Images

Introduction to this format

This type of numerical reasoning question is slightly more difficult than those given in the previous chapter. In this chapter the questions are sentence-based, requiring you to extract the appropriate calculation from the information given. More complex questions based on tables and graphs can be found in the chapters that follow.

image

The ‘milk round’ is a metaphor traditionally used in the UK to describe the process of companies visiting universities each year to advertise the opportunities available and recruit graduates – the metaphor being based on Britain’s long-standing door-to-door milk delivery service. Recruiters are generally large business organisations with their own in-house graduate trainee schemes. Since the late 1990s this process of physically visiting universities has given way to an online version where graduates can research training schemes and apply for jobs.

Graduate aptitude tests have always formed some part of the graduate recruitment process but, in recent years, with the dramatic increase in numbers of graduates, their use has become more widespread as an effective way for companies to assess large numbers of graduates. Numerical reasoning tests are commonly used both as a means of selecting graduates for interview and as a part of the interview process.

There are many websites that offer free practice opportunities for this popular test format. Search under ‘numerical reasoning test practice’ and take your pick.

Guidance for numerical comprehension tests

The practice questions appear in sets of 10 questions. Each of these is followed by their respective 10-answer explanations. You are advised to:

  • allow yourself 3–4 minutes to complete each set of 10 questions;
  • read each question carefully – twice if necessary;
  • choose the correct answer from the multiple-choice options shown;
  • check your answers against the answer explanations that follow the test once you have completed all 10 questions;
  • do this before you move on to the next test so that you can apply anything you have learnt immediately to aid your memory;
  • use a calculator to answer the questions.
image
  • Keep things simple whenever possible so that you can focus on getting the calculation correct.
  • Don’t be distracted by complex business language, the size of the figures or the measurement units. Nine times out of ten the measurement units will be constant throughout the question and answer.
  • If you can get the right answer by doing a rough calculation then by all means do so.

Numerical comprehension practice test 1

1A financial company’s balance sheet includes property assets of £212 million and £40 million in derivative assets. What is the effect on the balance sheet of the property assets rising by a quarter and the derivative assets dropping by three tenths?
(A) £265 million lower
(B) £41 million lower
(C) £12 million lower
(D) £41 million higher
(E) £265 million higher
2The sales of a multinational company are $480,000 in the Asia-Pacific region and $440,000 in the European region. If the total world-wide sales are $1,150,000 what fraction do these two regions combined represent?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 2/3
(E) 4/5
3The total regional assets of a global oil company are $950 million in North America and $178 million in Canada. What percentage are these combined regional assets of the total global assets of $9,400 million?
(A) 9.4%
(B) 10%
(C) 10.4%
(D) 12%
(E) 12.4%
4A transatlantic company’s quarterly costs are $48,000 in their sales division and $64,000 in their marketing division. What is the ratio of the sales to marketing costs?
(A) 2:3
(B) 3:2
(C) 3:4
(D) 4:3
(E) 3:5
5The global marketplace for outsourcing has been predicted to grow from £234,000 million in 2008 to £319,000 million in 2011. What is the total % increase predicted to be over these three years (to one decimal place)?
(A) None of these
(B) 2.1%
(C) 24.2%
(D) 36.3%
(E) 48.4%
6In an employee survey of 225 employees the response rate was six out of 10. How many employees did not complete the survey?
(A) 40
(B) 60
(C) 90
(D) 135
(E) Can’t tell
7A company pays an interim dividend of 6.2p per company share. A shareholder has 3,250 shares. What is the total value of their interim dividend payment?
(A) £201.50
(B) £211.50
(C) £325.00
(D) £2,015.00
(E) £3,250.00
8An Internet company pays corporation tax at 21%. If the amount of corporation tax paid is £143,850 how much are the company’s taxable profits (in £1,000s)?
(A) 80
(B) 600
(C) 650
(D) 680
(E) 685
9Market expectations are that a house builder’s annual profits will fall by 35%. If the previous year’s annual profits were £4.6 million what are the expected profits for the current year (in £100,000s)?
(A) 29.70
(B) 29.90
(C) 30.10
(D) 2.97
(E) 2.99
10In France the monthly sales of a new cosmetics product were €60,600. If the sales in Germany and Spain were each a third of this, what were the total sales across the three European countries (in euros)?
(A) 101,000
(B) 100,000
(C) 91,000
(D) 11,000
(E) 10,100

