QMI1500 Elementary Quantitative Methods

QMI1500
Elementary Quantitative Methods
Department of Decision Sciences
Assignment questions, Semester 2, 2020

Question 1

Dinesh began working as an assistant to a photographer. The photographer gives him R280 per photograph assignment for supplies and pays him R150 per hour The photographer charges customers R1360 per assignment and calculates profit as a(1360 − 280 − 150h)

where h = number of hours spent completing an assignment a = number of assignments completed.

The expression that shows the total profit created as a result of six photography assignments, is

• a(1360 − 280 − 900).
• 6480 − 150h.
• 8160 − 280 − 900h.
• 6480 − 900h.

Question 2

Simplifying

Question 3

Simplifying

Question 4

If a : b = 4 : 5, b : c = 3 : 4 and c : d = 6 : 7, then find the ratio a : b : c : d.

Question 5

After a discount of 8,5% was offered, a store sold an item for R6950,82. The store still made a 20% profit on sale. The price that the store originally paid for the item is

1. R1272,00.
2. R5300,00.
3. R5088,00.
4. R4726,00.

Question 6

There are seven candidates for a position. In how many ways can a selection of four be made amongst them, so that

1. two persons whose qualifications are below par are excluded?
2. two persons with good qualifications are included?

Pick the option below that has both answers correct.

• a. 5; b. 10
• a. 35; b. 21
• a. 120; b. 20
• a. 5; b. 20

Question 7

Consider the following number line:

If B = -1 and C -A =1,25, then D =

1. 0.
2. 0,25.
3. -0,5.
4. -0,25.

Question 8

Which of the following statement/s is/are correct?

Question 9

Simplifying

Question 10

A water container is in the form of a rectangular tank. Its base is 20cm by 17cm and the depth of the water in the container is 28cm. Tony adds one and a quarter litres, 350ml and 100ml water to the container:

Calculate by how many centimetres the level of the water in the tank has risen.

1. 4cm
2. 33cm
3. 5cm
4. 20cm

Question 11

A large department store wishes to carry out a survey by issuing a questionnaire to a sample of 100 of its 2000 account holders. The sample is to be selected as follows:

Each customer will be allocated a number from 1 to 2000. A table of random numbers from 1 to 20 will then be used to select the first member of the sample. Every succeeding 20^th member of the population of account holders will then be selected.

This form of sampling is called

1. systematic sampling.
2. stratified sampling.
3. simple random sampling.
4. multi-stage sampling.

Questions 12 to 13 are based on the following information:

A toy manufacturer sells three ranges of toys based on the different age groups of children. The manufacturer wants to construct indexes of the prices and quantities of the products that had been sold. The prices and quantities sold for the years 2016 and 2019 are shown below:

Question 12

The Laspeyers price index for 2019 with 2016 as the base year, rounded to two decimal places, is

1. 130,38.
2. 119,15.
3. 118,40.
4. 131,20.

Question 13

The Paasche quantity index for 2019 with 2016 as the base year, rounded to two decimal places, is

1. 119,15.
2. 155,34.
3. 131,20.
4. 130,38.

Question 14

CountryWide Travel had daily sales of R24635 on Monday, R23655 on Tuesday, R23506 on Wednesday, R22870 on Thursday, R24309 on Friday and R25475 on Saturday. In order to be more competitive in the market, the manager has said that they have to increase each day’s sales by 2% in the coming week. If each day’s sales are increased by exactly 2%, the mean daily sales of the coming week will be

1. R24556,50.
2. R28890,00.
3. R24075,00.
4. R29467,80.

Question 15

A woman’s salary for the years 2015, 2017 and 2019 as well as the CPI for these years are given in the table below. The base year is 2015 with a CPI fo 100.

Consider the statements below.

A: The difference between her nominal salary of 2017 and 2015 is less than the difference between her real salary of 2017 and 2015.

B: The difference between her nominal salary of 2017 and 2015 is greater than the difference between her real salary of 2017 and 2015.

C: The difference between her nominal salary of 2019 and 2015 is less than the difference between her real salary of 2019 and 2015.

Which of the statement/s is/are true?

[1] Only C [2] Only B [3] Only A [4] Only B and C

Question 16

The following observations are arranged in ascending order:

6; 14; k − 5; 17; k + 1; 2k − 13; 30; 32; 34; 2k + 3

The median of the data is 24. Which statement regarding the observations is NOT correct.

• The value of the 6^th observation is 27.
• The value of the 10^th observation is 43.
• The value of the 5^th observation is 20. [4] The value of the 3^rd observation is 15.

Question 17

The pie chart below shows the non-managerial workforce employed by a factory:

Answer the following questions:

1. Write down the fraction of the non-managerial workforce that are clerks. Write the fraction in simplest form.
2. If there are 20 mechanics, how many non-managerial employees are working in the factory?

Pick the option below that has both answers correct.

Questions 18 and 19 are based on the following information:

The following data show prices, in rand, of meal options at Bob’s Burgers:

Question 18

Bob wants to construct a frequency distribution for this data. The number of meals that belong in the interval R75,00 – R90,00 is

[4] 4.

Question 19

The standard deviation of the prices of the meal options, rounded to two decimal places, is

• R73,20.
• R21,15.
• R72,00.
• R20,43.

Question 20

The box-and-whiskers diagrams below show the weights of hand luggage, in kilograms, for three samples of 100 passengers each on a flight:

The box-and-whiskers diagram that represents a sample that has the following characteristics:

range of the weights of the hand luggage is 21kg

50% of the weights lie between 11kg and 17kg

is

[1] C. [2] A. [3] B.

[4] A or C.