C03 EXAMS (2001 - 2003)

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C03 - Fundamentals of Business Mathematics

21 May 20011.1The numbers of rejects from 50 samples of the same size is as follows:

Number of rejects in each sample: 0 1 2 3 4 5

Number of samples (frequency of rejects): 5 10 10 20 5 0

The arithmetic mean number of rejects per sample is

A 22 B 24 C 3 D 20

1.2 The unit price of Brand X in May 2000 and May 2001 was as follows:

Year 2000 2001

Unit price of Brand X 140 175

The price relative for Brand X in May 2001, with base May 2000 = 100 is

A 80 B 120 C 125 D 135

1.3 On which ONE of the following graphics can the Median readily be found

without further calculation?

A Bar chart B Cumulative frequency curve C Histogram D Pie

chart

1.4 A retailer buys a box of a product, which nominally contains Q units. The

planned selling price of each unit is P. If both P and Q have been rounded to

10%, then the maximum rounding error in total revenue is

A 10% B 20% C 21% D 01Q x

01P

1.5 The telephone costs of a company last year were 10,000, including Value Added

Tax(VAT) at 175%. It has been decided to allocate 60% of these telephone costs,

excluding VAT, to Central Administration and to allocate 30% of the remainder, excluding

VAT, to Finance.

The telephone costs (to the nearest ) to be allocated to Finance will be closest

to

A 990 B 1,021 C 1,100 D

1,135

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1.7 A companys market for computer supplies has trebled in value in exactly sixyears. The annual equivalent percentage growth rate in this market is (to 2decimal places) closest to

A 1225 B 2009 C 2457

D 3333

1.8 The following statements are often made about simple random sampling.

(i) It ensures a representative sample.

(ii)It eliminates selection bias.

Which one of the following is always true?

A (i) only B (ii) only C Both (i) and (ii) D Neither (i)

nor (ii)

1.9 A machine was purchased for 100,000. Depreciation is calculated using the reducing

balance method (that is, a constant percentage is applied each year to the written

downvalue). In the last balance sheet, the net book value of the machine, exactly four

years old, was shown as 50,000.

In the next balance sheet the machine should be shown to have a net book value,

rounded to the nearest 100, closest to

A 37,500 B 40,000 C 42,000 D 43,500

1.10 In a particular country, a tax at 40% is payable on any gains on house sales not due to

inflation. A house was purchased there for $75,000 and sold for $250,000. Over the same

period, the countrys house price (inflation) index rose from 120 to 240.

The tax (to the nearest $) payable on the house sale is

A $28,000 B $37,500 C $40,000 D $70,000

1.11 Each of the following diagrams shows a histogram of data with equal area. The verticaland horizontal scales of each histogram are identical. Which set of data (histogram) has the

largest standard deviation?

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1.12 The lengths of steel rods are Normally distributed with a mean of 100mm and a

standard deviation of 5mm.

The percentage of steel rods with a length of less than 95mm is closest to

A 5% B 16% C 20% D 34%

1.13 The calculation of a rank correlation coefficient [formula given in the

Mathematical Tables sheet 3 on page 19], shows that ten pairs of data are found to be

perfectly negatively correlated.

Therefore, the value of d equals

A zero B 165 C 330 D none of

these.

1.14 A 100,000 mortgage, with interest compounded at 11% each year, is to be repaid by

10equal year-end payments of X, the first being due one year after the mortgage was

contracted.

X is closest to

A 16,111 B 16,273 C 16,981 D 25,937

1.15 The quarterly sales (units) of a company are given in the table below.

Year Q1 Q2 Q3 Q4

1997 13 52 56 79

1998 29 43 48 80

1999 24 55 46 75

Read the following statements.

(i)Annual sales are static.

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(ii)The fourth quarter, Q4, has the highest quarterly sales in each of the three years.

(iii)The mean sales for the second quarter (Q2) equals the mean quarterly sales for the

whole period, 1997-99.

Which is true?

A (i) only B (i) and (ii) only C (ii) and (iii) only D (i), (ii) and

(iii)

1.16 An accountant has to check a sample of invoices. The invoices are divided into three

groups, by value: under 100, 100 500 and over 500. Samples are then

selected randomly from each group.

Which ONE of the following sampling methods is involved?

A cluster B multi-stage C quota

D stratified

1.17 The equations of two straight lines are given below:

Y = 7 + X Y = 9 + 3X

These lines intersect where the (X, Y) co-ordinates are equal to

A (1,6) B (1,6) C (1,8)D none of these

The following information is to be used for sub-questions 1.18 and 1.19

A scatter diagram shows the weekly total costs of production () in a certain factory plotted

against the weekly output (units). A broadly linear pattern is evident, with r = 09. The

regression equation is

COSTS = 1,500 + (15 x OUTPUT).

