**UNIVERSITY EXAMINATIONS: 2016/2017**

**EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION **

**TECHNOLOGY**

**DBIT 302 FUNDAMENTALS OF MANAGEMENT MATHEMATICS**

**DATE: JULY, 2017 TIME: 1 ½ HOURS**

**Instructions: Answer question one (compulsory) and any other two questions.**

**QUESTION ONE (Compulsory)**

(a) Using relevant examples briefly explain the following terms as used in set theory

(i) Disjoint sets (2 Marks)

(ii) Universal set (2 Marks)

(iii) Subset (2 Marks)

(v) Compliment of a set (2 Marks)

(b) XYZ College offers three courses, namely; Accounting, Information Technology and

Statistics. The marketing department of the college has conducted a survey on the 500 students to

determine the number of students enrolled for each of the three courses. The results of the survey

were as follows;

329 students were enrolled for Accounting

186 students were enrolled for Information technology

295 students were enrolled for Statistics

83 students were enrolled for Accounting and Information technology

217 students were enrolled for Accounting and Statistics

63 students were enrolled for Statistics and Information technology

Required:

(a) Represent the above data in a Venn diagram. (5 Marks)

(b)The number of students enrolled

(i) Accounting only (2 Marks)

(ii) Statistics only (2 Marks)

(iii) Information Technology (2 Marks)

(iv) Exactly 2 courses

(v) Statistics and Information Technology but not Accounting. (2 Marks)

(c) A certain audit firm has two categories of employees, auditors and assistant auditors. The

total monthly salary of 1 auditor and 5 assistant auditors amount to Sh. 456,755 whereas the total

monthly salary of 3 auditors and 9 assistant auditors amount to Sh. 985,005. The firm has a total

of 6 auditors and 14 assistant auditors. The employees contribute 12 percent of their monthly

salaries towards their Sacco society.

Required:

(i) Form simultaneous equations to represent the above information (2 Marks)

(ii) The monthly salary of an auditor and an assistant auditor (3 Marks)

(ii) The employees’ total monthly contribution towards their Sacco society. (2 Marks)

(d) Distinguish between simple interest and compound interest (2 Marks)

(Total: 30 Marks)

**QUESTION TWO**

(a) Solve the following simultaneous equations

X+2Y=3

X-2Y=11 (5 Marks)

(b) James bought 5 kgs of maize and 6 kgs of beans for Sh. 280 at ABC market and he also

bought 7 kgs of Maize and 9kgs of beans for Sh. 410 at QRS market. Determine the price per

kg of maize and a kg beans. (6 Marks)

(c) Solve the following quadratic functions;

(Total: 20 Marks)

**QUESTION THREE**

(a) XYZ limited conducted a market survey to investigate customer’s loyalty to the company’s

three types of product namely; A,B and C. the survey covered a total of 100 customers. The

following were the findings.

22 customers were loyal to product A

18 customers were loyal to product B

16 customers were loyal to product C

10 customers were loyal to both product A and B

7 Customers were loyal to both product A and C

6 customers were loyal to both product B and C

4 Customers were loyal to all the three products.

Required:

(i) Represent this information in a Venn diagram (5 Marks)

(ii) Determine the number of the customers who were loyal to at least one of the three products.

(2 Marks)

(iii) Determine the number of customers who were not loyal to any of these three products.

(1 mark)

(iv) Determine the number of customers who were loyal to exactly two products. (2 Marks)

(b) Show the sum of n item in an arithmetic progression (2 Marks)

(c ) Show how to get the last term in an arithmetic progression (2 Marks)

(d) James intends to buy a washing machine for her dry cleaning business. The cash price of the

washing machine is sh. 84,000. Determine how long it would take for James to raise the amount

enough to buy the machine if he invest sh. 30,000 at a rate of 20% p.a interest compounded

annually (6 Marks)

(Total: 20 Marks)

**QUESTION FOUR**

(a) An investor deposited sh.Z in a fixed deposit account that pays interest at a rate of 10% p.a

for 3 years. He also invested sh.T in an investment fund that pays interest at a rate of 15% p.a.

for 3 years. The investor received accrued interest payments of sh.25, 345 and sh.60, 650 from

the fixed deposit account and the investment fund respectively.

Required:

(i) The values of Z and T if the fixed deposit account and the investment fund paid

Simple interest over the 3 years period. (6 Marks)

(ii) The value of Z and T, to the nearest sh.100, if the fixed deposit account paid

interest compounded quarterly and the investment fund paid interest compounded

annually over the 3 year period. (6 Marks)

(b) Mr.Kamau invested sh.15, 000 and 20,000 at simple interest rates of x% p.a and y% p.a

respectively. The investments earned him a total interest of sh.11, 400 after a period of 3 years.

If he had invested sh.35,000 at a simple interest rate of ((x + y)/2) per cent p.a, the investment

would have earned him a total interest of sh.11550.

Required:

The rate of interest represented by x% and y%. (8 Marks)

(Total: 20 Marks)

**QUESTION FIVE**

(a) Distinguish between simple interest and compound interest. (4 Marks)

(b) Jane invested Sh. X in an investment fund at 10% p.a interest compounded annually;

determine how long it will take Jane to get twice the amount she invested. (4 Marks)

(c ) Determine the rate of interest on Sh. 129, 000 invested to yield Sh. 5, 000compound interest,

interest compounded annually for 5 years. (5 Marks)