ICAN KNOWLEDGE LEVEL QUANTITATIVE TECHNIQUE IN BUSINESS ...starrygoldservices.com/icanknow16/icanqtmkqa.pdf · QUANTITATIVE TECHNIQUE IN BUSINESS MOCK EXAMINATION QUESTIONS FOR MAY

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ICAN KNOWLEDGE LEVEL

QUANTITATIVE TECHNIQUE IN BUSINESS

MOCK EXAMINATION QUESTIONS FOR MAY 2016 DIET.

INSTRUCTION: ATTEMPT ALL QUESTIONS IN THIS SECTION

OBJECTIVE QUESTIONS

1. The middle term in a set of ordered observations is referred to as

A. Geometric mean

B. Median

C. Mean

D. Mode

E. Harmonic mean

2. Which ONE of the following diagrams does NOT depict the information

in a frequency distribution for numerical data?

A. Histograph

B. Histogram

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C. Bar Chart

D. Frequency Polygon

E. Pie Chart

3. What is the standard deviation of the JAC Airlines' revenue profile for

four years if the revenues for those years are ₦20m, ₦25m, ₦18m and

₦24m?

A. 2.86

B. 2.87

C. 2.88

D. 2.89

E. 2.99

4. Which of the following sets of data is an array?

A. 7, 14, 21, 26, 22, 30




B. 30,22,26,21,14,7

C. 7,14, 21, 30, 22, 26

D. 7, 14, 21, 22, 26, 30

E. 30,22,21,14,26,7

5. In a company having 100 employees, 80 earn ₦800.00 per hour and

the remaining 20 earn ₦1000.00 per hour. What is the mean earnings

per hour?

A. ₦940 per hour

B. ₦840 per hour

C. ₦740 per hour

D. ₦640 per hour




E. ₦540 per hour

6. The simplest measure of dispersion is the

A. Mean deviation

B. Standard deviation

C. Range

D. Co-efficient of variation

E. Mean Absolute Deviation (MAD)

7. If an asset can be replaced at the same cost and there is no time value

of money, then the problem of obtaining the optimal replacement

interval involves the following EXCEPT

A. Finding the cumulative operating/maintenance cost

B. Finding the total depreciation

C. Adding (A) and (B) above to get total cost

D. Finding the year at which marginal cost is minimized

E. Finding the year at which Average Cost is minimum




8. Simulation method that uses random numbers to predict system

behaviour is called

A. Markov chain simulation

B. Box Jenkins simulation

C. Random variable simulation

D. stochastic simulation

E. Monte Carlo simulation

9. Probability is important in business because most decision-making in

business involve

A. Mutually exclusive situations

B. Most-likely situations




C. Equally-likely situations

D. Uncertainty situations

E. Certainty situations

10. Random experiments in probability analysis are experiments

whose outcomes

A. Cannot be predicted

B. Cannot be predetermined

C. Cannot be easily determined

D. Cannot be biased

E. Can be determined from records

11. If the Z-score for a normal distribution is 1.89, then the area under

the normal curve to the right of Z is

A. 0.02

B. 0.03

C. 0.04

D. 0.47




E. 0.97

12. The measure that explains how well the regression line fits a set of

data on daily sales of a product is known as co-efficient of

A. Rank Correlation B. Product-Moment Correlation C. Determination D. Variation E. Linear Regression

13. The table below shows the quantity of

Newspaper sold daily in a week by a vendor:

Days of

the week

Mon Tues Weds Thur Fri Sat Sunday

Quantity sold 550 450 500 370 420 620 490




The three day moving average to Friday is

A. 400

B. 430

C. 470

D. 550

E. 570

14. The scatter plot depicting the association that exists between price of an item

and quantity supplied is such that all the points fall on a straight line and their

movement is in downward trend then the type of correlation exhibited in the

graph is known as

A. Perfect positive

B. Positive

C.Perfect negative

D.Negative

E. Zero




15. An Accountant plans to give his wife a precious gift on her 50th birthday in

172 years' time. He intends to start with a deposit of N5,000 and doubles the

amount every month throughout this period. Assuming no interest is paid on this

account, determine the accumulated amount in this account at the end of this

period

A. ₦1,510,715 B. ₦1, 410,715 C.₦1,310,715 D.₦I, 210,715 E. ₦1,110,715

16. A woman made weekly donations according to an Arithmetic Progression

(AP). How many donations did she make if her first donation was ₦5,000, her

second donation was ₦6,000 and her last donation was ₦49,000?

A. 44

B. 45

C.46




D.47

E. 48

17. Three sisters: Mary, Mabel and Vera shared the sum of ₦900,000 as

proceeds from their father's real estate in the ratio 7:8:9 respectively. How much

did Mabel get?