Review your answers to practice test 1

1Answer (D) is correct: £41 million higher
£212 million × 1/4 = £53 million
£40 million × 30/100 = £12 million
£53 million – £12 million = £41 million
2Answer (E) is correct: 4/5
$480,000 + $440,000 = $920,000
$920,000/$1,150,000 = 920/1,150 = 4/5
3Answer (D) is correct: 12%
$950 million + $178 million = $1,128 million
$1,128 million/$9,400 million × 100% = 12%
4Answer (C) is correct: 3:4
£48,000:£64,000 = 3:4
5Answer (D) is correct: 36.3%
£319,000 million – £234,000 million = £85 million
£85 million/£234,000 million × 100% = 36.3%
6Answer (C) is correct: 90
100% – 60% = 40% of employees did not complete the survey
225 × 40/100 = 90 employees
7Answer (A) is correct: £201.50
6.2p × 3,250 shares = £201.50
8Answer (E) is correct: 685 (in £1000s)
£143,850 = 21%
100% = 100 × 143,850/21 = 685,000
9Answer (B) is correct: 29.90 (in £100,000s)
£4.6 million × 65/100 = £2.99 million
10Answer (A) is correct: 101,000
French monthly sales = €60,600
German sales = €20,200
Spanish sales = €20,200
Total sales across the three European countries (in euros) = 60,600 + 20,200 + 20,200

Numerical comprehension practice test 2

1A multinational shipping company has annual profits of $42.6 million. What is this in £ (at an exchange rate of $1.40 to the £)?
(A) £300 million
(B) £30.61 million
(C) £30.52 million
(D) £30.43 million
(E) £30 million
2At an exchange rate of €1.20 to the £, what is the cost (in £) of three boxes of office paper at €6.60 per box?
(A) £12.50
(B) £14.50
(C) £16.50
(D) £18.50
(E) £23.76
3A company profit and loss account contains the following operating costs: infrastructure (£2.1 million); transport (£2.8 million); and salaries (£7.7 million). What is the ratio between the operating costs for infrastructure, transport and salaries?
(A) 3:4:11
(B) 2.8:2.1:7.7
(C) None of these
(D) 28:77:21
(E) 7:8:1
4Sales team A makes sales of £92,500, £69,000, £115,600 and £89,000 for Quarters 1–4, respectively. If there were 15 members in this team, what sales is each sales person making on average per month (to the nearest £)?
(A) £2,034
(B) £16,474
(C) £32,949
(D) £43,932
(E) £65,898
5A broadband provider has two packages: one costs £24.00 per month, the other an extra £5.00 per month for a superfast broadband option. What is the annual difference in cost between the two packages?
(A) No difference
(B) £40.00
(C) £50.00
(D) £60.00
(E) £70.00
6The current year’s UK earnings for an airline operator are predicted to be 15% less than last year’s £4.85 million. The current year’s US earnings are predicted to be 25% more than last year’s £10.3 million. What is the difference in earnings predicted to be between the UK and US (to the nearest million)?
(A) £5 million
(B) £6 million
(C) £7 million
(D) £8 million
(E) £9 million
7The market share of a leading CD retail chain is 28.4%. Its two main rivals have 14.2% and 10.8% of the market share, respectively. Given a total market size of €53 million, what is the value of the market outside these three retailers (to the nearest million euros)?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
8A world-wide tour operator has 3,500 employees. There is an average of 250 employees in each of the eight European countries where it operates. What fraction of employees work in Europe?
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
(E) 5/7
9An IT consultancy company pays 8% of its total annual costs on rent and 74% on salaries. If its total annual costs are £620,000, what is the total of the other costs (excluding rent and salaries)?
(A) £49,600
(B) £99,200
(C) £111,600
(D) £229,400
(E) £458,800
10The average salary of an electrician at a car manufacturer is £44,500 and is due to rise in line with inflation of 3% a year over the next 3 years. What is the electrician’s average salary in 3 year’s time?
(A) £45,835
(B) £47,626
(C) £48,505
(D) £48,626
(E) £48,835

