Conceptual Clarity in Maths

8/3/2019 Conceptual Clarity in Maths

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Lets face it, Quantitative Aptitude (QA) is the section that many absolutely dread. To top it,the importance of QA has only increased in the newly announced format of CAT 2011. As pera previous analysis on PaGaLGuY, this might increase the proportion of tough questions in thepaper and smart selection of questions alone might not save the day. To solve the toughquestions, you would need to improve upon conceptual clarity.

The importance of conceptual clarity

Consider the following categorization of important sub-topics in QA into groups on the basis ofhow frequently they appear together in questions.

Group I: Questions related to percentages, compound interest & simple interest, profit, loss,discounts, mark up, and indexing.

Group II: Questions related to algebra, linear equations, quadratic equations, maxima &minima, inequalities, functions, binomial applications, 2-D co-ordinate system.

Group III: Questions related to ratio, proportion, partnership, work, time, speed and distance.

In the CAT, a tough quant problem usually does not contain a single concept in a complexform as much as it does many concepts entwined together. In throwing such questions into thequestion paper, the makers of CAT want to see how good you are at breaking down a largeproblem into smaller ones in order to arrive at the answer.

In each of the above groups, one main concept binds the group together. For example inGroup I, the main concept that binds all the group members together is percentages. If youimproved your skills at calculating percentages, your efficiency at solving compound andsimple interest, profit and loss, discounts, markup and indexing questions would automaticallyincrease.

Which means that solving Group I problems requires you to understand the percentagesconcept and build your skills at calculating percentages faster. This is easy to do.

Example: What is 40% of 10?

The straight way of finding it is to use the percentage formula. But there is an even moreintuitive and better method.

40% of 10

= 10% of 10 + 10% of 10 + 10% of 10 + 10% of 10

= 4 x (10% of 10)

= (50% of 10) (10% of 10)

How to find the 10% of anything? Simply move the decimal point one place to the left. So 10%of 10 becomes 1.0 = 1. And hence,

40% of 10

= 10% of 10 + 10% of 10 + 10% of 10 + 10% of 10 = 1 + 1 + 1 + 1 = 4

= 4 x (10% of 10) = 4 x 1 = 4

= (50% of 10) (10% of 10) = 5 1 = 4


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It may be easier to understand the concept of percentages pictorially. Imagine a 10-part pizza.40% would then be equivalent to four pieces of the pizza (Part I in the diagram). Increasingthis pizza by 10% would then mean adding an eleventh piece of 10% size to the circle (Part II).

Lets see what the connection is among percentages, profit & loss and compound & simpleinterest in the following Set 1 questions,

Q1. As income in 2011 is Rs 20,000 per month. If it increases by 10% next month, what willbe the next months salary?

Q2. A buys an item for Rs 20,000 and sells it for a 10% profit, what is the selling price of theitem?

Q3. Town As 2011 population is 20,000 per 1,000 acre. If the population increases by 10%,

what will be As population in 2012, per 1,000 acres?

All three of the Set 1 questions are essentially the same. The income in first questioncorresponds to the price of the item in the second and population in the third. The basicquestion remains the same What happens if we add an eleventh piece to the pizza?

Lets pump up the complexity of the above three questions a bit in Set 2,

Q1. As income in 2011 is Rs 20,000 per month. If it increases by 10% next month, what willbe the next month salary? If the salary further increases by same percentage point in thesubsequent month, what will be the final salary amount?

Q2. A buys an item for Rs 20,000 and increases the amount by 10% twice successively, whatis the selling price of the item?

Q3. Town As 2011 population is 20,000 per 1,000 acre. If the population increases by 10%,what will be As population in 2013 per 1,000 acres considering similar increase year on year?

The three questions now deal with an increase over an increase.

Q1 Q2 Q3 ValuePercentage

change

Increased

value

Set

1 Income

Item

price Population 20,000 10% 22,000


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Set

2Income

Item

pricePopulation

22,000 (after

increase of

10%)

10% (over an

increase)24,200

Now with practice if you learn to identify that the core of all such questions is percentageincreases over a base value, gradually it will cease to matter to you whether the question isabout income, price, number, area, volume or weight.

This is how the CAT examiners have been confusing test-takers by mixing up terminology frommultiple subjects to see if you can identify the main concept and crack the question faster.

In Group II, building conceptual clarity in algebra will make solving questions related to therest of the group items easier. For Group III, conceptual clarity in ratios and proportions will dothe trick.

Make Math practice fun

Those who are not from engineering and science backgrounds often complain about the lackof comfort with maths. In reality, Math can be made an integral part of your life. For instance,when buying fruits and vegetables at supermarkets, observe as the cashier puts an item onthe weight machine and then types in a code that displays the final price of that item. Knowingthe kilogram price of that item, can you calculate the price in your head during the fewseconds that the attendant types in the code? With practice, you can!

If the speed of the cash register discourages you, start with the receipt instead. Select a fewitems from the printed receipt and perform the calculations in your head on your way backhome. Initially, you can try calculating to the nearest whole number approximation andgradually move towards precision.

For example, 800 g of Rs 130 per kg apples would cost 80% of 130, as 800 g is 80% of 1,000gor 1 kg. This will help you get comfortable with percentages. Eventually a comfort zone willemerge and you will start building your own little tricks and shortcuts. All the best!

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Conceptual Clarity in Maths