beginner’s guide to the epso numerical reasoning test
TRANSCRIPT
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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Interpretation of the information
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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Interpretation of Information
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
Total Rainfall (mm) 123 148 221 142
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Interpretation of Information
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
Total Rainfall (mm) 123 148 221 142
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Interpretation of Information
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
Total Rainfall (mm) 123 148 221 142
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Interpretation of Information
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
Total Rainfall (mm) 123 148 221 142
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Interpretation of Information
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
Total Rainfall (mm) 123 148 221 142
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Interpretation of the information
Numerical Reasoning
Calculation
Estimation
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Interpretation of the information
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
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 difference between the population of Bulgaria and Croatia?
Subtraction
Numerical Reasoning
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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
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
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
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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Interpretation of the information
Numerical Reasoning
Calculation
Estimation
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Interpretation of the information
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
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 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?
€ 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
Percentage and Percentage Point
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?
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%
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
Percentage and Percentage Point
20% - 30% = -10% (i.e.
a 10% decrease)
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
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%
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
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?
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
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
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
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
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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Interpretation of the information
Numerical Reasoning
Calculation
Estimation
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Interpretation of the information
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
What is the total sum of column A?a. 953b. 966c. 1053d. 1066e. 1092
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
What is the total sum of column A?a. 953b. 966c. 1053d. 1066e. 1092
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
What is the total sum of column A?a. 953b. 966c. 1053d. 1066e. 1092
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
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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
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
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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)
City 1 € 152 0.68City 2 € 152 0.48City 3 € 152 0.26City 4 € 152 2.47
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)
City 1 € 152 0.68City 2 € 152 0.48City 3 € 152 0.26City 4 € 152 2.47
What is the total price of all products sold in City 1:
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)
City 1 € 152 0.68City 2 € 152 0.48City 3 € 152 0.26City 4 € 152 2.47
What is the total price of all products sold in City 1:
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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Interpretation of the information
Numerical Reasoning
Calculation
Estimation
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Interpretation of the information
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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