Review your answers to practice test 2

1Answer (D) is correct: £30.43 million
$42.6 million/1.40 = £30.43 million
2Answer (C) is correct: £16.50
€6.60 × 3 = €19.80
19.80/1.20 = 16.50
3Answer (A) is correct: 3:4:11
Infrastructure (£2.1 million): transport (£2.8 million): salaries (£7.7 million)
2.1:2.8:7.7
Dividing by 7 gives 3:4:11.
4Answer (A) is correct: £2,034
Total sales of team A = £92,500 + £69,000 + £115,600 + £89,000 = £366,100
Average per sales person = £366,100/15 = £24,407
Average per sales person per month = £24,407/12 = £2,034
5Answer (D) is correct: £60.00
Package 1 = £24.00 × 12 = £288.00 a year
Package 2 = (£24.00 + £5.00) × 12 = £348.00 a year
Annual difference in cost between the two packages = £348.00 – £288.00 = £60.00
6Answer (E) is correct: £9 million
The current year’s UK earnings for an airline operator are predicted to be 15% less than last year’s.
UK earnings: £4.85 million × 85/100 = £4.1225 million
US earnings: £10.3 million × 125/100 = £12.875 million
Difference in earnings predicted between the UK and US = £12.875 million – £4.1225 million = £8.7525 million
To the nearest million: £8.7525 million = £9 million
7Answer (A) is correct: 25 (to the nearest million euros)
28.4% + 14.2% + 10.8% = 53.4%
100% = €53 million
Value of the market outside these three retailers = 100% – 53.4% = 46.6%
46.6/100 × €53 million = €24.7 million
8Answer (D) is correct: 4/7
250 × 8 = 2,000
2,000/3,500 = 4/7
9Answer (C) is correct: £111,600
8% + 74% = 82% on rent and salary costs
Total annual costs = £620,000 = 100%
Total of other costs (excluding rent and salaries) = 18% of £620,000
£620,000 × 18/100 = £111,600
10Answer (D) is correct: £48,626
Year 1 increase = £44,500 × 103/100 = £45,835
Year 2 increase = £45,835 × 103/100 = £47,210
Year 3 increase = £47,210 × 103/100 = £48,626