Fifty data points have been included in the analysis, with output ranging from 100 units to1,000units. Output next week is planned to be 500 units.

1.18 Read the following statements about estimates.

(i)Weekly fixed costs are approximately 1,500.

(ii)Variable costs are approximately 15 per unit on average.

(iii)Next weeks production costs are likely to be about 9,000.

Which one of the following is true, all other things being equal?

A (i) and (ii) only B (i) and (iii) only C (ii) and (iii) only D (i), (ii) and

(iii)

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1.19 Read the following statements:

(i)There is very little correlation between weekly costs of production and production level.

(ii)90% of the variation in weekly costs is attributable to the amount produced.

(iii)Given the information, any forecast using the regression equation is likely to be very

unreliable.

Which one of the following is justified?

A (ii) only B (i) and (iii) only C (ii) and (iii) only D None of

them

1.20 Three independent experts have estimated the probability of a companys futureannual sales:

Sales High [1m] Medium [0 5m] Low [0 25m]

Expert W 02 03 05Expert X 0.1 04 05Expert Y 01 06 03

The highest expected value for the companys estimated annual sales is given by

A W only. B X only. C Y only. D Both W and

Y.

1.21 Details of an index number are given below:

Group Base Weight Index

Food & Drink 100 50 140

Travel & Leisure 100 30 130

Housing 100 20 120

All items 100 100 ??

The All items index number is closest to

A 130 B 133 C 135 D 146

1.22 For the following set of ten numbers, the median is 15:

10 11 12 13 14 16 17 18 19 20+X

This statement is false if X equals

A 5 B 4 C 3 D 2

1.23 Which of the following could have a value of 2 (minus 2)?

(i)Correlation coefficient

(ii)Slope of a regression line

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(iii)Variance

A (ii) only B (i) and (ii) only C (i) and (iii) only D (ii) and

(iii) only

1.24 The following data represents a time series for the last seven days:

2 6 10 6 10 14 10

Which ONE of the following moving averages would result in a straight-line

graph?

A 2-point B 3-point C4-point D None of

these.

1.25 Three people are carrying out independent functions during an internal audit. It is

known that in each of the three separate areas being investigated there is a serious error.

From past experience, it is estimated that the (independent) chances of the individuals

finding the serious error in their area are 8, 07 and 06.

The probability that at least one of the serious errors will be found is

A (08 x 03 x 04) + (02 x 07 x 04) + (02 x 03 x 06)

B 1 (02 x 03 x 04)

C 1 (0 8 x 07 x 06)

D none of the above.


19 November 2001

1.1 The sales of a product increase at a rate of 1% each month, month on month,

for a year. This is equivalent to an annual percentage rate of expansion closestto

A 113% B 120% C 127%

D 130%

1.2 An annual (year-end) income of 10,000 is required in perpetuity. If there is a

fixed interest rate of 8% each year and administrative charges are ignored, the

lump sum investment necessary now is closest to

A 9,260 B 80,000 C 100,000 D 125,000

1.3 The numbers of hours worked last week by a companys 11 employees were:

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P Q R S T U V W X Y Z

35 36 36 36 40 38 40 37 35 42 43

The median number of hours worked last week was

A 36 B 37 C 38 D 39

1.4 The straight lines Y = 2X + 4 and Y = 12 2X intersect where (X, Y) equals

A (2, 0) B (0,12) C (0,4)

D (2,8)

1.5 A 1% random sample of mail order customers, each with a serial number, is to

beselected. A random number between 00 and 99 is chosen, and turns out to be29.Customers with serial numbers 29, 129, 229, 329 and so on are then selected to be the

sample.

This type of sample is termed

A biased. B multi-stage. C quota. D

systematic.

1.6 The following formula is used in loan calculations:

When the formula is rearranged, with N in terms of the other letters, N is equal

to

1.7 The formula simplifies to

1.8 A garage has experienced the following regular weekly demand for its hire cars over the

last 50 weeks:

Weekly demand for hire cars: 0 1 2 3 4 5 or more

Number of weeks (frequency): 10 5 15 15 5 0

The expected value of weekly demand equals

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A 20 cars. B 22 cars. C 25 cars. D none of

these.

1.9 In the equation C = 6 + 05Q, C denotes the total cost of sales (in thousands of $) and

Q denotes the number of units sold (in thousands).

The total cost of sales for 3,000 units is therefore

A $1,50600 B $6,00150 C $7,50000 D $19,500

00

1.10 The rank correlation coefficient between the ages and the scrap values of a certain

type of machine equals

1. This value means that

A no correlation exists between the ages and the scrap values of these machines.

B perfect correlation exists.

