NUMERICAL REASONING

GRAPHS AND TABLES TEST

 

This is a numerical reasoning test similar to those used by many employers when recruiting graduates. It also shows how to work out the answers. This test is very similar to those used for finance job recruitment: banking, accountancy and insurance.

Although this test is fairly typical of the types of test many employers use, please remember that it is for practise only. It is not being taken under examination conditions, and therefore although you are given a score, this is just to satisfy your curiosity and to give you a target to aim for.

You are strongly recommended to use a calculator and scrap paper during this test. Please have a pen and scrap paper to hand before you start.

The test will start with 3 example questions which will not be marked or timed. The test consists of 22 questions and you will have 25 minutes to answer these. As this is a practice test you can continue to answer questions after the formal test has finished if you wish to. Click on the "Go to First Example" button below to begin. Click on the button to the left of your answer to answer it. You can change your answer by clicking on another button.You can also go back to the previous question, by clicking on the previous question button. Questions have graphs or tables which you will need to refer to. These will be displayed above the question.

 

WHAT YOUR SCORE MEANS

As mentioned before, this test is for practice only, so you should not regard your result as of importance chiefly because the test was not taken under proper test conditions e.g. in a silent room with no disturbances. Your performance can also be distorted if you have a cold, or have not slept well. Also, evidence shows that international students or those from ethnic minorities may be disadvantaged in this type of test, due to language and cultural differences. If your first language is not English, your score is likely to be lower on verbal tests than native English speakers. Mature students may also sometimes be disadvantaged and you should remember that your degree subject may change your performance - for example scientists are likely to do better on mathematical tests and Humanities students on verbal tests. Even your ability to use a mouse may influence your score! Having said all this it is still natural for you to want some feedback on your performance.

Score

If your maths is a bit rusty, an excellent place to brush up your skills is the BBC Skillswise web site

For further example tests and help with tests, see our Aptitude Tests page with tips on how to pass tests. There are now several free practice aptitude tests available on the University of Kent Careers web site. The tests are Numerical Reasoning , Verbal Reasoning , Verbal (Synonyms) , Letter Sequences (logical thinking), Diagrammatic/Spatial and computer aptitude

The answers to this test are not confidential and are as follows (answer numbers refer to the option choice between 1 and 5):

 

Question

1

2

3

4

5

Answer

3

1

2

4

2

Question

6

7

8

9

10

Answer

5

1

2

5

2

Question

11

12

13

14

 

Answer

4

4

5

3

 

Question

15

16

17

18

 

Answer

3

1

5

5

 

Question

19

20

21

22

Answer

2

3

2

2

 

How to work out the answers

 

EXAMPLE 1) How many owner-occupiers lived in semi-detached properties? (to nearest thousand)
Total sample = 127,000
29% live in semi-detached properties
29% x 127,000 = 29/100 x 127000 = 36830
37,000 to nearest thousand

EXAMPLE 2) How many owner-occupiers lived in flats and terraced properties? (to nearest thousand)
Total sample = 127,000
12% live in flats and 21% live in terraced houses
33% x 127,000 = 33/100 x 127,000 = 41,910
42,000 to nearest thousand

EXAMPLE 3) 59% of the people living in bungalows were retired. How many people is this? (to nearest thousand)
20% of 127,000 live in bungalows = 20/100 x 127,000
59% of these are retired
59/100 x 20/100 x 127,000 = 14986
15,000 to nearest thousand

ACTUAL TEST

1) What was the population of Botsibia (millions) in 2006 ?
Number of cars in Botsibia in 2006 = 5.3 million
0.32 cars per person in Botsibia in 2006
Therefore 1 car for every 3.125 people (1 divided by 0.32)
Population = number of cars x Number of people per car = 5.3 x 3.125 = 16.5625 million

2) How many million cars were there in Korgolia in 2001?
Population of Korgolia in 2001 = 18.3 million
Number of cars per person = 0.5
Number of cars = population x number of cars per person = 18.3 x 0.5 = 9.15 million = 9.2 million to 1 decimal place

3) Which country had the greatest percentage change in the number of cars per person between 2001 and 2006?