Numerical comprehension practice test 3

1Demand for office rental property in an office block fell by a quarter during 2008. If it was 82% full at the start of 2008 what was the percentage occupancy by the end of 2008?
(A) 615%
(B) 61.5%
(C) 56%
(D) 5.6%
(E) 6.15%
2A sales rep spends one-fifth of his time travelling and a third of his time meeting clients. In a typical 30-hour week how many hours approximately does this sales rep spend on other tasks (apart from travelling and meeting clients)?
(A) 14
(B) 12
(C) 11
(D) 9
(E) 7
3A consultancy’s operating costs to turnover ratio is 3:20 each year. If the company’s turnover is £213,250 in Year 1, £268,460 in Year 2 and £328,915 in Year 3 what are the total operating costs for the three-year period?
(A) £121,594
(B) £211,694
(C) £328,915
(D) £528,894
(E) £810,625
4An expenses budget of £640 is spread amongst seven teams, although one team gets twice as much as the others who each receive an equal amount. How much do the other six teams receive each?
(A) Can’t say
(B) £60
(C) £70
(D) £80
(E) £90
5Of the 42 staff employed by a market research company in a ratio of 2:1 at two sites, the workforce at the company’s smaller site is to be cut by a half. What fraction of total staff does this reduction represent?
(A) 1/9
(B) 1/8
(C) 1/7
(D) 1/6
(E) 1/5
6Advertising spend by a utility company is predicted to grow by £125,000 a year. If the current advertising spend is £725,000 then what will the advertising spend be in five year’s time?
(A) £125,000
(B) £135,000
(C) £1,250,000
(D) £1,350,000
(E) £1,400,000
7The carbon dioxide emission rate for the average car is 145 g/km. How much carbon dioxide (to the nearest kg) would be emitted over a 145 km journey?
(A) 21 kg
(B) 19 kg
(C) 17 kg
(D) 15 kg
(E) 12 kg
8The market for online advertising in the UK is estimated to be worth £3.2 billion. The error band for this is 1/20th higher and 1/20th lower. What are the lower and higher estimates of the online advertising market?
(A) £3.02 billion–£3.34 billion
(B) £3.04 billion–£3.36 billion
(C) £3.06 billion–£3.38 billion
(D) £3.08 billion–£3.40 billion
(E) £3.10 billion–£3.42 billion
9A company’s value increased by 4% in Year 1, by 5% in Year 2 and by 4.5% in Year 3. If the company was valued at £2.15 million at the start of Year 1 then what is its value at the end of Year 3?
(A) £2.41 million
(B) £2.44 million
(C) £2.45 million
(D) £24.1 million
(E) £24.5 million
10The total cost of a litre of milk is 24.5p. What is the profit (to the nearest £) on 2,500 gallons of milk that is sold in two-litre cartons for £1.05 (1 gallon = 4.546 litres)?
(A) £5,967
(B) £3,182
(C) £2,784
(D) £597
(E) £318

Review your answers to practice test 3

1Answer (B) is correct: 61.5%
82% × 3/4 = 61.5%
2Answer (A) is correct: 14
1/5 + 1/3 = 3/15 + 5/15 = 8/15
1 – 8/15 = 7/15
7/15 × 30-hour week = 14 hours
3Answer (A) is correct: £121,594
Total costs = £213,250 + £268,460 + £328,915 = £810,625
Operating costs = 3/20 × £810,625 = £121,593.75
4Answer (D) is correct: £80
Let x = amount that each team gets:
2x + 6x = 640
x = 640/8 = 80
5Answer (D) is correct: 1/6
42 staff in a 2:1 ratio means that 14 staff work at one site and 28 staff at the other site. So, cutting the workforce at the company’s smaller site by 50% = seven staff:
7/42 = 1/6
6Answer (D) is correct: £1,350,000
£725,000 + (5 × £125,000) = £1,350,000
7Answer (A) is correct: 21 kg to the nearest kg
145 × 145 g = 21,025 g
1,000 g = 1 kg
So 21,025 g = 21,025 kg
8Answer (B) is correct: £3.04 billion–£3.36 billion
£3.2 billion × 95/100 = £3.04 billion
£3.2 billion × 105/100 = £3.36 billion
9Answer (C) is correct: £2.45 million
This requires you to work out cumulative interest:
£2.15 million × 104/100 = £2.23 million
£2.23 million × 105/100 = £2.34 million
£2.34 million × 104.5/100 = £2.45 million
10Answer (B) is correct: £3,182 (to the nearest £)
Note firstly that profit = total sales – total cost.
Note secondly that the calculation needs to be in litres throughout.
Milk quantity sold (in litres) = 2,500 gallons × 4.546/2
So, total sales (of 2,500 gallons of milk) = £1.05 × (2,500 × 4.546/2) = £5,966.63
Total cost (using litres of milk) = 24.5p × 2,500 × 4.546 = £2,784.43
Profit = total sales – total cost = £5,966.63 – £2,784.43 = £3,182.20
..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset