Example Calculation

2015 2016

Number sold Value Number

sold Value

Product A 260 € 140 290 € 150Product B 542 € 80 482 € 80Product C 253 € 140 230 € 160

Which product had the highest total value of sales in 2016?

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Example Calculation

2015 2016Number

sold Value Number sold Value



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Example Calculation

2015 2016

Number sold Value Number

sold Value



€ 43,500

€ 38,560

€ 36,800

2016 Total Sales

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Calculation

Percentage and Percentage Point

2012 2013 201420% 30% 20%

What is the percentage point increase between 2012 and 2013?

What is the percentage increase between 2012 and 2013?

What is the percentage point decrease between 2013 and 2014?

What is the percentage decrease between 2013 and 2014?

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Calculation






30% - 20% = 10%

2012 2013 201420% 30% 20%

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Calculation

Percentage and Percentage Point The

percentage point increase of 10% needs to be compared to the original 2012 figure. 10% is half of 20%, so the percentage increase is 50%!

2012 2013 201420% 30% 20%





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Calculation


20% - 30% = -10% (i.e.

a 10% decrease)

2012 2013 201420% 30% 20%





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Calculation

Percentage and Percentage Point The

percentage point decrease of 10% needs to be compared to the original 2013 figure. 10% is a third of 30%, so the percentage decrease is 33%!

2012 2013 201420% 30% 20%





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Calculation


2012 2013 201420% 30%

20%





50% increase 33% decrease

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Calculation

Different Routes to Answer Price of

ProductQuantity

sold (thousands)

City 1 € 152 0.68City 2 € 152 0.48City 3 € 152 0.26City 4 € 152 2.47

What is the total value of product sold, across all 4 cities?

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Calculation


ProductQuantity

sold (thousands)


Total (thousands)

€103.36€72.96€39.52€375.44

What is the total value of product sold, across all 4 cities?Method 1: Figure out the total per city, then add these up

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Calculation


ProductQuantity

sold (thousands)


Method 2: Figure out the total quantity across all cities, then multiply by the product price

What is the total value of product sold, across all 4 cities?

= 3.89

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Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning

Calculation

Estimation

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EstimationShould be quicker than calculation

Look in the answer options for numbers that are similar

Note whether you round up or down

May allow narrowing of options even if not giving you the

full answer

Estimate into:3982 * 2 4000 * 268.1% 2/34561 + 567 the final digit will be 8

Large Round numbers

Fractions Last digits

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Estimation

A B1 156 0.092 193 0.223 249 0.314 468 0.42

What is the total sum of column A?a. 953b. 966c. 1053d. 1066e. 1092

Example #1

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Estimation

A B1 156 150 0.092 193 200 0.223 249 250 0.314 468 475 0.42


Large scale estimation make this much easier! 150 + 200 + 250 + 475 ≈ 1075

Example #1

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Estimation

A B1 156 150 0.092 193 200 0.223 249 250 0.314 468 475 0.42


Large scale estimation make this much easier! 150 + 200 + 250 + 475 ≈ 1075

Example #1

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A B1 156 0.092 193 0.223 249 0.314 468 0.42


Estimation

Final figures can also help narrow down answer. 6 + 3 + 9 + 8 = 26

Thus, the final figure is going to be 6

Example #1

44

A B1 156 0.092 193 0.223 249 0.314 468 0.42


Estimation

Final figures can also help narrow down answer. 6 + 3 + 9 + 8 = 26

Thus, the final figure is going to be 6

Example #1

45

Example #1b

Estimation

A B1 156 0.092 193 0.223 249 0.314 468 0.42

What is the total sum of column B?

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Example #1b

Estimation

A B1 156 0.09 0.12 193 0.22 0.23 249 0.31 0.34 468 0.42 0.4

What is the total sum of column B?

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Example #2

Estimation

Price of Product

Quantity sold

(thousands)


What is the total price of all products sold in City 1:

a. €98,450b. €103,360

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Example #2

Estimation

Price of Product

Quantity sold

(thousands)



a. €98,450b. €103,360

Our estimatesBut which answer is right?

€150 x 2/3 *1000 ≈ € 100 000€150 x 2/3 (of a thousand) = € 100 000

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Example #2

Estimation

Price of Product

Quantity sold

(thousands)



a. €98,450b. €103,360

Our estimates €150 as an estimate is slightly too low.2/3 as an estimate is slightly too low.

Thus, the final estimate overall will be slightly too low!€150 x 2/3 *1000 ≈ € 100 000

€150 x 2/3 (of a thousand) = € 100 000

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Numerical Reasoning

Calculation

Estimation

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Numerical Reasoning

Calculation

Estimation

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Estimating or Calculating?

How different are the answer options? Are there any obvious differences between them?

Do you have time for both estimating and calculation?

Charts can make exact calculation impossible!

Do words suggest estimation will work (for example, “approximate”)

How much time do you have left?

Can you use estimating to narrow down choices?

Can you use estimating to check a calculated answer?

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Tips and Tricks

You won’t instantly understand the information – take a moment to identify:

1. the information you need for your answer2. where this lies in the table

Sometimes common sense can help!

Just because you calculate an answer, doesn’t make it right!

Look for clearly incorrect answers and rule them out

You may not need to use all the zeroes!

Figure out which calculations you struggle with and practise these

Practice - try to simulate assessment conditions

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Beginner’s Guide To The EPSO Numerical Reasoning Test

Thank you for attending the webinar!

Following on from this theory based session is our

Pro Tips For The EPSO Numerical Reasoning Test Webinarwhere we put learning into practice

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Beginner’s Guide To The EPSO Numerical Reasoning Test