Numerical Test Tutorial – Kenexa Style
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Data Context 2
PSL Numerical Test: Data Context 2
Price indices
Question 5: What would the price of a tonne of corn would be in Year 10 if it rose by 6% per annum from its
Year 6 price?
A: $744.86
B: $567.89
C: $652.65
D: $788.78
E: $444.12
Price of Corn
Year
$ Price per ton
Consumer Price Index
(31-Dec)
(1-Jan – 31-Dec)
1 $ 400
3.10%
2 $ 415
3.50%
3 $ 420
2.20%
4 $ 450
5.50%
5 $ 510
4.10%
6 $ 590
6.20%
One of the most common data contexts is asset prices and indices, with questions
focussed on past growth or future growth based on an annual rate.
Shortcut method: Note that compounded growth by 6% over
4 years i.e. (1+6%)^4-100% = 26% will only be slightly higher than direct multiplication i.e. 6% x 4 years = 24%. So to estimate you could take 6%x4+1=124% or 1.24 AND multiply this by 590 = 731.6. Because the answer should only be slightly lower the real answer, the closest answer choice would be 744.86.
Task: Calculate the compounded price growth of corn for the 4 years (from 6th to 10th year), then multiply Year 6 price
by this number.
Solution: From 6th year through 10th year there would be 4 years. Using standard formula (1+6%)^4 = 1.26248
1.26 (compounded price growth rate) x 590 (Year 6 price) = 744.86
PSL Numerical Test: Data Context 2
Price indices (e.g. CPI, RPI)
Solution to Question 5: What would the price of a tonne of corn would be in Year 10 if it rose by 6% per
annum from its Year 6 price?
Price of Corn
Year $ Price per ton Consumer Price Index
(31-Dec) (1-Jan – 31-Dec)
1 $ 400 3.10% 2 $ 415 3.50% 3 $ 420 2.20% 4 $ 450 5.50% 5 $ 510 4.10% 6 $ 590 6.20%
Tip 2: This is for estimation questions only: When annual
rate is below 10%, the compounded growth rate over a few
years is only slightly higher than direct multiplication of growth rate by the number of years. So you can multiply growth rate by the number of years, then look for a slightly bigger number as the correct answer.
Data Context 8
PSL Numerical Test: Data Context 8
Comparing Market Shares
Question 29: Between which two years did WPP’s percentage share of the global advertising market sales
increase?
A: 2006-2007
B: 2007-2008
C: 2008-2009
D: 2009-2010
E: 2010-2011
Typically compares market shares of one or several companies in a specific market in terms of
revenue, sales or costs.
22.54 23.61 22.02 23.92 19.22 18.53 12.43 13.33 14.68 15.68 16.75 17.58 5 10 15 20 25 2006 2007 2008 2009 2010 2011 b ill ion s $
Global Advertising Market Sales ($ billions)
WPP The rest
Task: First of all, understand the question and look for clues in the graph. For example, “percentage share of global sales” means that you need to calculate the ratio of WPP sales to the total sales (including WPP), for each year. Then you need to identify where this percentage has fallen from the previous year. The problem is that 1 minute would not be sufficient to calculate the above percentage shares of WPP for each of the 6 years! See Shortcut method below.
Solution: Traditional method would be to calculate WPP market share as % of total market for each year (as follows).
2006: 22.54 / (22.54 + 12.43) = 64.46% 2007: 23.61 / (23.61 + 13.33) = 63.91%
2008: 22.02 / (22.02 + 14.68) = 60% 2009: 23.92 / (23.92 + 15.68) = 60.4% - an increase from 2008
PSL Numerical Test: Data Context 8
Comparing Market Shares
Solution to Question 29: Between which two years did WPP’s percentage share of the global advertising
market sales increase?
22.54 23.61 22.02 23.92 19.22 18.53 12.43 13.33 14.68 15.68 16.75 17.58 5 10 15 20 25 2006 2007 2008 2009 2010 2011 b ill ion s $
Global Advertising Market Sales ($ billions)
WPP The rest
Shortcut:
The graph comes with an answer. Notice that the trend for “The Rest” of the world is up while WPP trend is down with an upward spike in 2008-2009 period. The task is to identify the period where WPP market share increased from the previous year. WPP actual sales increased from 2008 to 2009. Hence, 2008 and 2009 would be the best data points to start with - to save a lot of time! If you don’t have time to calculate you could just choose 2008-2009 period from the graph.
Indeed, 23.92 / (23.92 + 15.68) = 60.4% which is an increase from 22.02 / (22.02 + 14.68) = 60%
Tip: Look for clear trend changes and noticeable
Data Context 4
PSL Numerical Test: Data Context 4
Pie charts with several % components (of total sales, costs or investment value)
Question 12: If 11% of the value of the China holding is moved to India, what proportion of the total fund
will the India investment represent?
A: 11.7%
B: 12.5%
C: 10.1%
D: 9.9%
E: 9.5%
Pie charts are used for data representation, especially, when the data has various
compositions. Most common pie charts show sales, cost and investment values.
Brazil 5% China 10% India 9% Russia 12% UK 39% US 25%
Current Value of Global Government Bond
Fund
Shortcut: There is no need to use the actual value of the Fund in
the calculations. Simply, take 10% China holding, multiply by 11%, then add the result to the existing 9% India holding:
10% x 11% + 9% = 10.1%
Task: The key task is to calculate the value that will move from China holding to India holding. Then add it to the actual value of existing India holding, then divide the sum by the total value of the Fund.
Solution: Total value of China holding: 210m x 10% = 21m 11% of China holding: 21m x 11% = 2.31m
Total existing value of India holding: 210m x 9% = 18.9m Total new value of India holding: 18.9m + 2.31m = 21.21m. Percentage representation: 21.21m / 210m = 10.1%
PSL Numerical Test: Data Context 4
Pie charts with several % components (of total sales, costs or investment value)
Solution to Question 12: If 11% of the value of the China holding is moved to India, what proportion of the
total fund will the India investment represent?
Brazil 5% China 10% India 9% Russia 12% UK 39% US 25%
