skillz - mathematics

Advanc'edge MBA / June 2003

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Mathematics and Data Interpretation- Arppana George

SolutionTotal Revenue = Number of units Revenue per unitLet x be the number of units. Revenue per unit is Rs.350.Statement of Total Revenue = 350xTotal Cost = Fixed Cost + Total Variable CostThe variable cost per unit is Rs. 250. Therefore the variable cost for x units = 250x.Statement of Total Cost = 50000 + 250x

Break-Even Chart: The break-even point is defined as the point where sales or revenuesequal expenses. There is no profit made or loss incurred at the break-even point. This figureis important for anyone that manages a business since the break-even point is the lower limitof profit when setting prices and determining margins. Obviously the break-even point becomesvery important when calculating a strategy for net profit.

The break-even margin is a ratio that shows the gross-margin factor for a break-evencondition. The formula is total expenses divided by net revenues multiplied by 100 toget a percentage. This ratio is helpful when setting prices, with competitive bidding and

1. ExampleA Market research by ABC consultantsrevealed that a new product Hanoi yetto be launched in the market by PQRmanufactures can be sold at Rs.350 perunit. The Cost analysis provided thefollowing information.Fixed cost per month = Rs.50000Variable cost per unit = Rs.250Production capacity per month = 750 units.You as the manager of ABC consultant have

Mathematics and Data Interpretation are the cornerstone for decision-making and various quantitativeactivities in commerce and industry. Math skills, such as logical thinking, problem solving anddata analysis, are closer to those actually used in a competitive workplace than, skills learnedin other subjects. This being the case, an MBA entrance exam invariably tests the students reasoning,interpretation and mathematical skills.

For the mathematically disinclined, it maybe difficult to link data analysis and real life applications.Let us consider a real life example:

to provide the following information to yourclient PQR manufacturers:

1. A statement ofw the total revenue,w the total cost;

2. A detailed break-even chart;3. Computation of the break-even pointw with respect to volume,w as a percent of capacity,w with respect to value.

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Break Even Chart

300000

250000

200000

150000

100000

50000

0

Sale

s (R

s)

(0, 0)0

(750, 262500)

(750, 237500)

(0, 50000)

break even volume

Volume of Output (in units)

750

profit

break even sales

breakevenpoint

fixed cost

loss

Total Revenue

Total Cost

Fixed Cost

when negotiating contracts with vendors and accounts.When the production is nil i.e., (x = 0), total revenue generated is 0 since total revenue generated= 350x. So the line graph representing total revenue will start at the origin of the graph withsales in value as the y axis and sales in volume as the x axis. When the production is 750i.e, maximum capacity for a month the total revenue generated = 750 350 = 262500.Hence the line graph should pass through the point (750, 262500).The Fixed cost of the product Hanoi is Rs.50000.The total cost = 50000 + 250xWhen x = 0, total cost = 50000 + 250(0) = 50000.Hence the total cost line will originate at (0, 50000)When x = 750, total cost = 50000 + 250(750) = 237500.Hence the total cost line will pass through the point (750, 237500).

Computation of break even point with respect to volume:Total Revenue = Fixed Cost + Total Variable Cost + Net IncomeAt break even, Net income = 0Total Revenue = Fixed Cost + Total Variable Cost350x = 50000 + 250x350x 250x = 50000; 100x = 50000; x = 500x = 500 is the break even point in units. Which implies that PQR manufacturers must sell500 units to break even.

Computation of break even point as a percent of capacity:Capacity is 750, break even point is 500(500/750) 100 = 66.66%Thus 66.66% of units must be sold to break even.


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A B C D E Rounder Allopathic 15 58 13 10 4 Ayurvedic 48 15 24 8 5 Homeopathic 20 23 50 7 0 Galaxy Allopathic 10 48 17 19 6 Ayurvedic 34 24 24 15 3 Homeopathic 30 20 48 0 2 Dr Vain Allopathic 10 55 14 12 9 Ayurvedic 45 20 25 8 2 Homeopathic 23 23 46 0 8

Computation of break even point with respect to value:The number of units is 500 and the revenue per unit is Rs.350.The break even point in value = 500 350 = Rs.175000

As demonstrated by the above example, data analysis is an integral part of any market research.A few other fields where data analysis skills are indispensable are HR, Production and Operation.

In an entrance exam, where the test maker wants to assess the students data analysis skills, answersto such elaborate questions would be difficult to score. A better method to test the students skillsis to provide the relevant data and put forth multiple-choice questions. Also, the difficulty levelof such questions can be controlled by changing the options, since more homogeneous the options,the finer the distinction, students must make in order to identify the correct answer.

Consider the example given below which effectively tests the students data reading, analysingand interpretation capabilities.

2. ExampleThree leading drug manufacturing companiesRounder, Galaxy and Dr Vain havelaunched painkillers in allopathic, ayurvedicand homeopathic forms. The chief ingredientof the ayurvedic painkillers is A, of theallopathic medicine is B and of thehomeopathic painkillers is C. Dis a sweetening and colouring agent in all

the medicines used in various proportions.E is an illegal stimulant, 1mg of whichincreases the effectiveness of ingredientsB and C by 2%, while it reduces theeffectiveness of A by 1%. The drug willbe banned if it contains more than 10%of E.

The effectiveness of the drug depends only on the components A, B and C. The effectivenessof A, B and C is in the ratio 2: 3: 1.