A. ₦262,500.00 B. ₦300,000.00 C.₦337,500.00 D.₦352,173.00 E. ₦373,043.00

18. The term used to describe the process of working backwards in

time to find the present values from future value of investment is

known as

A. Discount

B. Discounting




C. Discount rate

D. Annuity

E. Amortisation

19. The borrower who pays-off ahead of time

pays higher effective rate

A. Discounted loan

B. Standing loan

C. Amortised loan

D. Ordinary loan

E. Bank loan

20. A stationary point for the function f(x) is a

point at which

A. F’(x)≤0




B. F’(x)=0

C. F’(x)≥0

D. F’’x)=0

E. F’’(x)≠0

Given the following sample data of stock returns of a company: 11, 6, -8, 10,

0, -5, 1, 15 and 4.

Use the data to answer questions 1 to 4.

21. What is the median return of stock for the company?

A. 5 B. 4 C. 0 D. 6

22. Determine the arithmetic mean return for the stocks.

A. 34 B. 9 C. 3.78 D. 6.02

23. What is the standard deviation for the stock returns?

A. 8.83 B. 76.04 C. 14.29 D. 3.78

24. Determine the mean absolute deviation for the stock returns.

A. 7.68 B. 6.02 C. 14.29 D. 3.78




25. Which of these statements is true of Geometric mean (GM),

Arithmetic mean (AM) and Harmonic mean (HM) for a given set of data?

A. AM>HM>GM B. AM>GM>HM C. GM>AM>HM D.

HM>AM>GM

26. Given a sequence 2,4,6,8. Find the 22nd term and the sum of the first

30 terms.

A. (40,900) B. (44,900) C. (44,930) D. (40,930)

27. The first two terms of an AP are -2 and 3. How many terms are needed

for the sum to equal 360?

A. 10 B. 11 C. 12 D. 13

28. The sum of the 3rd and 7th terms of an AP equal 6, their product is 8.

Find the sum of the first sixteen terms of the sequence.

A. 18 B. 20 C. 22 D. 24

29. Find three numbers in Geometric progression whose sum is 28 and

whose product is 512.

A. 4, 8 and 16 B. 6, 8 and 12 C. 4, 6 and 8 D. 4, 12 and 16.




30. The cost of kerosene per litre increases from N60 to N85. What is the

percentage rate of increase?

A. 20.7% B. 27.0% C. 25.7% D. 30.7%.

31. A sales girl gave a change of N1.15 to a customer instead of N1.25.

Calculate her percentage error.

A. 4% B. 6% C. 8% D. 10%

32. The sum of three consecutive numbers is 36. Find the numbers.

A. 11, 12 and 13 B. 10, 12.5 and 13.5 C. 11, 12.5 and 12.5

D. 10, 12 and 14

33. Simplify 2x-5/3 - 3x-1/4 = 3/2

A. X = -35 B. X = -45 C. X = +35 D. X = +45

34. Evaluate 1 – (21/3 X 11/4) + 3/5




A. 15/30 B. - 513/30 C. -15/30 D. 513/30 Simplify 272/3 X 81/3 X 361/2

X 50

A. 36 B. 72 C. 128 D. 108

35. Find the values of x and y in the equation: x-2y = 4; 2x+5y=17

A. (6,1) B. (-6,1) C. (6, -1) D. (-6,-1)

36. Solve the inequality; 6x – 2 ˂ 2x + 8

A. X ˂ 2/5 B. X > 5/2 C. X ˂ 5/2 D. X > 2/5

37. Find the equation of the straight line with the coordinates A (9, 5) and

B (12, 13).

A. Y = 19 – 8/3. X B. Y = 19 + 8/3.X C. Y = 8/3.X – 19 D. Y = 8/3 x +

19

38. The expression that best represents coefficient of determination is:

A. 0 ˂ 1 ˂ r2 B. 0 ˂ r2 > 1 C. 0 > r2 > 1 D. 0 ˂ r2 ˂ 1




39. The statistical analysis from a country’s total export in respect of three

products A, B and C is as follows:

Product Mean Variance

A 25 4

B 50 15

C 40 8

The product that has the most reliable export performance is:

A. Product A B. Product B C. Product C D. None of the above.

40. A type of linear correlation coefficient that apportions to the scores

obtained from the variables under study is:

A. Multiple regression coefficient B. rank-order correlation coefficient

C. Pearson’s product moment correlation coefficient D. coefficient

of variation.

41. Given that the coefficient of correlation is calculated to be 0.726,

determine the variation that is due to or explained by unknown variables.

A. 0.527 B. 0.473 C. 0.726 D. 0.224




Information

The regression line equation is deduced to be y = 15.28 + 5.4x. Where y

is the amount of money invested in thousands of Naira and x is the

number of investors.

Use this information to answer questions 23 and 24.

