Numerical Test Tutorial – SHL type format One of only two ‘numerical test’ tutorials you need for Graduate & Internship jobs
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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
Corporate / Investment Banking Test ** 21 questions 21 minutes
Can’t go back to change answers
Can’t go back to change answers
Usually non-interactive
Tailor made for some top banks
* Incl. retail banking numeracy tests that tend to be simpler than investment banking or Big4 accounting firm tests
** 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 4 th quarter inflation index for Producer Prices?
106 104 102 100 98 96
(101/102)*100
94 Q1
Q2
Q3
Q4
Retail Price Index (RPI)
Consumer Price Index (CPI)
Producer Price Index (PPI)
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 4 th 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. 3rd 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 (PP I)
Q3
Q4
Consumer Price Index (CPI) Wh olesale Pri ce In dex (WP I)
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
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 s d n u o P h s i t i r B n o i l l i m £
650 600 550 500 450 400
9%
350 300
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 20 08 period.
Tip: 750
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.
s 700 d n 650 u o 600 P h 550 s i t 500 i r B 450 n 400 o i l l i 350 m 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
South America
1.8
US
24,000,000 240,000,000 300,000,000
1.5
1.9
10 years ago
Now
0
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 The answer must be in 100’s of millions, therefore:
14
2.4 x 100,00,000 = 240,000,000
12
Shortcut: Look at the red arrows. You just need to sum up t hose numbers that are positioned diagonally – then take their difference. I.e. (6.2 + 1.8) – (3.1 + 2.5) = 2.4
1.4 1.6 Rest of World
10 8 6 4 2 0
0.8 0.9
6.2
Asia Pacific
3.1 1.8
South America
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
Question 13 If production costs for L’Oreal are 2 times those for
100%
80%
7% 18%
26% 15% 6%
60%
Unilever, what is the gross margin (sales minus production costs) of Unilever?
10% 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
Global Toiletry Sales: Unilever and L'Oreal 100% 80%
7% 18%
26% 15% 6%
60%
“Cannot Say”.
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.
10%
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 High
Today's Low
Change on Benchmark 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 High
Today's Low
Change on Benchmark 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 ou r copyright All the data presented in tables and graphs is not real world data but it was specifically created for illustration purposes only.
