Numerical Test

Numerical Test Guide – SHL type format One of only two ‘numerical test’ guides you need for Graduate & Internship jobs

Graduate test solutions by

www.graduatemonkey.com

Numerical Test Structure and Use  SHL is one of the biggest recruitment test providers supplying blue chip companies globally  Many banks, audit, marketing and consulting firms use SHL (test system) as part of their graduate recruitment and industrial placement/internship programmes:  3 categories of timed tests used: numerical, verbal and abstract reasoning  Cannot go back to change the answer once you have clicked “Next”  Non-interactive but somewhat challenging at the higher end (e.g. Investment Banks)

Numerical Reasoning Test Standard Non-Banking Numeracy Test *  18 questions  25 minutes  Can’t go back to change answers  Usually non-interactive * Incl. retail banking numeracy tests that tend to be simpler than investment banking or Big4 accounting firm tests

Corporate / Investment Banking Test **  21 questions  21 minutes  Can’t go back to change answers  Tailor made for some top banks ** Incl. some Big4 accounting firm tests

Data Context 2: Line charts: inflation indices

Numerical Test: Data Context 2 Line charts: inflation indices Inflation indices are used to measure change in the prices of a group of goods and services monthly, quarterly or annually. Retailer Price Index and Consumer Price Index are the most common indices.

Comparing several indices

Question 4 If the inflation indices were rebased at 100 again at the 3rd quarter, what would be the 4th quarter inflation index for Producer Prices?

106 104 102 100 98 96

(101/102)*100

94

Q1

Q2

Retail Price Index (RPI) Producer Price Index (PPI)

Q3

Q4

Consumer Price Index (CPI) Wholesale Price Index (WPI)

(102/101)*100 (100/102)*100

(102*100)/101 Cannot say

Numerical Test: Data Context 2 Line charts: inflation indices Inflation indices are used to measure change in the prices of a group of goods and services monthly, quarterly or annually. Retailer Price Index and Consumer Price Index are the most common indices.

Question 4 If the inflation indices were rebased at 100 again at the 3rd quarter, what would be the 4th quarter inflation index for Producer Prices?

Solution to Question 4 Task: Figure out how rebasing would affect the 4th quarter figure for Producer Price Index (PPI). Solution: Rebasing an index from a certain quarter (month or year) simply means dividing all the index figures by the value given for that month, then multiplying all of them by 100. E.g. 3 rd quarter PPI 102 – so all the index figures will be divided by 102.Therefore, rebasing 4th quarter PPI would be: (4th quarter PPI / 3rd quarter PPI) x 100 = (100/102)x100 = 98.04

Tip:

106 104

Rebasing an index for period A means dividing all the index values by the value of A, then multiplying them by 100 – this is always the same.

102

100 98 96 94 Q1

Q2

Retail Price Index (RPI) Producer Price Index (PPI)

Q3

Q4

Consumer Price Index (CPI) Wholesale Price Index (WPI)

Data Context 3: Line charts: comparing company sales by brands

Numerical Test: Data Context 3 Line charts: comparing company sales by brands Compares how the sales values of several brands have changed over time

£ million British Pounds

Company sales by brand

Question 5 What was the highest proportional increase in sales value, in comparison with the previous year, for any of the three brands?

750 700 650 600 550 500 450 400 350 300

9% 2005

2006

Everyday Value

2007

2008 Premium

2009

2010 Finest

25% 14.3%

10% Cannot say

Numerical Test: Data Context 3 Line charts: comparing company sales by brands Compares how the sales values of several brands have changed over time

Question 5 What was the highest proportional increase in sales value, in comparison with the previous year, for any of the three brands?

Solution to Question 5 Task: This problem has a simple two step solution. First, look at the lines on the graph and identify the one with the steepest rise. Then, calculate the percentage change by dividing the two figures between which the increase had occurred. Solution: If you look closely at the lines on the graph, the steepest rise occurred in the Finest brand from 2007 to 2008 period.

When you a graph and the question asks you to determine the biggest change in values, whether it is a rise or drop, then first identify the steepest line or part of the line. It will save you time and you could answer the test within 15 seconds.

£ million British Pounds

Tip: 750 700 650 600 550 500 450 400 350 300

2005

2006

Everyday Value

2007

2008 Premium

2009

2010 Finest

Data Context 4: Stacked column charts: comparing data across time

Numerical Test: Data Context 4 Stacked column charts: comparing data across time Stacked columns typically show how several categories contributed from one period to another, in total and across divisions.

Annual Road Travellers (100 million drivers) 14 1.4 12

Question 9 Over the last decade by how many drivers did the increase in in Asia Pacific region exceed the increase in European region?

1.6

10 Rest of World 8

0.8 0.9

6.2

Asia Pacific

6

Europe

3.1 4 2.5 2 0

South America

1.8

US

24,000,000 240,000,000 300,000,000

1.5

1.9

10 years ago

Now

340,000,000 Cannot say

Numerical Test: Data Context 4 Stacked column charts: comparing data across time Stacked columns typically show how several categories contributed from one period to another, in total and across divisions.

Question 9 Over the last decade by how many drivers did the increase in in Asia Pacific region exceed the increase in European region?