You have to calculate the percentage for each country for 2001 and 2006: a lot of work, although those strong on mental arithmetic may be able to make rough estimates to quickly remove the countries with lower percentage changes.

E.g. to calculate the percentage ownership of cars in Normark in 2001. Number of cars per person = number of cars / population = 17 / 22.5 = .756. To convert this to a percentage multiply by 100 = 75.6%. the other countries are done in the same way, giving the results shown below. For Korgolia in 2001 and Botsibia in 2006, we are already told the number of cars per person.

Normark Serbistan Botsibia Velumbia Korgolia
2001
75.6%
19.7%
31.6%
94.6%
50.3%
2006
86.3%
31.9%
32.1%
101.8%
53.7%

 

Serbistan 19.7% to 31.9%

4) If in 2001 the ratio of cars per person in Velumbia had been the same as that of Normark, how many cars would there be in Velumbia?
The ratio of cars per person in Normark in 2001 is 17 million cars divided by 22.5 million people = 0.7556 cars per person.
Therefore the number of cars in Velumbia would be:
The population of Velumbia in 2001 x the ratio of cars per person in Normark
= 9.2 million people x 0.7556 = 6.95M cars

5) If between 1987 and 2007 the trend for fashion ties had been the same as for cravats, how many fashion ties would have been sold in 2007?
Cravats sold in 1987 = 4074
Cravats sold in 2007 = 4116
Percentage increase in sales of cravats 1987 to 2007 = (4116 / 4074 x 100) - 100 = 1.03%
Fashion ties sold in 1987 = 71400
Multiply by 101.03% = 71400 x 101.03 = 72135 = 72100 to nearest 100

6) For all types of tie together, what is the percentage decline between 2002 and 2007? (to nearest five percent)
Total sales in 2002 = 83820

Total sales in 2007 = 56000
Percentage of sales 2007 over sales 2002 = sales in 2007 / sales in 2002 x 100 = 56000 / 83820 x 100 = 66.8
Therefore drop in sales = 100 - 66.8% = 33.2% drop = 35% to nearest 5%

7) What is the approximate absolute change in percentage market share for fashion ties between 1987 and 2007?
Market share in 1987 = number of fashion ties sold divided by total number of ties sold x 100

= 71400 / 134484 x 100 = 53.1%
Market share in 2007 = 21371 / 56000 x 100 = 38.2
Change = 14.9% = 15% to nearest percentage point

8) If the average retail price for silk ties in 2002 was £17.50 plus Value Added Tax at 17.5% what was the total value of silk ties sold in 2002? (to nearest £1000)
Price of one tie = £17.50
Price of one tie including tax = £17.50 x 1.175 = £20.56
Total value of ties sold = price per tie x amount sold = £20.56 x 18557
= £381,531.92
= £382,000 to nearest £1000

9) How many Dollars was one Euro worth in May?
Value of 1 Pound in Dollars in May = $1.984
Value of 1 Pound in Euros in May = E1.468
Value of 1 Euro in dollars = 1.984/1.468 = $1.35

10) What was the percentage drop in the value of the Pound compared to the Euro over the year?
Value of Pound in Euros in January = 1.507
Value of Pound in Euros in December = 1.384
Change in value = 1.507 - 1.384 = 0.123
Percentage change = (change in value / original value) x 100
= (0.123 / 1.507) x 100
= 8.16% = rounds to 8%

11) If you converted 67 Euros to Pounds in February, how many Dollars (to the nearest Dollar) would this be worth in November?
£1 = 1.497 Euros in February
Therefore 67 Euros = 67 / 1.497 pounds = £44.76
£1 = $2.071 in November
Therefore £44.76 = 44.67 x 2.071 dollars = $92.70 = $93 to nearest dollar

12) What was the percentage increase in the price of oil between 1998 and 2006?
1998 price = 12.7
2006 price = 65.1
Percentage increase in price = (Change in price/original price) x 100
Change in price = 65.1 - 12.7 = 52.4
Original Price = 12.7
Percentage increase in price = (52.4 / 12.7) x 100
= 4.126 x 100 = 412.5% which rounds to 413%

13) If the total oil supply had grown at the same rate as the former USSR oil supply between 2000 and 2006 how much would this have exceeded the demand in 2006?
USSR oil supply in 2000 = 7.9. In 2006 oil supply = 12.2.
Therefore change in USSR supply = 12.2/7.9 x 100 = 154.4%
Total oil supply in 2000 = 77.1
Supply in 2006 = total supply in 2000 x change in supply for USSR 2000-2006
= 77.1 x 1.544 = 119.0
Demand in 2006 = 84.7.
Therefore difference between supply and demand = 119 - 84.7 = 34.3

14) In which year was the largest combined change in supply from the previous year for OPEC, the former USSR and other Non-OECD countries?

