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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

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

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

2. Determine the arithmetic mean return for the stocks.

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

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

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

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

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

5. 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

6. 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)

7. 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

8. 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

9. 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.

10. 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%.

11. 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%

12. 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

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

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

14. 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

15. 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)

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

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

17. 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

18. 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




19. 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.

20. 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.

21. 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.

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

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

23. 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

24. Compute the mean weekly sales.

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

25. Calculate the standard deviation of weekly sales.

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

26. 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.

27. 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

28. 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

29. 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

30. 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




31. 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

32. 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

33. 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

34. 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




35. 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

36. 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

37. 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

38. 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




39. Which of the following is not a differentiation?

A. Rate of exchange B. derivative C. slope

D. interception

40. 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

41. 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

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

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




43. How many constraints have the dual problem?

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

44. 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

45. 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

46. 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%

47. 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




48. 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

49. 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.

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

The record below shows the scores obtained by some students in a

Mathematics est:

12 15 20 25 30 20 30 15 12 12 15 12 25 12 20 12 20 12 15 25




12 15 12 15 12 15 12 20 20 30 30 25 15 30 20 15 25 30 15 12 12 15 12 15 12 30 20 20 12 15 Compute the following: a. Range

b. Mean deviation

c. Variance

d. Standard deviation

QUESTION 4

Consider the weights of a number of 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 following: a. Range

b. Mean deviation

c. Variance

d. Standard deviation

e. Upper quartile

f. Lower quartile

g. Inter-quartile range

h. Semi inter-quartile range



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