42. What is the amount of money invested by 120 investors?

A. N2,481,600 B. N20,680 C. N140,680 D. N663,280

43. What is the implication of the slope of the regression equation?

A. If the number of investors increases by one, amount invested will

increase by N5,400

B. An increase of one investor leads to N15.28 increase in investment

C. An increase of one investor leads to an increase of N20,680 in the

amount invested

D. Amount invested increases by N15,280 if the number of investors

increases by one.

Information




The weekly sales of a particular commodity is given below;

Weekly Sales (N’000) No of Weeks

61 – 65 9

66 – 70 12

71 – 75 10

76 - 80 15

Use the data to answer questions 25 and 26

44. Compute the mean weekly sales.

A. N32,830 B. N38,300 C. N23,570 D. N71,400

45. Calculate the standard deviation of weekly sales.

A. 5740 B. 32950 C. 6780 D. 4600

46. All these are characteristics of the normal distribution except:

A. It has a leptokurtic shape

B. The curve must be symmetrical about the vertical axis of the mean

C. It slopes downwards towards the left and the right axis

D. The mean = median = mode.




47. The value of a dual variable which represents each additional unit of

resource is the ……..

A. Marginal profit B. Shadow price C. Minimum profit D. Dual

price

48. If the primal has unbounded solution, the dual of the LP has no …….

A. Basic solution B. shadow price C. slack variable D. feasible

solution

49. The total revenue and total cost functions are respectively expressed

for a particular product as: R= 250q – 2q2, C = 10q + 500.

What is the quantity that maximizes profit?

A. 60 B. 50 C. 40 D. 80

50. A representation of data in which every observed value is paired with

number of times each observed value occurred is:

A. Cumulative frequency distribution

B. Sampling distribution

C. Frequency distribution




D. Data distribution

51. If A and B are two events with Pr(A) = 0.30, Pr(B) = 0.78 and Pr(A n B) =

0.16. Find Pr(A u B).

A. 0.84 B. 0.92 C. 0.48 D. 0.32

52. If the elements below the leading diagonal of a matrix are zeros, the

matrix is called a ……..

A. Diagonal matrix B. singular matrix C. null matrix D. triangular

matrix

53. IRR is an acronym standing for:

A. International Rate of Returns

B. International Rate Returns

C. Internal Rate of Returns

D. Inter Rate of Returns

54. How much will N125,000 amount to at 10% per annum compound

interest over 8 years ( 3sig. fig)

A. N225,000 B. N267,948 C. N270,000 D. N268,000




55. The standard deviation of a given data is 5.3, what is the variance?

A. 28.09 B. 23.02 C. 28.08 D. 10.60

56. Which of the following is not true of simulation?

A. To maintain various options of performance

B. To study complex problem of real life

C. To imitate a real world situation

D. To obtain more accurate results

57. The simulation method that involves the use of experimentation and

sampling principles is known as:

A. Computer simulation method

B. The special purpose programming method

C. Dynmo simulation method

D. Monte Carlos simulation method

58. Given the demand function P = 150 – 3x – x2, calculate the elasticity of

demand at x = 5.

A. -1.69 B. -2.5 C. -0.42 D. -1.23




59. Which of the following is not a differentiation?

A. Rate of exchange B. derivative C. slope D. interception

60. If the Total Cost function is given by TC = 18q – 5q2 + q3, calculate the

value of the minimum Average Cost.

A. 2.5 B. 11.75 C. 6.25 D. 10

Use the given primal problem of an LP below to answer Questions 42 –

44.

Max. Z = 20x1 + 30x2

s.t 3x1 + 2x2 ≤ 200

x1 + 2x2 ≤ 100

4x1 + x2 ≤ 80

x1 , x2 ≥ 0

61. The objective function of the dual problem will be C =

A. 30y1 + 20y2 B. 200y1 + 100y2 + 80y3 C. 80x1 + 100x2 + 200x3 D.

3y1 + 2y2 + 80y3

62. The RHS of the constraints of the dual problem will be




A. (200,100) B. (3, 4) C. (20,30) D. (100,80)

63. How many constraints have the dual problem?

A. 4 B. 3 C. 5 D. 2

64. The process where a system move from one state to another

depending upon the immediate processing state with a constant

probability is known as:

A. Monte Carlo simulation method

B. Vogel’s approximation method

C. Markov process

D. Simplex method

65. The ranking made by 2 judges X and Y on 5 contestants in a Dancing

competition are as follows:

Candidate A B C D E

Judge X 4 2 5 3 3

Judge Y 2 5 2 2 3

Find the Spearman’s rank correlation coefficient.




A. O.85

B. 0.10

C. 0.58

D. 0.192

66. Suppose that there is a 30% chance that the government will approve

a new drug and a 60% chance that Drug Co’s shares will double in price as

a result. What is the probability that the drug will be approved and that

Drug Co’s shares will double in price?