C weak negative correlation exists.

D a calculation error has been made.

1.11 The lengths of a very large batch of metal rods are Normally distributed with ameanlength of 300 millimetres and a standard deviation of 10 millimetres.

The percentage of the batch which is longer than 285 millimetres is closest to

A 43%

B 57%

C 84%

D 93%1.12 A $20,000 new car depreciates in value by 20% 2% each year (year-end). (The car

depreciates by the reducing balance method, which means that a constant percentage is

applied each year to the written down value.)

Therefore, after 3 years, the cars value is most accurately estimated by

A between $9,491 and $11,027

B $10,240 $1,024

C $10,240 $205

D between $12,168 and $13,448

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1.13 A traders weekly costs, TC, are less than or equal to $100. Weekly revenue, R, is a

minimum of $120.

Which ONE of the following statements is true?

A TC < $100 and R > $120 and R > TC

B TC $100 and R $120 and TC > R

C TC $100 and R > $120 and R < TC

D TC $100 and R $120 and R > TC

1.14 A company has to repay a mortgage by making 10 year-end payments of $50,000.

Thecompound interest rate is fixed at 8% each year.

Therefore, the size of the mortgage is closest to

A $266,750 B $307,250 C $335,500 D $356,900

The next two sub-questions, 1.15 and 1.16 are based on the following data.

1998 1999 2000 2001

Weekly money wages index (1998 = 100) 100 105 110

115

Index of inflation (1990 = 100) 180 190 200

210

1.15 Read the following statements about the period 1998 to 2001:

(i) Inflation has increased by more than money wages.

(ii) Money wages have increased by 5% each year, year on year.

Which ONE of the following is true?

A (i) only B (ii) only C Both (i) and (ii) D Neither (i)

nor (ii)

1.16 Real wages are money wages that have been adjusted for inflation, that is,

deflated.

Over the period 1998 to 2001, real wages have (approximately)

A remained unchanged.

B decreased by 143%.

C decreased by 167%.

D increased by 145%

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The next three sub-questions, 1.18 1.20 , are based on the following data.

A multiplicative time series model should be assumed.

The next three sub-questions, 1.18 1.20, are based on the following data.

A multiplicative time series model should be assumed.

Quarterly sales (units) of Brand X, 2001

Q1 Q2 Q3

Sales (units) 1,600 4,400 1,680

Seasonal variation 20% +100% 30%

1.18

The trend value for Q 1 sales (units) is

A 1,280 B 1,920 C 2,000

D none of these.

1.19 The seasonal variation for Q4 in 2001 is

A 50% B 0% C +50%

D none of these.

1.20 The forecast for the fourth quarters sales (units), Q4, in 2001, assuming the

trend pattern continues, is closest to

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A 1,300 B 2,300 C 3,800

D 5,200

1.21 The staff in the Complaints Department of an airline are available to answer the

telephone at random times, which amount to 20% of the working day on average.

The probability that a customers call is answered for the first time, on their fifth

attempt is

A (02)5 B (02)4 (08) C (08)4 (02)

D 1

The next four sub-questions, 1.22 1.25, are based on the following table of

data.

1.22 The probability that a randomly-selected Brand X buyer is from the Northand under 25years of age is (to 2 decimal places)

A 008 B 025 C 031

D 056

1.23 The probability that a randomly-selected Brand X buyer is from the West or

under 25 years of age is (to 2 decimal places)

A 008 B 048 C 056

D none of these.

1.24 The probability that a randomly-selected Brand X buyer, who is under 25

years of age, is from the South is (to 3 decimal places)

A 0115 B 0286 C 0375

D none of these.

1.25 The probability that two randomly-selected Brand X buyers are both under

25 years of age is (to 2 decimal places)

A 009 B 031 C 062

D none of these.

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20 May 2002

1.1 An index number increases each year by 10% of its value in the previous year.

If its value in 1999 was120, its value in 2002 is closest to

A 150. B 156. C 160. D 162.

1.2 In a time series of the unit sales of shoes, random variation could be caused by

A a general trend.

B seasonal effects due to the weather.

C cyclical effects resulting from a change in fashion.

D unexplained or freak events.

1.3 An annual year-end income of 15,000 is required in perpetuity. Assuming a

fixed rate of interest of 9% each year, and ignoring administrative charges, the

sum required now to purchase the annuity isclosest to

A 13,650.

B 135,000.

C 150,000.

D 167,000.

1.4 Which ONE of the following describes a qualitative variable?

A The number of invoices selected for an internal audit.

B The number of errors discovered in batches of invoices.

C The $ value of the error made in invoices in a batch.

D The type of error made in invoices.

