Subject: QUANTITATIVE TECHNIQUES IN BUSINESS (QTB)

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PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector

Explains the concept of a national budget, surplus and deficit budget implications, and challenges in the implementation of national budgets in Nigeria.

Question

In government’s quest to optimally develop and efficiently manage available resources, national budgets are usually prepared to put economic development firmly on course.

Required:

a. Describe briefly a national budget. (3 Marks)

b. Explain briefly the implication of each of the following for the performance of the economy: i. A surplus budget ii. A deficit budget (4 Marks)

c. Explain FOUR problems to be encountered in the effective implementation of national budgets in Nigeria. (8 Marks)

Answer

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Tags: Budget Implementation, Deficit Budget, National Budget, Surplus Budget
Level: Level 2

Topic: Budgeting
Series: MAY 2018

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

Question

a. If N250,000 is invested in an account that earns 4% per year compound interest, what is the:
i. value of the investment after 5 years? (3 Marks)
ii. total interest earned? (2 Marks)

b. When it was apparent that your parents could not afford to finance your university education, you sought and obtained a 4-year loan of N250,000.00 from Education Bank Limited. The bank imposed a simple interest rate of 7½%.
i. How much do you need to pay off the bank now

(4 years after) that you are through with your study?

(7 Marks)
ii. If you decide to be paying N25,000 every month from now and the bank agreed to reduce the interest rate to 1% per month on the unpaid balance at the beginning of the month, how much additional total interest will be paid? (8 Marks)

Answer

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Tags: Compound Interest, Interest calculation, Loan Repayment, Simple Interest
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

Question

In a particular organisation, an experiment which was conducted to determine the gasoline mileage of a particular type of car yielded the following data:

Miles per gallon	Percent
10 and under 12	4
13 and under 15	8
16 and under 18	14
19 and under 21	26
22 and under 24	12
25 and under 27	11
28 and under 30	10
31 and under 33	7
34 and under 36	6
37 and under 39	2

Required:

i. Draw the frequency polygon for gasoline mileage. (5 Marks)
ii. Draw the ogive for gasoline mileage. (5 Marks)

Answer

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Tags: Frequency Polygon, Gasoline Mileage, Graphical Representation, Ogive
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

Question

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates	1	2	3	4	5	6	7	8	9	10	11	12
Score in QTB (x)	35	77	95	28	76	80	90	62	39	65	90	37
Score in MI (y)	50	82	89	58	65	61	84	59	48	53	80	52

Required:
i. Calculate the Spearman’s rank correlation coefficient between $x$ and $y$ . (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

Answer

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Tags: Correlation, Mock Examination Scores, Spearman’s Rank
Level: Level 1

Topic: Statistics
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

Question

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2005	22	35	82	37
2006	24	46	81	44
2007	25	40	87	49
2008	29	42	100	55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

Answer

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Tags: Least Squares, Sales Forecasting, Time series, Trend Estimation
Level: Level 1

Topic: Forecasting
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

Question

a. Calculate the various control levels from the following data on a given inventory item:

Normal usage: 1,600 per day
Minimum usage: 1,000 per day
Maximum usage: 3,000 per day
Lead time: 16 – 20 days
EOQ: 40,000
(9 Marks)

b. If the optimistic, most likely, and pessimistic times are given as 11 days, 15 days, and 18 days respectively, calculate the expected time of the project delivery.
(3 Marks)

c. The network for a small building project is shown below together with the time in days required to complete each task.

Required:

i. List the possible paths together with their durations through the network. (6 Marks)
ii. State the critical path and the project duration. (2 Marks)

(Total: 20 Marks)

Answer

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Tags: Control Levels, Critical Path, Economic Order Quantity (EOQ), Expected Time, Network Analysis
Level: Level 1

Topic: Operations Research
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q2 – Measures of Dispersion

Compare the risk and return of two investments by calculating mean and standard deviation.

Question

In finance, the standard deviation is frequently used to measure the risk of an investment.
An investor is considering two possible investments A and B. A sample of 10 rates of return is recorded for each investment. These rates of return, given as percentages, are as follows:

Investment A:
4, 6, 6, 5, 4, 5, 8, 5, 5, 8

Investment B:
0, -2, 6, 12, 9, 16, -4, 16, 25, 12

Required:
a. Calculate the mean rate of return for each of the two investments. (6 Marks)
b. Calculate the standard deviation of the rate of return for each of the investments. (6 Marks)
c. Which of the two investments is riskier and why? (8 Marks)

(Total: 20 Marks)

Answer

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Tags: Investment Analysis, Mean, Risk Assessment, Standard Deviation
Level: Level 1

Topic: Measures of Dispersion
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

Question

The Chief Accountant of Zeesco Plc. has a large sum of money which she plans to donate to 4 not-for-profit organisations. She plans to give of this amount to organisation A. Out of the remaining amount, she plans to give to organisation B. Also, she intends to give of the balance to organisation C and the rest to organisation D. If she plans to give 11 million naira to organisation D, how much does she plan to share among these organisations?

