 | With just a few months left for the CAT, we wanted to give you some pointers on how to approach the Quant section of the test. Collated and written in collaboration with our experts, this article gives you information for a last minute preparation. In the next month, we shall provide you with a similar write up on the English section. |
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 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, so that you can optimise your performance to clear the cut-offs.
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%.
Work till the end to get the answer
It is vital that in most questions, you follow your working towards the answer to the very end. If, midway through your calculations, you find that you can make what appears to be an “educated guess”, don’t pounce on it. Work till the end to find out what the answer is.
Consider the following problem.
Mark [1], if the question can be answered by one of the statements alone but not by the other.
Mark [2], if the question can be answered by using either of the statements alone.
Mark [3], if the question can be answered by using both statements together but not by either statement alone.
Mark [4], if the question cannot be answered, even by using both statements together
Mark [1], if the question can be answered by one of the statements alone but not by the other.
Mark [2], if the question can be answered by using either of the statements alone.
Mark [3], if the question can be answered by using both statements together but not by either statement alone.
Mark [4], if the question cannot be answered, even by using both statements together
Q. The following data is available about a class:
Statement I: The ratio of the number of girls who liked Maths to number of girls who disliked Physics, is same as the ratio of the number of boys who liked Maths to the number of boys who liked Physics.
Statement II: There were 195 students in the class.
How many students liked Maths?
From Statement I, we can see that Maths/girls disliked Physics = 54/45 = 6/5. If the total number of boys is b, then:
Since the total number of students is the same, the total of Maths and Physics should be the same.
Hence, b + 6x + 40 = b+5x + 50. Therefore, x = 10, and the question can now be answered.
Many of you will probably stop midway through using the information in Statement I, and assume that using both the statements, the answer can easily be arrived at.
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.
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. You also need to be able to do a fair amount of calculation without having to put pen to paper.
A few things that are a must-know for fast calculation:
1. Powers of 2 till 12.
2. Squares of numbers from 2 to 30
3. Cubes of numbers from 2 to 12
1. Powers of 2 till 12.
2. Squares of numbers from 2 to 30
3. Cubes of numbers from 2 to 12
These fast calculations are helpful not just for the DI portion but for the entire QA-DI section.
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!
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.
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.
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.
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.
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 Rs.10,00,000. The manufacturing cost per toy (which is variable and exclusive of the fixed investment) is Rs.60. The company decides to fix the selling price of each toy at Rs.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 lakhs. If cost price per unit is `60, then total production cost is 60 lakhs plus 10 lakhs; profit = 10 lakhs. If cost price per unit falls by 25%, or 60/4 = `15, then on 1 lakh units, profit increases by 15 lakhs or 150%. Think about it — this whole solution can be verbalised without 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.
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 lakhs. If cost price per unit is `60, then total production cost is 60 lakhs plus 10 lakhs; profit = 10 lakhs. If cost price per unit falls by 25%, or 60/4 = `15, then on 1 lakh units, profit increases by 15 lakhs or 150%. Think about it — this whole solution can be verbalised without 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.
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 racing 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.
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!
This is how you squeeze every mark and every second out of a paper!
Some points to remember
Let us take a detailed 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.
So how do you ensure that you do not have an unread question at the end?
Standalone questions first, sets later
Sets, be it DI or LR, take time to solve. In case you get stuck, chances are that you will not realise how much time you have lost till you have come out of them. So in both sections start with the standalone questions and then move on to the sets.
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 standalone question is after reading it. So while going through the standalone questions, don’t start solving straightaway. First decide whether you can solve it in two and a half minutes or less, only then proceed to solve it.
Use the MARK option to navigate smartly
As you navigate the standalone questions, you will definitely find questions that are solvable but might take about 3 to 4 minutes. 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 questions option 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 unless you are dead sure that you will get the answer within the next minute. Every extra two minutes that you spend on a question is letting go of an easy question somewhere; MARK the question and move on.
Do SET-based questions in the middle
Be it DI or LR, it is best that you do not start solving a set in the last 10 minutes of the test. The best thing to do is to take up the sets in the middle. Even so, choosing the right sets as well as the easier questions within a set is important.
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; avoid the speedbreakers and move on
Let us take a detailed 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.
So how do you ensure that you do not have an unread question at the end?
Standalone questions first, sets later
Sets, be it DI or LR, take time to solve. In case you get stuck, chances are that you will not realise how much time you have lost till you have come out of them. So in both sections start with the standalone questions and then move on to the sets.
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 standalone question is after reading it. So while going through the standalone questions, don’t start solving straightaway. First decide whether you can solve it in two and a half minutes or less, only then proceed to solve it.
Use the MARK option to navigate smartly
As you navigate the standalone questions, you will definitely find questions that are solvable but might take about 3 to 4 minutes. 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 questions option 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 unless you are dead sure that you will get the answer within the next minute. Every extra two minutes that you spend on a question is letting go of an easy question somewhere; MARK the question and move on.
Do SET-based questions in the middle
Be it DI or LR, it is best that you do not start solving a set in the last 10 minutes of the test. The best thing to do is to take up the sets in the middle. Even so, choosing the right sets as well as the easier questions within a set is important.
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; avoid the speedbreakers and move on
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