1.5 For a certain group of students, the coefficient of rank correlation between their

performance inAccounting and their performance in Law is 1. The coefficient of rank

correlation between their performances in Law and FBSM is also 1. Therefore, the

coefficient of rank correlation between their performance in Accounting and their

performance in FBSM is

A 2 B zero C +1 D impossible to determine from the

information given.

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1.6 An accountant has marked some performance criteria out of 20 and found the mean to

be 10 marksand the standard deviation to be 2 marks. The marks now have to be

expressed as a percentage.

What would be the new value of the standard deviation?

What would be the new value of the standard deviation?

A 10% B 20% C 10%

D 20%

1.7 An index number is made up of two items, food and non-food.

Sub-group Weight Index

Non-food 7 130

Food 3 ?

All items 10 12

The index number for the sub-group Food is closest to

A 120. B 122. C 124.

D 126.

1.8 The diagram below shows an ogive (cumulative frequency) for a sample of 400 items.

The point K on the X-axis represents the value

A which 75% of the sample take.

B below which 75% of the sample values lie.

C which 25% of the sample take.

D above which 75% of the sample values lie.

1.9 Sample 1: 2, 5, 5, 12

Sample 2: 1, 3, 5, 8, 8

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Which of the following statistics has the same value in both samples?

A Arithmetic mean B Standard deviation C Median D Mode

1.10 A companys market value has fallen from 32 billion to 2 billion in four years. Theaverage annual percentage decline in market value is closest to

A 20%. B 40%. C 50%.

D 100%.

1.11

On the basis of the scatter diagram above, which of the following equations

would best represent the regression line of Y on X?

A Y = X + 8 B Y = X + 8 C Y = X 8 D Y = X 8

1.12 A sample of 10% of CIMA students is required. Which ONE of the following

methods would provide the best simple random sample?

A Select every tenth CIMA student to arrive at their college/institute on one specific day.

B Select randomly, using random number tables, one in ten of every CIMA class.

C Select 10% of colleges/institutions providing CIMA courses, then from these choose all

students whoare registered with CIMA.

D Select 10% of all students registered with CIMA, giving each a chance of 0 1 of being

picked.

1.13 Two groups of stock, K and L, are valued. The first group, K, is valued at 10,000 5%

and the second group, L, is valued at 20,000 10%.

The maximum percentage error in the combined (K + L) stock valuation of

30,000 is closest to

A 75%. B 83%. C 100%.

D 150%

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1.14 The sales of a product are recorded monthly for 24 months. The four-point (centred)

moving averagesare calculated and plotted on a graph.

How many moving average points are plotted?

A 20 B 21 C 22 D 24

1.15 In a single throw of a pair of fair (six-sided) dice, what is the probability that

the result is two numbers which sum to 7?

A 1/12 B 1/6 C D

The following data should be used for 1.16 and 1.17

In an internal audit of 200 invoices, the following numbers of errors were discovered:

Number of errors: 0 1 2 3 4 5 6 or more

Number of invoices: 60 30 40 40 20 10 0

1.16 The percentage of invoices with errors is

A 30%. B 70%. C 80%.

D none of these.

1.15 In a single throw of a pair of fair (six-sided) dice, what is the probability that

the result is two numbers which sum to 7?

A 121 B 61 C 41 D 21


In an internal audit of 200 invoices, the following numbers of errors were discovered:

Number of errors: 0 1 2 3 4 5 6 or more

Number of invoices: 60 30 40 40 20 10 0

1.16 The percentage of invoices with errors is

A 30%. B 70%. C 80%.

D none of these.

1.17 The expected value of the number of errors per invoice is

A 18 B 2 C 21 D 3

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1.18 The number of daily complaints to a railway company has an average (arithmetic

mean) of 12 and astandard deviation of 3 complaints.

The coefficient of variation, measured as a percentage, is therefore

A 025%. B 4%. C 25%. D

400%.

1.19 The following formula is used in the financial analysis of dividends:

When the formula is rearranged, with P in terms of the other variables, P is equal

to

1.20 The length of telephone calls to a Software Support line is approximately Normally

distributed with a mean of 20 minutes and a standard deviation of 5 minutes.

The percentage of calls lasting under 30 minutes is closest to

A 2%. B 48%. C 83%.

D 98%.

1.21 A fixed-interest $200,000 mortgage, with annual interest compounded at 6% each

year, is to be repaid by 15 equal year-end repayments of $R.

The annual repayment $R will be closest to

A $14,133. B $20,593. C $31,954. D $83,400.

1.22 A companys security system is made up of three separate electronic alarms, which

operate independently. The security system operates provided that at least one of the

three alarms is working.

The probability of an alarm failing at any time is 1 in 100.The probability of the

security system failing is

A 1 in 100. B 3 in 100. C 1 in 10,000. D 1 in

1,000,000.

