SHL PRACTICE TESTS
CONTENTS
To take advantage of this Formula Cheat Sheet, it is important you practise every element in context
with practice questions.
Numerical Reasoning Tests normally require the following skills:
1.
2.
3.
4.
5.
6.
7.
Addition
Subtraction
Multiplication
Division
Averages
Percentages
Ratios
These are often presented in topics such as:
a)
b)
c)
d)
e)
f)
g)
h)
Speed, time and distance
Currency / foreign exchange
Labour or machine productivity
Energy production
Income, Turnover and Profit
Company valuation and share price
Fuel economy and car value
Cost and value of services, e.g. consultancy
However, all Numerical Reasoning Tests do not require any knowledge of these topics. They simply
require you to interpret the question correctly and apply the correct mathematical methods to answer
the question.
AVERAGES
Average
A central / mean value of a given set of numbers.
Example:
1, 6, 3, 7, 2, 10
Weighted Average
A method of computing an average when some elements carry more weight than others.
(
)
(
)
Example:
Item
Purchases
Cost
Total
Red Toy
100
£1.50
£150
Blue Toy
150
£0.50
£75
Green Toy
200
£3.00
£600
TOTAL
450
£825
Average transaction cost = weighted average =
This is slightly higher than (£1.50 + £0.50 + £2.00) / 3 due to the green toy skewing the weighted
average.
PERCENTAGES AND FRACTIONS
Percentage
Any proportion or share in relation to a whole, often expressed as 100%.
(
)
Calculate a percentage
For example, calculating one quarter into a percentage is as follows:
(
)
Percentage Change
An increase or decrease in which a variable gains or loses magnitude or value.
A positive figure shows a percentage increase.
A negative figure shows a percentage decrease.
For example, a stock appreciates in value from £1.00 to £1.20, what is the percentage change?
However, if the price of the stock depreciated from £1.20 to £1.00 we would calculate as follows:
(
)
(
)
Percentage Difference
The relative percentage difference between two arbitrary figures, where you cannot determine the
original value.
)⁄
(
For example, Shop A receives $360 in sales a day whereas Shop B receives $420 in sales, what is the
percentage difference?
)⁄
(
(
)⁄
We do not need the minus sign as we cannot determine the original value.
Percentage Points
Refers to an absolute increase or decrease expressed in percentages.
Ratios
The relative size of two or more values, usually separate by a colon sign.
a:b is given as a ratio
N is the total sum of items
The number of a items = (
)
For example, there are 120 people in a theatre. The ratio of men to women is approximately 2:5. How
many women are there?
(
)
We round up in this instance as it is not possible to have 0.7 of a person.
RATE FORMULAS
Speed, Time and Distance
For example, John drove 20 miles along a
highway for 20 minutes. What was John’s
average speed?
Distance = 20 miles
Time = 20 minutes or 0.33 hours
Speed = 20 / =0.33 = 60 miles per hour
Source: BBC
Converting miles per hour into metres per second
Assuming 1 mile = 1609 metres (will be given in test)
3600 seconds = 1 hour
For example, convert 70 mph into m/s.
(
)
Converting kilometres per hour into metres per second
For example, convert 70 km/h into m/s.
(
Converting metres per second into miles per hour
For example, convert 31.29 m/s into mph.
)
FINANCE
Return on Investment
Measures the profitability of an investment expressed as a percentage.
Fixed and variable costs
Fixed costs: Often called overheads, are the costs that do not change with output.
Variable costs: costs that vary with output.
Profit Margin
Measures the ratio of sales to earnings.