Kenexa Numerical Test Tutorial Sample

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Data Context 2 Price Indices

PSL Numerical Test: Data Context 2 Price indices 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. 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

A: $744.86

$ Price per ton (31-Dec)

Consumer Price Index (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%

B: $567.89

C: $652.65

D: $788.78

E: $444.12

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? Task:

Solution:

Calculate the compounded price growth of corn for the 4 years (from 6 th to 10th year), then multiply Year 6 price by this number. 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

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. 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.

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%

Data Context 8 Comparing Several Companies

PSL Numerical Test: Data Context 8 Comparing Market Shares Typically compares market shares of one or several companies in a specific market in terms of revenue, sales or costs. Question 29: Between which two years did WPP’s percentage share of the global advertising market sales increase?

Global Advertising Market Sales ($ billions) 25

billions $

20

22.02 23.92

23.61

22.54

15

10

12.43

13.33

2006

2007

19.22

15.68

16.75

2009

2010

18.53 17.58

WPP The rest

14.68

5

A: 2006-2007

B: 2007-2008

2008

C: 2008-2009

2011

D: 2009-2010

E: 2010-2011

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?

Solution:

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. 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

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 spikes in linear graphs for quick answers.

Global Advertising Market Sales ($ billions) 25 20 billions $

Task:

22.02 22.54

23.61

15 10

12.43 13.33

14.68

23.92

19.22

15.68

16.75

2009

2010

18.53 17.58

The rest

5 2006

2007

2008

WPP

2011

Data Context 4 Pie charts with value components

PSL Numerical Test: Data Context 4 Pie charts with several % components (of total sales, costs or investment value) Pie charts are used for data representation, especially, when the data has various compositions. Most common pie charts show sales, cost and investment values. 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? Current Value of Global Government Bond Fund Total value = £210 million US 25%

Brazil 5%

China 10%

India 9% Russia 12%

UK 39%

A: 11.7%

B: 12.5%

C: 10.1%

D: 9.9%

E: 9.5%

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? Task: Solution:

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. 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%

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%

Current Value of Global Government Bond Fund US 25%

UK 39%

Total value = £210 million Brazil China 5% 10%

India 9% Russia 12%

WHAT YOU JUST READ IS A SAMPLE FROM KENEXA STYLE NUMERICAL REASONING TEST TUTORIAL EBOOK

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