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1.22 A companys security system is made up of three separate electronic alarms, which

operateindependently. The security system operates provided that at least one of the three

alarms is working.The probability of an alarm failing at any time is 1 in 100.

The probability of the security system failing is

A 1 in 100. B 3 in 100. C 1 in 10,000. D 1 in1,000,000.

1.23You borrow 3,000 and pay 10% each year interest. Ignoring capital, if you

pay this interest at the end of each year, what is the present value of the

interest payable at the end of the third year?

A (3/10) x 300 x 3

B (3/7) x 300

C (10/11)

3

x 300

D (11/10)3 x 400

1.24 A manufacturer supplies components in boxes of 10, stating that there is a

(independent) chance of 10% of any one component being faulty.

In a large batch, the percentage of boxes containing no faulty components will

be closest to

A 10%.

B 35%.

C 50%.

D 90%.

1.25 A new lake is to be stocked with fish, according to the numbers in the table below.

Type of fish A B C D

Number of fish 400 300 200 100

Annual % increase 10 20 30 40

After one year, the percentage of fish of Type D in the lake will be closest to

A 10%.

B 12%.

C 14%.

D 20%.

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18 November 2002

1.1The expression simplifies to

1.3 The total profit, P, of an organisation is related to output (x units) by the expression:

P = 40 + 11x 2x2

The organisation will break even (that is, P = 0) with an output of

A 25 units. B 4 units. C 55 units. D 8 units.

1.4 3x + 2y =6x 2y = 2

The solution, in the form (x,y), to the above simultaneous equations is

A (0,3) B (2,3) C (2,0)

D (3,2)


The following time series represents the weekly sales (000) of a particular product:

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Week Sales000

1 2002 2403 250

4 2205 2306 260

1.5 The 2nd four-point centred moving average for the sales data will be

A 2355 B 2375 C 2395D none of these.

1.6 Assuming an additive model, and based on the information given, theseasonally-adjusted sales figure(000) for week 4 will be

A 2375 B 2225 C 2200D 2025


The numbers of houses sold by an estate agent in the last 8 weeks were:

4, 3, 2, 0, 0, 10, 1, 4

1.7 The median number of houses sold per week was

A 0 B 25 C 30 D 50

1.8 The arithmetic mean number of houses sold per week was

A 0 B 25 C 30 D 50

1.9 The following information shows the daily sales revenue (000) of a company producinga particular item of clothing, over a period of two years:

Sales Frequency000 %0 to under 10 510 to under 20 2020 to under 30 6030 to under 40 1040 to under 50 5

The expected daily sales (in 000) is

A 22 B 24 C 26 D none ofthese.

1.10 The estimated total cost of each unit of a product is 12 ( 1), and the estimatedselling price of eachunit is 20 ( 3). The estimated profit per unit will be

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A 8 ( 4) B 8 ( 3) C 8 ( 2) D 8 ( 1)

1.11 In order to carry out a survey into the spending habits of the population living in acertain region of theUnited Kingdom, a sample of individuals is to be selected. Thepopulation can be categorisedaccording to age group ("under 18", "18 to under 30", "30 to

under 60", "60 and above"). The samplewill consist of 05% of the membership of each agegroup. This method of sampling is an example of

A stratified. B quota. C systematic. Drandom.1.12 For a set of six pairs of observations for the variables X (number of employees in

hundreds) and Y (product sales in thousands of units), the following results were obtained:

X = 1 Y = 15 X2= 15 2= 65XY = 7

The correlation coefficient is nearest to

A 022 B 047 C 090 D - 032


The following table shows the index of prices (1995 = 100) for a certain commodity overtheperiod 1995 2000:

1995 1996 1997 1998 1999 2000

100 105 115 127 140 152

1.13 The percentage increase in the price between 1997 and 1999 is nearest to

A 250 B 223 C 217 D none of these.

1.14 It has been decided to rebase the index so that 1998 = 100. The index for2000 will now be nearest to

A 1931 B 1394 C 1250D 1197

The following data should be used for 1.15 to 1.17

The total overtime cost of a small company varies from week to week, and is found tobeNormally distributed with a mean of 800 and a standard deviation of 200.

1.15 In any given week, the probability that the overtime cost will exceed 1,000is

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1.16 In any given week, the probability that the overtime cost will be between700 and 900 is


1.17 In 10% of weeks, the overtime cost will approximately fall below

A 366 B 455 C 544D 633


2,000 is invested in a bank account. The account earns compound interest at 5% per year.

1.18 The cash value of the account, to the nearest , at the end of five years willbe

A 2,680 B 2,553 C 2,431 D 2,335

1.19 The investment will have almost doubled in value after

A 11 years. B 12 years. C13 years. D 14 years.

