ICAN KNOWLEDGE LEVEL QUANTITATIVE TECHNIQUE IN BUSINESS MOCK EXAMINATION QUESTIONS FOR NOVEMBER 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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 1
4. Determine the mean absolute deviation for the stock returns. 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 22 nd 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 3 rd and 7 th 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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 2
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 3
14. Evaluate 1 (2 1/3 X 1 1/4 ) + 3/5 A. 15/30 B. - 5 13/30 C. -15/30 D. 5 13/30 Simplify 27 2/3 X 8 1/3 X 36 1/2 X 5 0 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: STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 4
A. 0 1 r 2 B. 0 r 2 > 1 C. 0 > r 2 > 1 D. 0 r 2 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. STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 5
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 6
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 7
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 2q 2, C = 10q + 500. What is the quantity that maximizes profit? A. 60 B. 50 C. 40 D. 80 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 8
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 9
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 10
C. Dynmo simulation method D. Monte Carlos simulation method 38. Given the demand function P = 150 3x x 2, 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 5q 2 + q 3, 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 = 20x 1 + 30x 2 s.t 3x 1 + 2x 2 200 x 1 + 2x 2 100 4x 1 + x 2 80 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 11
x 1, x 2 0 41. The objective function of the dual problem will be C = A. 30y 1 + 20y 2 B. 200y 1 + 100y 2 + 80y 3 C. 80x 1 + 100x 2 + 200x 3 D. 3y 1 + 2y 2 + 80y 3 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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 12
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% STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 13
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, Σx 2 = 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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 14
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 15
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 16
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 17
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 STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 18
b. Mean deviation c. Variance d. Standard deviation e. Upper quartile f. Lower quartile g. Inter-quartile range h. Semi inter-quartile range STARRY GOLD ACADEMY +2348023428420, +2347038174484, info@starrygoldacademy.com, www.starrygoldacademy.com Page 19