Answer

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Tags: Algebraic Fractions, Charity Donations, Fractions, Proportional Distribution
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – May 2017 – L1 – SB – Q6b – Data Collection Analysis

Calculate the mode and Pearson's coefficient of skewness for a given distribution of marks.

Question

The table below shows the marks (%) scored in QTB by some candidates who wrote the ICAN Professional examination in May 2016 diet:

Marks %	Number of Candidates
20–29	7
30–39	17
40–49	13
50–59	9
60–69	4

If the mean mark is 41.7%, calculate the mode and Pearson’s coefficient of skewness. (10 Marks)

Answer

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Tags: Mode, Pearson’s Coefficient, Skewness
Level: Level 1

Topic: Data Collection
Series: MAY 2017

QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

Question

The cost of purchasing 8 calculators and 10 books is 158 (thousands of naira).
At another instance, the cost of purchasing 15 calculators and 3 books is 123 (thousands of naira).

Required:
i. Use the information above to write down a system of linear equations to describe the given cost scenario. (4 Marks)
ii. Solve the resulting system of equations. (4 Marks)
iii. Find the cost of each calculator and each book. (2 Marks)

Answer

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Tags: Cost Calculation, Linear Equations, Simultaneous Equations
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

Question

The weights of bags of Pando Yam produced by Swallow Company Limited are normally distributed with a mean of 3,020 grams and a standard deviation of 4 grams.

Required:
i. If a bag is picked at random, what is the probability that it weighs:

Less than 3,012 grams? (4 marks)
ii. Between 3,012 grams and 3,021.6 grams? (6 marks)
Show all the relevant normal distribution diagrams.

Answer

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Tags: Normal distribution, Pando Yam, Probability, Z-scores
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

Question

The marginal cost of producing a particular item is given by

Required:
i. Find the total cost function , if the cost of producing 2 items is N1,660.
(7 marks)

ii. Find the cost of producing 50 items.

Answer

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Tags: Business Finance, Integration, Marginal Cost, Total Cost
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q4b – Mathematics

This question covers estimating the value of a house with compound growth and determining a feasible tableau using the Least Cost Method in a transportation problem.

Question

i. A house built in Ikoyi increased in value by 8% in year 1, 25% in year 2, 35% in year 3, 43% in year 4, and 22% in year 5.

Required:
If the house cost N10,000,000 to build, estimate its value at the end of 5 years.
(3 marks)

ii. Calculate the average growth rate over the 5-year period.
(3 marks)

iii. A company’s Demand/Supply situations together with unit transportation costs are as shown below:

Supply	Factory A	Factory B	Factory C	Demand
400	3	6	7	400
550	7	5	3	550
500	5	4	6	500
700	3	2	4	700
Total	2150

Required:
Identify the initial feasible tableau using the Least Cost Method.

Answer

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Tags: Cost Allocation, Growth Rate, Least Cost Method, Transportation Problem
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q4a – Statistics

This question involves calculating expected returns from a gambler’s game of chance based on different scenarios.

Question

A gambler plays a game of chance in which he has a 60% chance of winning. If he wins, he collects N1,800, but if he loses, he pays N2,300.

Required:
i. Obtain the sample spaces respectively for 12 games and 14 games.
(2 marks)

ii. Calculate his expected returns for 12 games and 14 games.
(6 marks)

iii. Advise the gambler if he initially staked N1,000.

Answer

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Tags: Decision Making, Expected Returns, Game of Chance, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

Question

The annual expenditures (N’000) of a family from 2000 to 2009 were as follows:

Year	Expenditure (N’000)
2000	600
2001	610
2002	580
2003	590
2004	480
2005	560
2006	550
2007	620
2008	490
2009	530

Required:
a. Setting year 2000 as $x = 0$ , fit the least squares line for the annual expenditures.
(15 marks)

b. Forecast what the expenditure will be in the years:
i. 2012 (2½ marks)
ii. 2016 (2½ marks)

Answer

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Tags: Expenditure, Forecasting, Least Squares, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q2b – Mathematics

This question involves deriving the marginal revenue function and various constraints related to product demand and labor hours.

Question

i. The Students Union of a University plans to have an end-of-year party for all its members. The party is scheduled to take place at a major hotel that can accommodate up to 500 persons. The hotel was to charge N800 per person. At this gate fee, the hotel expects to sell 400 tickets. Market research postulates that for every N40 increase or reduction in the ticket price, the demand will fall or increase by 16 tickets.

Required:
If the variable cost per student for the dinner is N210, determine the Marginal Revenue (MR) function.
(6 marks)

ii. JANG PLC produces and sells two products G and H. G and H respectively make contributions of N10 and N15. The company wishes to maximize its profit. 4,150 units and 3,175 units of G and H, respectively, are to be sold. Direct labor hours per unit are 2.5 hours and 1.5 hours for G and H, while machine hours per unit are 45 minutes and 3 hours for G and H, respectively. Total direct labor hours available and total machine hours available are, respectively, 18,000 hours and 10,000 hours.