1.20 An individual who expects to retire in five years' time, estimates that his company

pension will be15,000 per year. Each year's pension will be paid as a lump sum at the end

of the year. If currentinterest rates are 6%, then the present value of the first

year's pension, to the nearest 5, will be

A 10,575 B 10,975 C 11,190 D 11,205

1.21 A credit card company states that its nominal annual interest rate is 18%. If interest

is chargedmonthly at 15%, then the annual percentage rate (APR), correct to 2

decimal places, will be

A 1956%. B 1925%. C 1881%. D none of these

The following data should be used for 1.22 to 1.25

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Two components, A and B, operate independently as part of a computer system. The

probabilitiesthat A and B will work correctly are 09 and 08 respectively.

1.22 The probability that both components will work correctly is

A 081 B 072 C 028 D 017

1.23 The probability that both components will not work correctly is


1.24 The probability that only one component will work correctly is

A 098 B 081 C 074 D 026

1.25 The probability that at least one component will work correctly is



19 May 2003

The following information is required for sub-questions 1.1 and 1.2

The Economic Order Quantity (EOQ) for a particular stock item is given by the expression:

1.1 If Co= 2 per order, D = 1,000 items and Ch= 025 per item, then EOQ

(rounded to the nearestwhole number) will be

A 400 B 320 C 160 D 126

1.2 If, for a different stock item, EOQ = 200 items, Co= 4 per order and D = 1,000

items, then Ch (in peritem) will be

A 005 B 010 C 015 D 020

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1.3 If the demand for a particular product is x (hundred units per week), then the weekly

profit (P) is given by the

Expression

P = 30 + 4x 2x2

The break-even demand (that is when P = 0) will be

A 500 units per week.

B 400 units per week.

C 300 units per week.

D 200 units per week.

1.4 The production costs per unit of a certain commodity are 20 ( 2) and the selling

price per unit is35 ( 3). In any given week, the sales are 90 ( 10) units. On the

basis of this information, the maximum profit per week is

A 1,000 B 1,600 C 1,800 D 2,000The following information is required for sub-questions 1.5 and 1.6

On a particular day, a companys finance department received 20 invoices, of which 3contained errors.

1.5 If two of the invoices are selected at random, then the probability (correct to2 decimal places) that neither of them will contain an error is

A 072 B 063 C 042 D 0 40

1.6 If two of the invoices are selected at random, then the probability (correct to

2 decimal places) that at least one of them will contain an error is

A 060 B 058 C 036 D 028


The following frequency distribution shows the number of days of absence due to sickness,

during the last year, of a randomly selected sample of 50 employees of a large

manufacturing company.

Days of absence Number of employees

0 2 15

3 5 10

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6 9 9

10 12 8

13 15 6

More than 15 2

1.7 The median number of days of absence due to sickness per employee will benearest to

A 3 days. B 4 days. C 5 days. D 6 days.

1.8 If the upper quartile is 11 days, and the lower quartile is 1 day, then thequartile deviation will be

A 12 days. B 10 days. C 6 days. D 5 days.

1.9 In the current financial year, an employees net income is 15,360, after totaldeductions of 40% fromher gross income. In the last financial year, her gross income was23,400.

In percentage terms, the increase in her gross income is

A94% B 86% C75% D67%

1.10 The following table of index numbers shows how the production of a particular modelof motorboat at aboat builders has changed over the period August 2002 to February 2003,with January 2002 = 100:

Aug Sep Oct Nov Dec Jan Feb

Production index 110 119 115 108 102 98 95I

If the actual production figure for August was 140 motorboats, then the number ofmotorboats produced in February 2003 was closest to

A 105 B 121 C 133 D 162

1.11 The following table shows the price of a certain commodity over the years 1998 to2001:

Year 1998 1999 2000 2001

Price () 270 311 342 383

If a chain-based index is used, the price index number for 2000 will be closest to

A 110 B 117 C 120 D 127

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1.12 A broker has estimated the profits or losses for a particular investment and theirrespective probabilities as follows:

Profit (000) -1 1 3 5

Probability 01 03 04 02

The expected profit (000) on this investment will be

A 2 1 B 22 C 23 D 24

1.13 The Personnel Department of a large manufacturing company wishes to measure thecorrelation between the performance of its employees on an aptitude test, and their abilityto carry out a specific work-related task.

