Quant matters: How to tackle CAT'ematics
|After last month’s English section, this time, we focus on the Quant section of the CAT. Collated and written in collaboration with our experts, in this article, you will find some pointers on how to approach the questions in this section of the test.|
The Advanc’edge Team
(with inputs from IMS Acads)
They say Mathematics is the language of nature, of everything around us, of the Universe itself. In the days of polymaths, who were scholars not just learned but full-fledged experts in several fields, mathematics was the subject that everyone knew and studied. The great philosophers of old, like Ptolemy, Aristotle and Plato, were all great mathematicians in their own right. Even now, almost every branch of science has mathematics at its core, in varying degrees of course. And since you’re preparing to study the science of management, you will need to know your math.
In the September issue of Advanc’edge, we broke down the English verbal section of the CAT, to give you an idea of what you will expect in the CAT. This time, we’re treating you to a snapshot of the Quant section, with examples of how to face the questions.
In the CAT, it all boils down to the cut-off score you can get. Sometimes, clearing the cut-off can be a matter of just one question here and there. Let us look at a few things in the QA-DI section that you should watch out for.
Look beyond the formula
While tackling any question, keep your eyes and ears open. Knowing the formulae to crack a question is, of course, imperative, but often, just by being aware of exactly what the question is, you needn’t even have to apply the formula.
For instance, consider the problem below.
Q. Two barrels A and C contain alcohol and water in the ratio 1:a and 1:c respectively. Equal quantities of the mixtures from A and C are mixed to get a mixture with alcohol and water in the ratio 1:b, where b is the arithmetic mean of a and c. What can be a possible value of a + b+ c, if a, b and c are integers?
1] 14 2] 10 3] 15 4] 8
This appears to be a straightforward problem, where you work in autopilot mode and fit the formula for mixtures into the question to arrive at the answer. However, consider this.
If b is the arithmetic mean of a and c, then 2b = a + c. This means that a +b + c = a + c + b = 2b + b = 3b. Hence, a + b + c has to be a multiple of 3. Select the answer that is a multiple of 3 from the given options, and Bob’s your uncle!
In this example, simply keeping your mind, eyes and ears open will lead you to the solution fairly easily.
Consider another question.
Q. A dishonest shopkeeper sells at cost price but makes a profit of 25% by using faulty weights. If he wants to make a profit of 12% how much discount should he offer?
1] 15.2% 2] 12.5% 3] 10.4% 4] 13%
By now all of you should be in the habit of using 100 instead of ‘x’ as the cost price to solve most Profit and Loss problems. So if 100 is the C.P, then 125 is the S.P since he is making a profit of 25%. A profit of 12% means an S.P of 112 and a discount of 13; 13 will be just over 10% of 125 (10% is 12.5, moving one decimal to the left). The answer will be the option closest to this figure, between 10 and 11%.
Q. A train approaches a tunnel PQ. Inside the tunnel is a dog located at a point that is the of the distance PQ measured from the entrance P. When the train whistles the dog runs. If the dog moves to the entrance of the tunnel P, the train catches the dog exactly at the entrance. If the dog moves to the exit Q, the train catches the dog at exactly the exit. What is the ratio of the speeds of the train and the dog?
1] 3:1 2] 4:1 3] 5:1 4] 6:1
You can very well get the answer if you form equations and solve them. However this question requires no equation to get the answer. Consider the following:
If the dog is seated at point R, at a distance of 5 units from P and 7 units from Q. If he runs towards P, the train reaches point P. That means by the time the train reaches point P, the dog has run 5 units. Instead, if the dog runs 5 units in the opposite direction, he will be at point S, which is 2 units away from Q. Train doesn’t care which direction the dog runs so the train is at point P when the dog has run 5 units and is at point S. Therefore additional distance the train has to run is 12 units and the additional distance the dog has to run is 2 units to reach Q together. Therefore the required ratio is 6:1.
DI is really not that tough
DI questions are more or less freebies, especially the ones that do not involve any deduction (like filling up empty tables, etc.) and are based purely on understanding the set and calculating precisely. At their toughest, they involve interpreting the meaning of the data given. But even then they offer a good value for time spent, since there is a very high chance of getting them correct.
For instance, in problems involving DI sets, the key to getting good at solving the sets is to understand that DI does not just mean painful number crunching. That would mean going at the problem with a hammer. You need to develop the ability to determine when to calculate and when to approximate. A few things that are a must-know for fast calculation:
- Powers of 2 till 12.
- Squares of numbers from 2 to 30
- Cubes of numbers from 2 to 12
Although you may think that you can rely on the on-screen calculator in CAT for calculations, using an on-screen calculator with a mouse, especially for large calculations is a time-consuming job. Knowledge of such points will expedite your calculations greatly.
It’s only logical
Quite often, you will come across a problem that looks quite tough, and appears to need a great deal of formula laying and solving. However, more often than not, it actually is just a matter of logical reasoning!
Consider the following example.
