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 – Q1 – Mathematics.

A multiple-choice question calculating future value based on compound interest over 15 years at 8% annually.

Question

How much will N22,500 amount to at 8% interest over 15 years compounded annually?

A. N71,337.81
B. N71,373.81
C. N71,378.81
D. N71,387.81
E. N71,733.81

Answer

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Tags: Compound Interest, Financial Mathematics, Future Value, Investment Growth, Time value of money
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – Nov 2014 – L1 – SA – Q20 – Mathematics of Business Finance

Identifies the conditions necessary for a firm to minimize operational costs.

Question

The sufficient and necessary conditions for a firm that wants to minimize its operational costs

Answer

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Tags: Derivatives, Minimization, Operational Costs
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q19 – Mathematics of Business Finance

Determines the interest rate condition for a sinking fund to have a lower periodic cost than amortization

Question

If the interest rate received on a sinking fund is ……………….., the periodic cost for the sinking fund is lower than that for amortization.
A. Lower than that charged on the debt
B. Equal to that charged on the debt
C. Higher than that charged on the debt
D. Equal to zero
E. Equal to one

Answer

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Tags: Amortization, Interest rates, Sinking Fund
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q17 – Mathematics of Business Finance

Calculates the estimated retailer’s daily cost based on sales and commission.

Question

A retailer sells 2,000 cups of ice cream daily at Bolekaja bus stop for N250 per cup. If the retailer’s commission on each cup is 27% of the selling price, the estimated retailer’s daily cost will be:
A. N250,000
B. N285,000
C. N325,000
D. N350,000
E. N365,000

Answer

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Tags: Commission, Ice Cream Sales, Retailer Cost
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q16 – Mathematics of Business Finance

Calculates the number of units produced based on labor and capital input.

Question

The number of units of goods produced when utilizing units of labor and units of capital is given by:

How many units of goods will be produced by using 81 units of labor and 256 units of capital?
A. 2,880
B. 2,908
C. 2,960
D. 5,360
E. 8,640

Answer

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Tags: Capital, Labor, Production Function
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q14 – Data Collection Analysis

Calculates the mean deviation of a given set of values.

Question

The mean deviation of the values: 7, 8, 10, 14, 25, 30 is:
A. 16.86
B. 14.89
C. 7.89
D. 6.89
E. 5.89

Answer

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Tags: Data Analysis, Mean Deviation, Measures of Central Tendency
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q13 – Data Collection Analysis

Determines the classification of the mode in a given data set.

Question

The mode in the set of data 2, 3, 5, 5, 5, 7, 7, 7, and 6 is described as:
A. Unimodal
B. Bimodal
C. Modal average
D. Trimodal
E. Multimodal

Answer

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Tags: Bimodal, Data Analysis, Mode, Unimodal
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q12 – Data Collection Analysis

Calculates the relative frequency of babies weighing between 4-5 kg.

Question

Given the frequency distribution of weights of babies at the post-natal ward of a University Teaching Hospital as:

Weight (kg)	Number of babies
2 – 3	32
4 – 5	17
6 – 7	11

Which of the following values represents the relative frequency of the class 4-5 kg weight of babies in the ward?
A. 0.17
B. 28%
C. 0.283
D. 17%
E. 0.17%

Answer

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Tags: Baby Weights, Frequency Distribution, Relative Frequency
Level: Level 1

Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q11 – Data Collection Analysis

Calculates the variance of a grouped data set representing traveling times.

Question

The following data are for the travelling time to and from work in hours per day for a group of factory workers:

No. of hours	No. of workers
Under 1	20
1 up to 2	10
2 up to 3	5
3 up to 4	4

The variance of the data is
A. 1.00
B. 1.01
C. 1.02
D. 1.12
E. 1.22

Answer

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Tags: Frequency Distribution, Travel Time, Variance
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q10 – Data Collection Analysis

Determines the cumulative frequency corresponding to a specific mark in a data set.

Question

: The following are the marks obtained by 10 students in a class mid-term examination: 30%, 40%, 50%, 30%, 30%, 30%, 40%, 60%, 40%, and 30%. The cumulative frequency that corresponds to 50% is:
A. 1
B. 5
C. 8
D. 9
E. 10

Answer

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Tags: Class Marks, Cumulative Frequency, Frequency Distribution
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

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.

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis"

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 – Q1 – Mathematics.

A multiple-choice question calculating future value based on compound interest over 15 years at 8% annually.

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QTB – Nov 2014 – L1 – SA – Q20 – Mathematics of Business Finance

Identifies the conditions necessary for a firm to minimize operational costs.

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QTB – Nov 2014 – L1 – SA – Q19 – Mathematics of Business Finance

Determines the interest rate condition for a sinking fund to have a lower periodic cost than amortization

You're reporting an error for "QTB – Nov 2014 – L1 – SA – Q19 – Mathematics of Business Finance"

QTB – Nov 2014 – L1 – SA – Q17 – Mathematics of Business Finance

Calculates the estimated retailer’s daily cost based on sales and commission.

You're reporting an error for "QTB – Nov 2014 – L1 – SA – Q17 – Mathematics of Business Finance"

QTB – Nov 2014 – L1 – SA – Q16 – Mathematics of Business Finance

Calculates the number of units produced based on labor and capital input.

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QTB – Nov 2014 – L1 – SA – Q14 – Data Collection Analysis

Calculates the mean deviation of a given set of values.

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QTB – Nov 2014 – L1 – SA – Q13 – Data Collection Analysis

Determines the classification of the mode in a given data set.

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QTB – Nov 2014 – L1 – SA – Q12 – Data Collection Analysis

Calculates the relative frequency of babies weighing between 4-5 kg.

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QTB – Nov 2014 – L1 – SA – Q11 – Data Collection Analysis

Calculates the variance of a grouped data set representing traveling times.

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QTB – Nov 2014 – L1 – SA – Q10 – Data Collection Analysis

Determines the cumulative frequency corresponding to a specific mark in a data set.

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