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STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 1
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 2
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 3
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 4
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 5
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 6
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 7
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 8
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 9
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 10
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
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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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 12
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 13
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.
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 14
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 15
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 16
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 17
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 18
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.
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 19
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 20
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 21
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 22
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 23
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.
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 24
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 25
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 26
D. N400,000
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 27
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 28
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.
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 29
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 30
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?
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 31
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 32
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 33
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
STARRY GOLD ACADEMY +2348023428420, +2347038174484, [email protected] , www.starrygoldacademy.com Page 34
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.