1999 2000 2003 2004 2005 2006
OPEC total 29.6 31 30.8 33.1 34.2 34.3
Former USSR 7.5 7.9 10.3 11.2 11.6 12.2
Other non-OECD 16 16.2 17.1 17.7 18.2 18.7
Total 53.1 55.1 58.2 61.9 64.1 65.3
Change from previous year
-
2 3.1 3.7 2.2 1.2

 

Change in 2004 was 3.7 from the previous year: the largest amount.

15) Which company had the widest range of share prices over the 5 years?
Pilemin Airlines Share price range 1.45 - 180 = 35p
RentaBanga 1.55 - 170 = 15p
Rupt Bank 0.45 - 1.65 = £1.25
Cash Casinos 0.40 - 1.20 = 80p
Stackem Supermarts 1.55 - 2.00 = 45p

16) Which year had the widest range of share prices?
2002 Range 0.4 - 1.95 = 1.55
2003 0.55 - 2.00 = 1.45
2004 0.85 - 1.75 = 0.90
2005 0.75 - 1.85 = 1.10
2006 0.9 - 1.65 = 0.75

17) Between 2002 and 2006 what was the approximate total change in share prices for all companies?
Total share price 2002 = £5.80
Total share price 2006 = 7.20
Percentage increase in price = (Change in price/original price) x 100
= (1.40 / 5.80) x 100 = 24.1% = + 25% to nearest 5%

18) If the proportional change in share price for Pilemin Airlines had been the same as that for Rupt Bank between 2002 and 2006 what would have been the value of Pilemin Airlines shares in 2006?
Share price for Rupt Bank 2002 = £0.45
Share price for Rupt Bank 2006 = £1.65
Change in share price for Rupt Bank 2002-06 = 1.20 / 0.45 = 266%
Price of Pilemin Airlines shares in 2002 = 1.45
Increase in price of Pilemin Airlines shares 2002 - 2006 = Price in 2002 x Change in share price for Rupt Bank
1.45 x 2.66 = £3.86
Therefore price in 2006 = original price plus increase in price = £1.45 + £3.86 increase = £5.31

19) If in 2006-07, the average share price changes by the same percentage as the average percentage increase between 2002 & 2003 for all these companies, what will be the change in average share price for all these companies between 2006 & 2007?
Total share price 2002 = £5.80
Total share price 2003 = 6.40
Percentage increase in price = (Change in price / original price) x 100
Change in average share price 2002 - 2003 = 0.60/5.80 x 100 = 10.34%
Average share price in 2006 = £7.20 / 5 = £1.44
Change in share price 2007 - 2007 = £1.44 x 10.34% = 14.89p = rounds to 15p

20) What was the approximate range in CPI values in 2001?
Largest = + 9.1 (Hungary)
Smallest = - 0.8 (Japan)
therefore range = 9.9 rounds up to 10

21) What was the mean percentage change in CPI for all countries from the previous year in 1998?
Total CPI change for all countries in 1998 = 0.9+0.7+0.6+14.2+2.0+0.7+15.9+1.8+1.6+1.5 = 39.8
Average CPI change = total change for all countries / number of countries = 39.8/10 = 3.98 which rounds to 4

22) If a printer cost 200 US Dollars in 1996 how much would it cost in 2000 assuming the price grew in line with US changes in CPI?
Cost in 2000 = original price x change in CPI 1996-97 x change in 1997-98 x change in 1998-99 x change in 1999-2000
= 200 x 1.023 x 1.015 x 1.022 x 1.034 = 219.45 which rounds to 219 dollars

 

 

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