Table Of ContentWorkbook
Numerical Reasoning tests
Careers Service
Contents
Contents.........................................................................................................................3
1. Numeric Reasoning Questions...................................................................................4
1.1. Tables of Data.....................................................................................................4
1.2 Maths Problems..................................................................................................4
2. Questions on Data Tables.........................................................................................5
2.1 Solutions............................................................................................................14
2.2 Further Questions on Data Tables......................................................................23
2.3 Solutions............................................................................................................24
3. Typical Maths Questions with Solutions.................................................................29
3.1 Maths Questions to Try......................................................................................33
3.2 Solutions - Maths Questions to Try..................................................................34
4. Question on Graphs..................................................................................................37
4.1 Solutions............................................................................................................38
3
1. Numeric Reasoning Questions
These notes cover two common types of question.
(cid:120) Answering questions about tables of data.
(cid:120) Solving maths problems.
1.1. Tables of Data
The first section is to do with reading information from tables of data and answering
questions about the data. This section is split into three parts.
1. A series of example questions which you answer. There will be partial help
plus guidance to answering the question using Hint Boxes. Typically you will
fill in the required information in the Hint Boxes and then this should give you
the answer.
2. Full answers to the questions so that you can compare your results.
3. Another new set of questions, without help, for you to do. Solutions are
available.
Required Numeracy Skills
You will need the following skills in order to tackle these questions:
(cid:120) Carefully reading of tables of data and understanding what is being
asked of you.
(cid:120) Comparing and making judgements on the basis of numerical values.
(cid:120) Estimating values quickly to give ball-park figures on which decisions
can be made.
(cid:120) Using percentages and ratios – in particular how to convert ratios to
percentages and also how to work out a percentage increase.
The Numeracy Refresher Booklet (NRB) covers all these important skills. For
example you may have to brush up on fractions or decimals before you can
confidently answer questions about percentages or even estimate ratios. Also you will
have know how to write decimals to a given number of decimal places – the NRB
covers this as well.
1.2 Maths Problems
You will be asked to solve problems which may involve the use of basic numeracy
skills such as calculating and using percentages and/or ratios. So all the basic
numeracy skills you needed for analysing data tables will also be used.
These problems are often stated in terms of “real-life” or context specific questions
e.g. case-studies relevant to the employer’s core activities.
It is important to fully understand the question and what it is asking you to do before
you start calculating. This type of question is often failed because the student is
solving the wrong problem!
In these notes you are given sample questions together with solutions.
Finally you can then attempt a new set of questions – solutions are given.
Note that the Numeracy Refresher Booklet has been designed to help you with these
types of questions as well as the data table questions.
4
2. Questions on Data Tables
The following table describes the income of various industries over a five year period.
There are nine questions in this section and each has a Hint Box for you to fill in if
you need help. The data table is repeated on each page.
The next section 2.1 contains full solutions to all these problems.
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 1.
Which industry had the largest increase in the euro amount of income from
Year 3 to Year 4?
For example, Financial Services has an increase of 100-92=8 billion euros from year
3 to year 4.
Answer:
Hint Box:
Write the increase (in billions of euros) and find the largest
Financial Services increase= 8 billion euros
Telecommunications increase=
Engineering increase=
Agriculture increase=
Manufacturing increase=
Transportation increase=
5
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 2.
Which industry had the smallest increase in the euro amount of income from
Year 1 to Year 5?
For example, Financial Services has an increase of 110-70=40 billion euros from
year 1 to year 5.
Answer:
Hint Box
Write the increase (in billions of euros) and find the smallest.
Financial Services increase= 40 billion euros
Telecommunications increase=
Engineering increase=
Agriculture increase=
Manufacturing increase=
Transportation increase=
6
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 3.
Which industry experienced the largest percentage increase from Year 4 to
Year 5?
This means that you have to work out the increase from Year 4 to Year 5 as a
percentage of the income in Year 4 for each industry and find the biggest percentage
increase. For example Telecommunications had an increase of 1 billion dollars from
23 billion euros in year 4 to year 5 and the percentage increase was therefore
1
(cid:117)100% (cid:32) 4.35% to two decimal places.
23
(Calculating to one decimal place would probably have been enough – but it could be
possible that there were two industries with the same % increase to one decimal
place)
Answer:
Hint Box
Find the percentage increase (in billions of euros) and find the largest
Financial Services % increase=
Telecommunications % increase= 4.35%
Engineering % increase=
Agriculture % increase=
Manufacturing % increase=
Transportation % increase=
7
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 4.
Which industry had the least percentage change from Year 1 to Year 4?
This means that you have to work out the increase from Year 1 to Year 4 as a
percentage of the income in Year 1 for each industry and find the smallest
percentage increase.
For example Manufacturing had an increase of 233-193=40 billion euros from 193
billion euros in year 1 to 233 billion euros year 4 and the percentage increase was
40
therefore (cid:117)100% (cid:32) 20.73% to two decimal places.
193
(Once again taking two decimal places to be on the safe side.)
Answer:
Hint Box
Find the percentage change for each industry and find the least
Financial Services % increase=
Telecommunications % increase=
Engineering % increase=
Agriculture % increase=
Manufacturing % increase= 20.73%
Transportation % increase=
8
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 5.
a)If the trend in the Transportation industry were to continue, write down the
most likely income for Year 6.
b) Which of the above industries would you find difficult to predict a
reasonably accurate figure for Year 6?
As an example, consider Financial Services.
The differences between successive years are in billions of euro:
Year 2-Year 1 Year 3-Year 2 Year 4-Year 3 Year 5-Year 4
12 10 8 10
These fluctuate between 8 and 12, and have an average value of 10. Since there is no
clear trend we can put forward an increase of 10 as a ball-park figure.
So the prediction would be 110+10 =120 for year 6.
But now consider Manufacturing, we find the differences between successive years:
Year 2-Year 1 Year 3-Year 2 Year 4-Year 3 Year 5-Year 4
5 8 27 34
There is no clear pattern – we need more data. So I would find this difficult to predict
other than Year 6 would be an increase on Year 5.
a)Prediction for Transportation in Year 6?
b)Make an estimate for Year 6 for each industry– write a question mark
if difficult to predict.
Prediction for Year 6 (billions of euros)
Financial Services 120
Telecommunications
Engineering
Agriculture
Manufacturing ?
9
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 6.
Which type of industry shows the steadiest rate of growth in income during
this period of five years?
Some industries are growing by about the same amount every year. Find the one that
in your opinion has the steadiest growth i.e. the increases from one year to another
have the smallest fluctuation. For example Agriculture has the following differences
from one year to the next:
Year 2-Year 1 Year 3-Year 2 Year 4-Year 3 Year 5-Year 4
2 0 4 21
There is a major fluctuation in the growth of income between years 4 and 5 and so the
growth in Agriculture income over the five years is not particularly steady.
Industry with steadiest rate of growth:
10
INCOME OF INDUSTRIES (in billions of euros)
Industry Year 1 Year 2 Year 3 Year 4 Year 5
Financial Services 70 82 92 100 110
Telecommunications 17 20 21 23 24
Engineering 33 40 44 49 54
Agriculture 26 28 28 32 53
Manufacturing 193 198 206 233 267
Transportation 38 41 44 47 51
Question 7.
In how many instances did a type of industry make a gain of 10% or more over
the previous year listed?
Looking at Financial Services we have
(cid:120) Year 1 to Year 2 increase of 12 on 70 - more than 10% increase ( 10% of 70
is 7 and 12 is greater than 7)
(cid:120) Year 2 to Year 3 increase of 10 on 82 - more than 10% increase ( 10% of 82
is 8.2 and 10 is greater than 8.2)
(cid:120) Year 3 to Year 4 increase of 8 on 92 - less than 10% increase ( 10% of 92 is
9.2)
(cid:120) Year 4 to Year 5 increase of 10 on 100 – a 10% increase ( 10% of 100 is 10)
So 3 instances of 10% increases or more for Financial Services.
Now do the same for the other industries. Try not to use a calculator as it is easy to
work out 10% of any number – just move the decimal point to the left one place.
Fill in the following table.
For each industry, answer Y if growth is 10% or more, N if less than 10%. Then count
the number of Y’s and put in last column.
Do this for all industries.
Finally add up the numbers in the last column and put in the last cell in this column.
Yr1-Yr2 Yr2-Yr3 Yr3-Yr4 Yr4-Yr5 10% or more
Financial Services Y Y N Y 3
Telecommunications
Engineering
Agriculture
Manufacturing
Transportation
Total Number of instances of 10% or more increases
11