Above values are in percentages of composition.1. If the side effects of a drug are proportional to the ratio of E to A, then which of the following

drugs has the least side effects?1] Rounder Ayurvedic 2] Galaxy Allopathic3] Dr Vain Allopathic 4] Dr Vain Ayurvedic



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2. By what percentage will the effectiveness of Dr Vain Ayurvedic painkiller, a 250 mg tabletbe affected if the component E is replaced with D?1] 2.2% 2] 5% 3] 1% 4] 4.5%

3. Which Companys homeopathic medicine is most effective, if each tablet is 100mg?1] Rounder 2] Galaxy3] Dr Vain 4] All three have equal effectiveness

Solution

1. 1] Rounder Ayurvedic: 5/482] Galaxy Allopathic: 6/103] Dr Vain Allopathic: 9/104] Dr Vain Ayurvedic: 2/45Hence the side effects are least for the ayurvedic pain killer from Dr Vain and the maximumfor the allopathic pain killer of the same brand. Hence, [4].

2. Effectiveness Dr Vain Ayurvedic painkiller with E (2% = 5mg)as a component:(45 2.5 2x) 0.95 + (20 2.5 3x)1.1 + (25 2.5 x)1.1 = 447.5 xEffectiveness Dr Vain Ayurvedic painkiller with E replaced by D.(45 2.5 2x) + (20 2.5 3x) + (25 2.5 x) = 437.5xDecrease in effectiveness = (447.5x 437.5x)/447.5x = 2.2%. Hence, [1].

3. Rounder : (20 2x) + (23 3x) + (50 x) = 159xGalaxy: (30 2x)0.98 + (20 3x)1.04 + (48 x)1.04 = 171.12xDr Vain: (23 2x)0.92 + (23 3x)1.16 + (46x)1.16 = 175.72. Hence, [3].

Data interpretation is directly connected to certain arithmetical and algebraic topics like percentages,CAGR (compounded average growth rate) ratio, proportion, etc. These are terms, which everymanager is expected to be familiar with. The applications of these in real and business life arewide and varied.

3. The following bar graphs provide the data for A, B, C, D and E (in terms of quantity aswell as value) which are considered as the only branded pencils available in the market.

The total market quantity wise = 285 mn unitsThe total market value wise = Rs.410 mn



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(Quantity wise sale million units)

2631

43

34

46

0

10

20

30

40

50

A B C D E

Brands

(Value wise sale million Rs.)

4349

38

5054

0

10

20

30

40

50

60

A B C D E

Brands

1. If Relative Market Potential RMP of two brands is defined as sharemarket % of Sumsharemarket %in Difference

then, what is the RMP of C and D in Quantity terms?1] 0.23 2] 0.17 3] 0.11 4] 0.09

2. What is the ratio of price per unit of the costliest and cheapest brand?1] 5 : 3 2] 7 : 4 3] 3 : 2 4] 15 : 8

3. If standard price ratio is defined as the market totalof Price Average

unbranded of Price Average branded of Price Average +,

what is the standard price ratio of pencil market?1 ] 2 2] 1.03 3] 1.1 4] 1.13

4. It is not true that1] Quantity wise branded : unbranded market ratio is 1.7 : 12] Almost 43% of the market value is attributed to unbranded market.3] Company D sells its pencils at Rs.1.47 per pencil on an average.4] The top brand has more than 15% share both value-wise and quantity-wise

Solution

1. Cs and Ds market share =

28543 100 15% and

28534 100 12%

12 1512 15

+ = 0.11. Hence, [3].

Alternatively,Since numerator and denominator are calculated with respect to the same base i.e., market



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ANIMAL WORDSCanine is an adjective relating to dogs. To which animals do these words refer:-

1. Aquiline2. Bovine3. Ursine4. Feline5. Porcine

6. Leonine7. Equine8. Ovine9. Asinine10. Vulpine

11. Lupine12. Sorcine13. Cervine14. Lepornine15. Sciurine

16. Elephantine17. Saurian18. Piscine19. Avian20. Simian

- K. Jaishankar

quantity wise we can neglect the base.

RMP = 34433443

+

100 = 77900

11%. Hence, [3].

2. By careful observation, we can find out that the costliest brand is A, price per unit of A

is 2643 = Rs.1.65. The cheapest brand is C, price per unit of C is

4338 = Rs.0.88

The ratio is 1.65 : 0.88 or 15 : 8. Hence, [4].

3. SPR =

285410

105176

180234 +

2. Hence, [2].

4. The market leader E has 13.1% share value wise and 16% quantity wise. Hence, [4].

Though most questions on data interpretationare not directly aimed at assessing the studentscalculation speed, some entrance exams do havecalculation intensive data interpretation ques-tions. The test maker here is testing the numbercrunching abilities of the student. Usually whena lot of calculation is involved to arrive atthe correct answer, the options would be veryvaried, giving enough room for approxima-tions.Data interpretation is one area of Mathematics,wherein a student need not learn formulae byrote. Hence, a student who may not necessarilybe good at quantitative problem solving canstill excel in data interpretation. Familiaritywith economic terms such as break even point

as used in the first example is advantageous,when it comes to easy comprehension of datainterpretation questions. Given the time con-straint of the examination, the students justhave to read the definition to know its relevanceto the question. Also coming across too manyterms that one is not familiar with, for the firsttime in an examination may mentally blockones understanding of the question and thusaffect scores. It is advisable for studentspreparing for such examinations to read thebusiness sections of daily newspapers. Thiswould help them not only in data interpretation,but also in group discussions and personalinterviews.


skillz - mathematics

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