The following table shows the rankings of 7 employees at both the test and the task:

Employee A B C D E F G

Test Rank 2 5 7 4 1 6 3

Task Rank 2 6 7 4 3 5 1

Spearmans rank correlation coefficient for this data is

A 062 B 072 C 082 D 0 92


A company uses regression analysis to examine the relationship between its total weekly

costs (C) and its weekly production level (P units). The following model was found to be a

suitable description of this relationship:

C = 1500 + 300P

1.14 If, in a particular week, the production level is 500 units, then the predictedcosts will be

A 150,000 B 150,300 C 151,000 D 151,500

1.15 The average variable cost per unit is estimated as

A 300 B 1,500 C 1,800 D3,030

1.16 A graphical presentation of classified data in which the number of items ineach class is represented by the area of the bar is called

A an ogive. B a histogram. C a bar chart. D acompound bar chart.

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1.17 A pie chart is to be drawn to represent the following data, which shows the breakdown

by departmentof the number of employees working on a particular project:

Department Number of Employees

Marketing 7

Finance 5

Personnel 8

Sales 10

The angle of the sector (slice), in degrees, of the pie chart representingFinance will be

A 30 B 45 C 60 D 90

1.18 A survey is to be carried out into the spending habits of the population of a large town

in the North East of England. It has been decided that five small areas are to be randomly

chosen, two close to the town centre and three in more outlying areas. In these areas, ten

interviewers are each required to interview a randomly selected sample of 30 people.

This system of sampling is an example of

A multi stage. B cluster. C quota. Dstratified.

1.19 On one particular checkout in a supermarket, the service times in minutes of fivecustomers were:

3, 2, 1, 5, 4

The standard deviation of these service times, correct to 1 decimal place, isclosest to

A 35 minutes B 2 0 minutes C 15 minutesD 10 minutes

1.20 At a second checkout in the same supermarket as in sub-question 1.19, the servicetime has an arithmetic mean of 5 minutes and a standard deviation of 1 minute.

The coefficient of variation will be

A 50% B 20% C 5% D 2%

1.21 The underlying trend in the demand for a particular product is constant (flat), and issubject toquarterly seasonal variations as follows:

Quarter Q1 Q2 Q3 Q4

Seasonality +50% +50% -50% -50%

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Assume a multiplicative model is appropriate. If the demand for the last quarter, Q2,was 240 units, then the forecasted demand for the next quarter, Q3, is

A 80 units. B 100 units. C 120 units. D 140 units.

1.22 A bank offers investors a nominal annual interest rate of 4% with interest paidquarterly.

The effective annual rate of interest is

A 406% B 404% C 402% D 401%

1.23 If 10,000 is invested now, at an interest rate of 6% compounded annually,then after 5 years the value of the investment will be closest to

A 13,226 B 13,382 C 13,562 D 13,598

1.24 A company pays rent of 50,000, annually in advance, on a building for aperiod of 5 years. The annual interest rate is 10%. The total present value of therental repayments will be closest to

A 212,650 B 210,800 C 208,500 D 189,550

1.25 An annuity requires the deposit of 100 per year for 5 years. The depositsare made at the beginning of each year and earn interest at 8% per year. At theend of the 5 years, the investment will be worth closest to

A 633 B 645 C 654D 660


17 November 2003

1.1 A large department store wishes to carry out a survey by issuing a questionnaire to asample of 100 of its 2,000 account holders. The sample is to be selected as follows:

Each customer will be allocated a number from 1 to 2000. A table of random numbers from1 to 20 will then be used to select the first member of the sample. Every succeeding 20thmember of the population of account holders will then be selected.

This form of sampling is called

A stratified. B multi-stage. C systematic.D quota.

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1.2 The yearly sales of a particular product from three factories are represented by thefollowing diagram:

This diagram is an example of

A a Histogram.

B a multiple Bar Chart.

C a Component Bar Chart.

D an Ogive.

1.3 The solution to the simultaneous equations:

4x + 3y = 262x - y = 8

in the form (x,y) is

A (2, 5) B (-5, 2) C (-2, 5)D (5, 2)

1.4

Which of the following equations best represents the above scatter diagram:

A Y = 2X + 3 B Y = 3X + 2 C Y = 3X 2 D Y = 2 - 3X

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1.5 A customer paid $230 for a television which had been reduced by 15%. The

original price of the television before the price reduction was closest to

A $243. B $265. C $271.D $276.

1.6 If the rank correlation coefficient between the performances of two groups of

fifteen people performing the same task was -01, which ONE of the following

statements is true?

A There is perfect agreement between the performances of the two groups.

B There is moderate agreement between the performances of the two groups.

C There is no agreement between the performances of the two groups.

D This is an impossible result.

1.7 Since 1995, the average annual salaries for a group of workers have been index-linked

to prices. The table below shows the price index since 1997:

(1995 = 100)

Year 1997 1998 1999 2000 2001 2002

Price Index 112 118 122 125 127 130

If the average salaries were $30,000 in 1997, then the average salaries of theworkers in 2002 would have been closest to

A $31,800. B $33,600. C $34,821. D $36,000.

