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 2017 – L1 – SA – Q11 – Data Collection and Analysis

This question calculates the first quartile age from an age distribution table of artisans.

Question

If the age distribution of the artisans in a tobacco company is tabulated as follows:

Artisan’s age (years)	Number of Artisans
20 and under 25	3
25 and under 30	14
30 and under 35	18
35 and under 40	11
40 and under 45	3
45 and under 50	1

Then the first quartile age is:
A. 28.38 years
B. 28.39 years
C. 28.93 years
D. 29.38 years
E. 29.93 years

Answer

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Tags: Age Distribution, Frequency Distribution, Quartile Calculation
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q10 – Data Collection Analysis

This question involves finding the standard deviation given the variance and mean.

Question

The variance of is 4, and the mean is 5. Find the standard deviation.

A. 2
B. 3
C. 2
D. 3
E. 16

Answer

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Tags: Business Statistics, Dispersion, Mean, Standard Deviation, Variance
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q9 – Data Collection Analysis

This question identifies the reasons why the mean is preferred for statistical calculations.

Question

The mean is the most commonly used statistics for further statistical calculations because it:
A. Tends to lie at the centre of a set of data
B. Is easy to calculate
C. Takes all observations in the data into consideration
D. Is the most popular
E. Is not affected by extreme values in the data

Answer

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Tags: Central Tendency, Mean Calculation, Statistical Calculations
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q8 – Data Collection and Analysis

This question calculates the median salary from a salary distribution.

Question

If the monthly salary of the staff of ABC Plc. is distributed as follows:

Monthly salary (N’000)	Number of staff
6 and under 12	2
12 and under 18	13
18 and under 24	16
24 and under 30	10
30 and under 36	2
36 and under 42	1
Total	44

Then, the median salary is:
A. N20,256
B. N20,265
C. N20,526
D. N20,625
E. N20,652

Answer

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Tags: Business Statistics, Frequency Distribution, Median, Salary Distribution
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q7 – Mathematics

This question assesses understanding of histograms and their characteristics.

Question

Which of the following is NOT TRUE about a histogram?
A. A vertical rectangle is drawn to represent each class of the frequency distribution
B. A histogram is a graph of a grouped frequency distribution
C. The frequency of a class is represented by the height of its rectangle.
D. Histogram and bar charts look similar but they are constructed very differently.
E. The frequency of a class is represented by the area of the bar corresponding to the class.

Answer

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Tags: Business Mathematics, Data Representation, Graphs, Histogram
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q6 – Mathematics

This question asks to calculate the marginal revenue at a given sales volume.

Question

If the sales function of a company is given as what is the marginal revenue when

A. 122
B. 120
C. 125
D. 130
E. 135

Answer

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Tags: Business Mathematics, Calculus, Derivatives, Marginal Revenue
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q5 – Mathematics

A multiple-choice question asking for the point where the slope of a given function is zero.

Question

If , then the point at which the slope is zero is:

A. (-3,7)
B. (3,7)
C. (-3,-7)
D. (3,-7)
E. (3,-11)

Answer

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Tags: Calculus, Differentiation, Functions, Mathematical Modelling, Slope
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q4 – Mathematics

A multiple-choice question calculating the income left after tax deductions from the taxable income.

Question

A man earns N150,000 per annum. He is allowed a tax-free pay of N40,000. If he pays 25 kobo in the Naira as tax on his taxable income, how much has he left?

A. N102,500
B. N112,500
C. N122,500
D. N132,500
E. N142,500

Answer

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Tags: Deductions, Income Tax, Personal Income, Taxable Income, Taxation
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q3 – Mathematics.

A multiple-choice question assessing knowledge of simultaneous equations and variable relations.

Question

Which of the following is NOT TRUE about simultaneous equations?

A. The number of variables must be equal to the number of equations.
B. Where two lines intersect, the values of the variables at that point must satisfy the equations.
C. The simultaneous equations must be satisfied by values of the variables as well as their reciprocals.
D. Their solution involves finding the values of the variables which are true to all the simultaneous equations.
E. The result of adding the equations or subtracting one equation from the other will be satisfied by the values of the variables.

Answer

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Tags: Algebra, Linear Equations, Mathematical Methods, Simultaneous Equations, Variables
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q2 – Mathematics.

A multiple-choice question calculating the variable cost per unit given total and fixed costs.

Question

A company produces 16,000 units of a product. The total cost of producing these units is N60,000. If the fixed cost is N12,000, the variable cost per unit of the output is:

A. N7.00
B. N6.00
C. N5.00
D. N4.00
E. N3.00

Answer

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Tags: Break-even Analysis, Costing, Fixed Costs, Production Efficiency, Variable Cost
Level: Level 1

Topic: Mathematics
Series: MAY 2017

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 2017 – L1 – SA – Q11 – Data Collection and Analysis

This question calculates the first quartile age from an age distribution table of artisans.

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QTB – May 2017 – L1 – SA – Q10 – Data Collection Analysis

This question involves finding the standard deviation given the variance and mean.

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QTB – May 2017 – L1 – SA – Q9 – Data Collection Analysis

This question identifies the reasons why the mean is preferred for statistical calculations.

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QTB – May 2017 – L1 – SA – Q8 – Data Collection and Analysis

This question calculates the median salary from a salary distribution.

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QTB – May 2017 – L1 – SA – Q7 – Mathematics

This question assesses understanding of histograms and their characteristics.

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QTB – May 2017 – L1 – SA – Q6 – Mathematics

This question asks to calculate the marginal revenue at a given sales volume.

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QTB – MAY 2017 – L1 – SA – Q5 – Mathematics

A multiple-choice question asking for the point where the slope of a given function is zero.

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QTB – MAY 2017 – L1 – SA – Q4 – Mathematics

A multiple-choice question calculating the income left after tax deductions from the taxable income.

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QTB – MAY 2017 – L1 – SA – Q3 – Mathematics.

A multiple-choice question assessing knowledge of simultaneous equations and variable relations.

You're reporting an error for "QTB – MAY 2017 – L1 – SA – Q3 – Mathematics."

QTB – MAY 2017 – L1 – SA – Q2 – Mathematics.

A multiple-choice question calculating the variable cost per unit given total and fixed costs.

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