Q. N is a natural number with a sum its digits as 3. If 1013 < N < 1014, then how many values can N have?
If the number is a 2-digit number, it will be either 21, 12 or 30. If it is 3-digit number, it will be 201,210, 102, 120, 300 or 111.
So, the number of values N can take depends on the number of digits. 101 has 2 digits, 102 has 3 digits and so on, until 1013 will have 14 digits. Hence, N will have 14 digits.
Now, N can either be a number with three 1s: start with 1 and have the remaining two 1s in any of the remaining 13 places; two places out of 13 can be chosen in 13C2 = 13*12/2 = 78 numbers with a 2 & 1: start with 2 and have the 1 in any of the 13 remaining places = 13 numbers ; start with 1 and have the 2 in any of the 13 remaining places = 13 numbers; or a number starting with 3 followed by 13 zeroes.
Therefore, the total number of values N can assume are 78 +13+13+1 = 105.
Don’t write if you don’t have to
It is an ingrained feeling in most of us that writing means that we’re really trying to solve the problem. However, read and understand the question fully before rushing to write. You are not saving any time by writing down anything before you have read the question. In fact, because you do not read properly you end up solving questions twice.
Secondly, write only when required. If you can solve a question mentally, why write and make equations like kids. By writing you are under-utilizing your mental ability and spending more time than required to solve questions.
Consider the following example.
Q. Kidsplay, a multinational toy manufacturing company decides to set up a plant in India. To set up a plant, the company has an initial fixed investment of `10,00,000. The manufacturing cost per toy (which is variable and exclusive of the fixed investment) is `60. The company decides to fix the selling price of each toy at `80. Assume there is no other cost or investment incurred by the company for selling or manfacturing the toys.
Using cost optimization measures, Kidsplay reduced the manufacturing cost per toy by 25%. As a result of this, on a production and sale of 1 lakh units of toys, the profit of the company increased by:
1] 100% 2] 120% 3] 125% 4] 150%
One lakh units’ selling price is `80 lakh. If cost price per unit is `60, then total production cost is `60 lakh plus `10 lakh; profit = `10 lakh. If cost price per unit falls by 25%, or 60/4 = `15, then on 1 lakh units, profit increases by `15 lakh or 150%. This solution can be verbalised without ever putting pen to paper!
Solving problems mentally and putting pen on paper only when required is a way of sharpening your mind to the tip of an arrow. It is not easy to make a full turnaround from a habit that is so ingrained. But it will definitely be worth the effort.
Look at the problem differently
How do you know that there might be an alternative method? Which problems do you choose to solve by the non-standard method?
Typically, it is either the most standard looking or the most unconventional looking problem that can have a short solution. By most standards, these are the questions that have some sort of symmetrical situation about them. Consider the problem below.
Q. On a 120-km race track, if P and Q start driving in the same direction from the same point and at the same time, then P wins the race by 25 minutes. If they drive towards each other from the opposite ends on the same track starting at the same time, the distances that P and Q cover when they meet are in the ratio 3 : 2. Find the speed of P’s car.
It is obvious that the lesser time in the first case, is related to the extra distance in the second case. You have to understand that there has to be a short method to solve this type of question. You cannot solve the question using equations.
When they are running in the opposite direction the distance covered is 3:2. Even when they are running in the same direction, the distances covered when P reaches the end will be in the ratio 3:2 (since their speeds are the same).
Therefore, when P is at 120, Q is at 80 and to cover 40, Q needs 25 minutes. So, Q’s speed is 40/(25/60) and P’s speed is 3/2 of Q’s speed.
This is how you squeeze every mark and every second out of a paper!
Some points to remember
Let’s take a look at the most important test-taking strategy as far the CAT is concerned: You shall not have unread questions at the end of a section.
If there has to be one golden rule that you are not supposed to break, this is the one. The CAT is not about answering tough questions, it is about selecting and answering the relatively easier questions.
How do you ensure that you don’t have an unread question at the end?
First pick, and only then solve
Based on your competence, you will have a fair idea by now as to how easy or difficult a question is after reading it. So while going through the questions, don’t start solving straightaway. First decide whether you can solve it in a minute or a minute and a half minutes or less, only then proceed to solve it right there. If not, move to next question.
Use the MARK option to navigate
As you navigate the questions, you will definitely find questions that are solvable but might take longer. Some of these might take time just because they are lengthy. Single out these questions to solve later. Use the MARK button to single out these questions so that you can use the REVIEW MARKED options to quickly reach these questions later.
Do not throw good money after bad money
The biggest mistake test-takers are guilty of is wasting time on questions on which they have already exceeded the average time of 2.5 minutes. If you have taken more than 2 minutes for a question, do not spend any more time on it. Every extra two minutes that you spend on a question is letting go of an easy question somewhere.
You need not do all the questions in a set.
Even sets that are easy overall might have a question which is a speed-breaker. Just because you spent time reading a set does not mean that you have to answer all questions.