Solution to Question 9 Task: Calculate the differences between now and 10 years ago separately for Asia Pacific and European regions . Then deduct the Europe figure from the Asia Pacific one. Calculations: Asia Pacific: 6.2 – 3.1 = 3.1 Europe: 2.5 – 1.8 = 0.7 Annual Road Travellers (100 million drivers) Asia Pacific minus Europe: 3.1 – 0.7 = 2.4 14 The answer must be in 100’s of millions, therefore: 1.4 2.4 x 100,00,000 = 240,000,000 12 1.6

Shortcut: Look at the red arrows. You just need to sum up those numbers that are positioned diagonally – then take their difference. I.e. (6.2 + 1.8) – (3.1 + 2.5) = 2.4

Rest of World

10 8 6 4 2 0

0.8 0.9

6.2

3.1 1.8

South America

Asia Pacific Europe

2.5

1.5

1.9

10 years ago

Now

US

Data Context 5: Stacked 100% column charts: comparing sales of 2 companies

Numerical Test: Data Context 5 Stacked 100% columns: comparing sales of 2 companies Bar charts typically compare sales or other financial data of two or more companies. 100% stacked column typically includes sales (or other data) breakdown by divisions or products.

Global Toiletry Sales: Unilever and L'Oreal 100% 80%

7%

10%

18% 26% 15% 6%

60%

Question 13 If production costs for L’Oreal are 2 times those for Unilever, what is the gross margin (sales minus production costs) of Unilever?

Africa Asia Pacific

14% 40%

35% 44%

20% 25%

South America

$2 billion

North America

$2.5 billion

Europe

0%

Unilever ($8,000)

L'Oreal ($24,000)

$3 billion $3.5 billion Cannot say

Numerical Test: Data Context 5 Stacked 100% columns: comparing sales of 2 companies Bar charts typically compare sales or other financial data of two or more companies. 100% stacked column typically includes sales (or other data) breakdown by divisions or products.

Question 13 If production costs for L’Oreal are 2 times those for Unilever, what is the gross margin (sales minus production costs) of Unilever?

Solution to Question 13 Task: First, we need to determine if we have sufficient data to calculate the required figure. The chart does not contain data on production costs or gross margin for either brand. L’Oreal S1 (sales) – P1 (production costs) = GM1 (gross margin) Unilever S2 – P2 = GM2 P1 = 2P2 therefore S1 – 2P2 = GM1 although S1 and S2 (sales figures) are known, we still have 3 unknowns in the two equations above – which cannot be solved. Therefore, the answer must be “Cannot Say”.

Global Toiletry Sales: Unilever and L'Oreal 100% 80%

10%

18% 26% 15% 6%

60%

Africa Asia Pacific

14% 40%

Tip: When you have 2 or more unknowns, then try to build equations to determine whether you can solve the problem. If the number of unknowns exceed the number of equations, the problem cannot be solved.

7%

South America

35% 44%

20% 25%

North America Europe

0%

Unilever ($8,000)

L'Oreal ($24,000)

Data Context 9: Data tables: currency exchange rates

Numerical Test: Data Context 9 Data tables: currency exchange rates Currency exchange data table typically shows trading highs and lows as well change on day and the closing rate. Typically, opening rate equals to the closing point rate minus change on day.

Currency exchange rates: Tenge per currency

Question 24

Today's Exchange Rates* for the Kazakh Tenge Currencies

Closing Point

Today's Today's Change on Benchmark High Low Day Index

Euro

194.32

196.44

192.15

0.65

190.78

US Dollar

150.81

152.65

149.13

-0.24

148.59

0.21

0.23

0.19

0.01

0.21

24.28

26.85

23.11

-0.31

24.18

Russian Rouble Chinese Renminbi

A company changes €150,000 euros to Kazakh Tenge at the "Day's High" rate to pay a debt of 30 million Tenges. Approximately what amount of Tenges is left over, or still owing, following this transaction?

534,000 Tenge still owing 534,000 Tenge left over

* Rates represent number of Tenge per stated currency

1,534,000 Tenge still owing 1,534,000 Tenge left over None of the above

Numerical Test: Data Context 9 Data tables: currency exchange rates Currency exchange data table typically shows trading highs and lows as well change on day and the closing rate. Typically, opening rate equals to the closing point rate minus change on day.

Question 24 A company changes €150,000 euros to Kazakh Tenge at the "Day's High" rate to pay a debt of 30 million Tenges. Approximately what amount of Tenges is left over, or still owing, following this transaction?

Solution to Question 24 Task: First, we need to work out how much Tenge one would get for EUR 150,000 at “Today’s High” rate. Then we need to subtract 30 million Tenge from this amount to arrive at the correct answer. Calculations: 1. Eur 150,000 x 196.44 (today’s high rate) = 29,466,000 Tenge 2. 29,466,000 – 30,000,000 = - 534,000 Tenge The answer: 534,00 Tenge would still be owed.

Today's Exchange Rates* for the Kazakh Tenge

Tip. When you are asked to convert a currency amount that corresponds to row headings (e.g. Eur corresponds to the row heading – Euro), then you always multiply this amount by the corresponding rate in this row. On the other hand, if you are asked to convert the main currency (which is in the title of the table such as Tenge), Into a currency that is in the row heading, then you always divide the given amount by the corresponding rate in this row.

Currencies

Closing Point

Today's Today's Change on Benchmark High Low Day Index

Euro

194.32

196.44

192.15

0.65

190.78

US Dollar

150.81

152.65

149.13

-0.24

148.59

0.21

0.23

0.19

0.01

0.21

24.28

26.85

23.11

-0.31

24.18

Russian Rouble Chinese Renminbi

* Rates represent number of Tenge per stated currency

Legal Rights and Disclaimer You are not allowed to share, post or distribute the given material prior to obtaining permission from the authors. Attempts to distribute the material via the internet may be detected and action may be taken against the person(s) who violate our copyright All the data presented in tables and graphs is not real world data but it was specifically created for illustration purposes only.