A. 18%

B. 30%

C. 40%

D. 70%

67. Given the number of trials (n) and probability of success (p) for a

normal distribution are 200 and 0.6 respectively. What is the standard

deviation?

A. 10.95




B. 48.0

C. 120.0

D. 6.93

68. The annual consumption of rice (y) kg of a certain family in the period

2000 to 2007 was calculated as: Σx= 56, Σy= 40, Σx2= 524, Σxy= 364. What is

the gradient of the trend line of the consumption of rice?

A. 0.425

B. 4.25

C. 0.579

D. 1.45

69. A sum of N500, 000 was invested by two partners in a business which

yielded a profit of N900, 000. If the profit was shared in the ratio 4:5, the

difference between the amounts received by the partners is:

A. N100,000

B. N150,000

C. N250,000




D. N400,000




THEORY QUESTIONS

INSTRUCTION: ATTEMPT QUESTION 1 AND ANY OTHER FOUR OF YOUR CHOICE.

Question 1

a. Gbakoko Nig Limited manufactures electronic components of television

sets. The cost of production and selling price for each component are N240

and N360 respectively. The company’s total overhead cost is N93, 600.

i. Derive the total revenue and total cost functions.

ii. Calculate the number of components to be produced if the

manufacturer is to break even and how many components to be sold

to realize a profit of at least N360, 000.

b. Two out of every five students from NASCOL Local Government Council are

awarded scholarships to tertiary institutions. If 400 students from the Local

Government are randomly selected, calculate the probability that:

i. At least 150

ii. Between 140 and 175




iii. At most 135

Of the students are awarded scholarships.

Question 2

Consider the weights of a number of professional students given below

measured in Kilograms:

18 34 20 39 36 32 29 19 25 38

25 22 25 28 37 40 27 39 23 19

30 19 21 25 40 27 32 18 19 40

26 18 39 31 19 29 30 40 21 26

40 20 37 33 26 35 29 35 25 18

Using a class interval of 18-20, 21-23, 24-26, ….

Compute the values of the following statistics

a. the arithmetic mean

b. median and

c. Mode.




Question 3

1. The Production Manager of Abraham Group of Companies with ten plants

of similar sizes producing Tissue papers have observed the following

pattern of expenditure on inspection and defective parts delivered to their

customers.

Observation Inspection Defective

Number Expenditure Parts

1 15 60

2 24 45

3 25 50

4 30 35

5 35 42

6 40 46




7 45 28

8 65 20

9 70 22

10 75 15

Required:

i. Determine the relationship between the inspection expenditure and

the number of faulty items delivered.

ii. To what extent can they predict the number of faulty parts delivered

from knowledge of expenditure on inspection?




Question 4

Tony Farms wishes to study the relationship between his revenue and the

average revenue in Lagos. Taking a sample of 11 villages, recording for each

the average revenues in 2002, and the results showed.

Average Revenue (N) Tony Revenue (N)

26 56

18 38

28 64

20 48

16 34

18 40

26 60

24 52

16 30

28 66




14 32

Find the equation of the least square line and use it to estimate Tony

Farms revenue if the average revenue is N22.

Question 5

a. ADESCO Limited makes two different brands of golf gloves. One is a full-

fingered glove and the other is half-fingered model. ADESCO Limited

ordered more gloves than it can produce in terms of upcoming glove

session. The scarce resource in the manufacture of these gloves is 200

hours in the cutting and sewing department, 250 hours in the finishing

department and 150 hours in the packaging and shipping department.

The department time requirements and the profit per box are given below;

Cutting & Finishing Shipping& Profit

Sewing Packaging




Full 3hours 1hour 1hour 30

Half 1hour 2hours 1hour 25

i. Find the optimum product mix for ADESCO Limited assuming the

company wants to maximize.

ii. What is the maximum amount of profit ADESCO Limited can earn?

b. List and discuss the basic assumptions of linear programming model.

Question 6

a. Three factories are operated in three different locations by AMZAT

Manufacturing Company, Zaria. The products are to be shipped to three

different warehouses. The location and capacity of these warehouse and

the factories are;

Warehouse Requirement Factory Capacity

Kaduna 1,200 1 600




Katsina 800 2 1,000

Sokoto 1,000 3 1,400

The cost estimation

From To Kaduna Katsina Sokoto

1 5 6 8

2 4 7 7

3 6 8 6

Determine which factory should ship what quantity to each of the three

warehouses to minimize freight cost.

b. List and discuss the basic assumptions of transportation model.



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ICAN KNOWLEDGE LEVEL QUANTITATIVE TECHNIQUE IN BUSINESS ...starrygoldservices.com/icanknow16/icanqtmkqa.pdf · QUANTITATIVE TECHNIQUE IN BUSINESS MOCK EXAMINATION QUESTIONS FOR MAY