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CAT: Quant questions you can expect
Sidharth Balakrishna
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October 31, 2008

The 'Quant' section in CAT is said by some to be unpredictable and tricky and consequently, not that easy to prepare for. This section sometimes springs a few surprises on unsuspecting candidates. After all, in the English section, it is almost certain that one will come across Reading Comprehension passages and in the Data Interpretation section, one can predict that one will find at least some questions dealing with tables, charts or graphs. In the Quant section, however, you cannot definitely state that you will a particular type or genre of questions!

However, this only tells part of the story. Indeed, the questions cannot be predicted, like in any good test; however, certain types of questions are certainly found virtually every year. There will almost always be questions pertaining to Algebra, in the sense you will have to find the missing value 'x' by solving certain equations. Hence, you need to make sure that you are good in the ability to write correct equations and then solve them quickly, whether mentally or on paper.

Therefore, the first step is to make sure that you are strong with your basics and fundamentals. You should ensure that you possess a fair degree of comfort when dealing with numbers. After that you have to play around with them. Some compare this to working on a computer -- if a problem crops up, you may not be prepared beforehand to handle such as issue, but if you are familiar with the basic commands, you can perhaps work your way to addressing the issue. One must not get scared and panic in this situation!

It is certainly a good idea to also go through previous years' question papers of CAT and the other B-school entrance exams and try to figure out what are the common types of questions that come year after year and also the kind of skills required of you to solve them.

Let us now look at the various types of questions that have made an appearance in the entrance exams of management schools.

The Number System
Not as important for CAT in recent years, but still fairly important in the entrance exams of other B-schools, the number system deals with irrational or rational numbers, fractions including mixed fractions, compound fractions (when the numerator and denominator are themselves fraction) complex fractions (a combination of other types of fractions) and continued fractions, etc. You could expect questions dealing with prime numbers and co-primes and their properties.

You will also find questions on indices and surds. These include numbers raised to the power of some other number. Once again, questions centre around the properties of indices. Other questions pertain to your knowledge of the rules of divisibility and the cyclicity of numbers.

This section requires you to have a working knowledge of the properties of numbers to solve questions. Did you know that any power of the number five always ends in 25? Thus given a question that requires you to calculate some impossibly high power of the number five, you can eliminate all options that do not end in 25.

As an example of the type of questions in this section, you could be asked to find the units place of 1! + 2! +3! +4! +...+70! How would you do this? You obviously cannot first calculate all the factorials of numbers uptil 70! But here is something useful: the factorials of every number starting from 5 has zero in the units place (5!=120, 6!=720 etc). And whenever you add a number with zero in the units place to any other number, the resultant number always naturally has the same digit in the units place as that of the other number. So all we need to do is find the sum of (1! +2! +3! +4!) which is 33; hence our answer is that the digit three will be in the units place.

Percentage
You can almost always find questions pertaining to 'percentages' in any question paper of a management school entrance test. The types of questions that appear under this category are:

• Simple percentage-related problems, especially when there are successive percentage changes
• Profit and loss based questions when the selling price, cost price, gain or loss may have to be calculated
• Manipulated/ faulty weight balances that do not show a correct weight thus leading to an increased profit/ loss on items sold
• Simple interest and compound interest problems
• Marked up pricing and discounts on items
• Problems pertaining to indexation and the use of indices

A fairly typical example of the easiest type of question that you could find in the profit and loss type of questions states that "a trader sells 50 toys and gains the selling price of 12 toys. What is his profit or loss percentage?" You will need to have a thorough understanding of concepts and basics here.

Factors, HCF and LCM
Questions pertaining to the HCF and LCM of numbers are a favourite of examiners, especially for institutes like the Faculty of Management Studies (FMS), the Indian Institute of Foreign Trade (IIFT), Narsee Monjee (NMIMS) and a host of other management schools. You will be tested on whether you know when to apply the concepts of finding factors of a number, their HCF and LCM and whether you have understood where this is useful.

For example, a popular question runs like this: "There is a corridor with 100 doors all of which are closed. A person comes and changes the state (ie opens) all the 100 doors. Next, a second person comes and changes the state (ie closes) of every second door (therefore doors 2, 4, 6, 8...100). This is followed by a third person who comes and changes the state of every third door (therefore doors 3, 6 ,9...99) and so on. After the hundredth person does this, what is the state of the ninety-ninth door (is it open or closed?). The answer to this is actually quite simple, when you think of it. It depends on how many people have changed the state of the ninety-ninth door: and this is all the factors of the number 99.

Similarly, you could be asked: there is a rectangular piece of cloth with dimensions 32 metres x 12 metres. What is the least number of squares that can be cut out of this rectangular piece without any cloth being wasted? The answer here first requires you to find the HCF of 32 and 12 and then proceed.

Time, Speed and Distance
Another important genre of questions. Earlier there used to be individual questions on these; now we often see caselets (or two-three linked questions) pertaining to this variety of questions.

The concept of relative speed (when two objects are moving in either the same or in opposite directions) and circular motion are often found here.

A typical question could be as follows: "Two boys begin together to write out a booklet containing 545 lines. The first boy starts with the first line, writing at the rate of 120 lines an hour; and the second starts with the last line (line 545) then writes line 544 and so on, proceeding backwards. He writes at the rate of 60 lines per hour. At what line will the two boys meet?". You could use the ratio of their speeds to easily find the solution.

Ratio and proportion/ mixtures and solutions
Some of these questions deal with the method of 'alligation' to solve questions -- note that alligation does not give actual numbers but only the ratio of two or more items. Further, do make sure that you have really understood alligation before applying it!

You could get questions dealing with relative efficiency of people, time taken to complete some task, fixed and variable costs using a constant which will have to be calculated, etc

Mixtures and solutions seem to attract considerable interest of examiners. Maybe its because you have to understand what is happening and conceptualise the method of solving the question, rather than just applying a formula. Questions dealing with the addition of new quantities to an already existing solution, replacement of one part of the mixture with another. Once again, alligation can be used to solve some of these questions.

Geometry
The number of questions pertaining to Geometry has been found to vary considerably over the years, but the last few years have seen geometry making a regular appearance. CAT has sometimes sprung Time, Speed, Distance questions combined with geometrical figures. A thorough knowledge of geometry, considerable and regular practice, and a good ability to logically think through problems will be required to do these questions well.

You have to be prepared to deal with any kind of figures in this section, be it the conventional circles and rectangles or figures that you may have never seen before. You may find that the solution can be worked out in modules, when you attack different parts of the question in turn.

Probability
CAT typically does not have a large number of questions dealing with probability or permutations and combinations, unlike some other entrance exams such as XAT or JMET. However, some of the IIMs sometimes require you to solve a question pertaining to probability or the usage of a decision tree during the interview stage.

Watch out for the application of conditional probability whenever you get a question pertaining to probability. Also make sure you are calculating the probability for what is asked, not something else (be careful of silly mistakes).

Summary
The Quant section can spring a surprise on you, especially if you are not fully prepared for the examination paper. However, if you prepare systematically and regularly, you should face too much of a problem in clearing the cut-off in this section of the CAT paper.

You can always expect questions that test your fundamentals in Maths and your ability to apply formulae and concepts properly. Many questions are typically variations of the standard types you might have come across during your preparation, hence do not panic when you see the paper!

The author is an MBA from IIM Calcutta and is employed with a management consultancy. He is also a visiting faculty with MBA coaching centres in New Delhi [Images] and a freelance writer on travel and management related issues.

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