1.8 A toy manufacturer sells 3 ranges of toys. The following table shows sales informationfor the last two years:

Quantity(000s)

Range: Price ($/unit) 2001 2002A 10 30 40B 15 50 70C 30 10 15

A relatives quantity index, to the nearest whole number, for the year 2002, with2001 as the base year, will be

A 144 B 141 C 139 D 69

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1.9 The sum, S, of the first n terms of a geometric series with first term a and common ratior , is given by the formula:

The sum of the first 8 terms of a geometric series with common ratio 3 is 19,680.

The first term of this series is

A 7 B 6 C 5 D 4

The following data are to be used to answer questions 1.10 and 1.11 below.

A cell phone retailer conducts a survey of 200 cell phone purchasers, and obtains thefollowing resultsrelating to their ages in years:

Age Under 25 25 to 50 Over 50

Male 40 30 40

Female 60 20 10

1.10 The probability that a randomly selected purchaser is male and aged 50 or

under is

A 015 B 027 C 035 D 064

1.11 If the selected purchaser is female, the probability that she is aged 25 to 50is

A 010 B 022 C 025 D 035

1.12 The following table shows the number of cars of a particular model sold by a dealerover the last five weeks:

Week 1 2 3 4 5

Cars sold 8 3 7 9 4

The expected number of cars of this model to be sold in the year (50 weeks) is

A 300 B 310 C 325 D 350

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1.13 A car insurance company estimates that in a given year, each policyholder will make a

"small" claim of $500 with a probability of 01, a "moderate" claim of $1,000 with a

probability of 005, or a "large" claim of $2,000 with a probability of 001.

In order to break even, between premiums taken in and claims paid out, the

company should set the annual premium for each policy at

A $100. B $120. C $140.D $160.

The following data are to be used to answer questions 1.14 to 1.16 below.

Flights arriving at an airport are subject to delays. The length of the delays is normallydistributed with a mean of 20 minutes and a standard deviation of 8 minutes.

1.14 The probability that a flight will be delayed by less than 10 minutes isnearest to

A 0894 B 0494 C 0250D 0106

1.15 The probability that a flight will be delayed by between 15 and 25 minutes is nearestto

A 0268 B 0465 C 0535D 0 732

1.16 Approximately 20% of the flight delays are less than

A 11 minutes B 13 minutes C 15 minutesD 17 minutes


The records of a supplier of an automobile part show that the quarterly demand over the

past three years was as follows:

2000 2001 2002

Quarter 1 2 3 4 1 2 3 4 1 23 4

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Demand 142 54 162 206 130 50 174 198 126 42162 186

(000 units)

1.17 Using a 4-point centred moving average, the trend component of thedemand (000 units) for Quarter 4of the year 2000 will be closest to

A 206. B 166. C 160. D 138.

1.18 If an additive model is assumed, and the seasonal components of the

demand for quarters 2, 3 and 4 are -88, 30 and 66 respectively, the seasonal

component of the demand (000 units) for Quarter 1 will be

A 80 B -80 C 27 D -27

1.19 A small manufacturing company owns two machines, A and B. Machine A is valued at

$15,000 10%,and machine B is valued at $25,000 5%.

The maximum percentage error in the combined value of the two machines is

closest to

A 70% B 75% C 100%D 150%

1.20 Which ONE of the following statements regarding sample measures is INCORRECT?

A The arithmetic mean is always distorted by extreme values.

B The median will not be distorted by extreme values.

C The mode can be distorted by extreme values.

D The standard deviation can be distorted by extreme values.


$20,000 is invested at an interest rate of 4%, which is compounded annually.

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1.21 After 10 years, the investment will have a value, to the nearest $, of

A $23,798. B $25,408. C $27,398. D $29,605.

1.22 The investment will have approximately doubled after

A 18 years. B 20 years. C 22 years. D 25 years.

1.23 An individual has taken out a mortgage of $150,000, at a fixed interest rate

of 5% per annum over 20years. Repayments will commence one year after the

mortgage is taken out. The annual repayments will be closest to

A $12,276. B $12,036. C $11,796. D $11,076.

1.24 If the annual rate of interest is 475%, the amount (to the nearest $) that

should be invested now in order to receive $5,000 per annum in perpetuity, with

receipts starting one year from now, is

A $100,653. B $102,365. C $103,526. D $105,263.

1.25 An item of machinery that was purchased 5 years ago for $100,000 now has

a value of $50,000.Assuming the reducing balance method of calculation, the

annual rate of depreciation to the nearest whole percentage point will be

A 17%. B 15%. C 13%.D 11%.

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C03 EXAMS (2001 - 2003)

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