Required:
Derive the following constraints: the direct labor, machine time, sales demand for G, sales demand for H, and non-negativity constraints. (4marks)

Answer

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Tags: Constraints, Linear Programming, Marginal Revenue, Sales Demand
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q2a – Mathematics

This question requires calculating the compound interest rate using logarithms.

Question

A barber invests N100,000 for 5 years. At the end of the investment period, he receives a cash transfer of N120,600 as final settlement of the investment.

Required:
Use logarithm (to base 10) to determine the compound interest rate on the investment.

Answer

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Tags: Business Finance, Compound Interest, Interest Rate, Investment, Logarithm
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q1b – Mathematics

Draw cost graph, estimate production units, deduce fixed costs and cost equation for an aluminum manufacturing company.

Question

An aluminum manufacturing company in Lagos incurs a daily total cost of N5,000 for one unit of production. To produce 4 units, the company spends N30,000 as its total cost.

Required:

i. Draw a graph to depict the above information.
(3 marks)

ii. Use your graph above to estimate the number of units to be produced to incur a total cost of N70,000.
(2 marks)

iii. Deduce

The daily fixed costs of the company from the graph above (1 mark)
From the above, obtain the equation representing the company’s activity (3 marks)

iv. Comment on the results obtained in (iii) above.
(1 mark)

Answer

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Tags: Cost Analysis, Cost Functions, Fixed Costs, Graphing
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

Question

Assume that the management of Community Bank Limited wants to invest up to N100,000 in inventory considered to be either conservative or speculative. The company’s board-approved investment policy is that the investment in conservative inventory should be at most N80,000, while the investment in the speculative inventory should be at least N12,000. Assume further that N1.6 return is expected on each naira invested in the conservative inventory, N2.0 return is expected on each investment in the speculative inventory, and that monetary policy regulations require that investment in the speculative inventory should be at most one-third of the investment in the conservative inventory.

Required:

a. State the type of Operations Research problem described above. (2 Marks)

b. Formulate mathematically the:

i. Objective function. (4 Marks)

ii. Constraint inequalities. (8 Marks)

iii. Investment problem. (6 Marks)

(Total: 20 Marks)

Answer

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Tags: Constraints, Inventory Management, Investment policy, Linear Programming, Optimization
Level: Level 1

Topic: Operations Research
Series: NOV 2015

QTB – May 2016 – L1 – SB – Q1a – Mathematics

Calculate profit in year 5 for new product with given growth rates for units produced, selling price, and production costs.

Question

A company plans to introduce a new product into the market. 6,000 units are to be produced in the first year with an annual growth rate of 3.5%. Selling price is to be set at N1,050 per year with an annual growth rate of 6.5%.

Required:

If the production costs are to be pegged at N850 in the first year with an annual growth rate of 5%, calculate the profit earned in year 5.

Answer

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Tags: Business Finance, Compound Growth, Profit Calculation
Level: Level 1

Topic: Mathematics
Series: MAY 2016

Subject: QUANTITATIVE TECHNIQUES IN BUSINESS (QTB)

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PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector

Explains the concept of a national budget, surplus and deficit budget implications, and challenges in the implementation of national budgets in Nigeria.

You're reporting an error for "PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector"

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance"

QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

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QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

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QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

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QTB – Nov 2014 – L1 – SB – Q2 – Measures of Dispersion

Compare the risk and return of two investments by calculating mean and standard deviation.

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QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

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QTB – May 2017 – L1 – SB – Q6b – Data Collection Analysis

Calculate the mode and Pearson's coefficient of skewness for a given distribution of marks.

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QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance"

QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5b – Statistics"

QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5a – Mathematics"

QTB – May 2016 – L1 – SB – Q4b – Mathematics

This question covers estimating the value of a house with compound growth and determining a feasible tableau using the Least Cost Method in a transportation problem.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q4b – Mathematics"

QTB – May 2016 – L1 – SB – Q4a – Statistics

This question involves calculating expected returns from a gambler’s game of chance based on different scenarios.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q4a – Statistics"

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

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QTB – May 2016 – L1 – SB – Q2b – Mathematics

This question involves deriving the marginal revenue function and various constraints related to product demand and labor hours.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q2b – Mathematics"

QTB – May 2016 – L1 – SB – Q2a – Mathematics

This question requires calculating the compound interest rate using logarithms.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q2a – Mathematics"

QTB – May 2016 – L1 – SB – Q1b – Mathematics

Draw cost graph, estimate production units, deduce fixed costs and cost equation for an aluminum manufacturing company.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q1b – Mathematics"

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

You're reporting an error for "QTB – Nov 2015 – L1 – SB – Q6 – Operations Research"

QTB – May 2016 – L1 – SB – Q1a – Mathematics

Calculate profit in year 5 for new product with given growth rates for units produced, selling price, and production costs.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q1a – Mathematics"

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