Five Ways To Drastically Improve Your Quant Skills - Notes, Skill Development Notes | EduRev

: Five Ways To Drastically Improve Your Quant Skills - Notes, Skill Development Notes | EduRev

 Page 1


The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
Five Ways To Drastically Improve Your 
Quant Skills 
 
 
 
Most of the MBA entrance examinations require you to be extremely quick, agile and 
efficient a problem-solving. The MBA aspirants spend several hours mastering the ways 
to speed up their problem-solving abilities. 
 
The usual tools for speeding up problem-solving are : finding short-cuts, memorizing all 
the formula, learning tricks to compute faster, etc. 
 
These tools do have a role to play, but they do nothing to enhance your problem-solving 
abilities.  
 
 
Try out these tips and see your problem-solving abilities soar up instantly. 
 
 
Tip No. 1  
The best way to speed up calculations is to eliminate the need of 
calculations. 
 
Most problems in CAT/GMAT are actually meant to test your ability to look at a 
complex scenario and find simple solutions to it. You are wannabe managers, right ? A 
manager is not somebody who is a mathematical genius, but somebody who is proficient 
at efficient utilization of resources.  
 
In most problems, a bulk of calculation can be avoided by using logical arguments.  
 
This is the best way to speed up calculations – avoid the need for calculations. Before 
rushing on to make a calculation – stop to see if there are logical explanations that can 
resolve things to a great degree ? You will be surprised, that in most cases, this actually 
turns out to be so. The questions for these examinations are carefully crafted not to test 
whether you can find a cube-root, but to find out whether you can find the inherent 
patterns in the problem and reveal the underlying simplicity. 
 
Consider the following problem : 
 
S is a 6-digit number that begins with 1. When the digit “1” is moved from the left-most 
to the right-most place, the resultant number is three times the original number. The sum 
of the digits of S is : 
 
Page 2


The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
Five Ways To Drastically Improve Your 
Quant Skills 
 
 
 
Most of the MBA entrance examinations require you to be extremely quick, agile and 
efficient a problem-solving. The MBA aspirants spend several hours mastering the ways 
to speed up their problem-solving abilities. 
 
The usual tools for speeding up problem-solving are : finding short-cuts, memorizing all 
the formula, learning tricks to compute faster, etc. 
 
These tools do have a role to play, but they do nothing to enhance your problem-solving 
abilities.  
 
 
Try out these tips and see your problem-solving abilities soar up instantly. 
 
 
Tip No. 1  
The best way to speed up calculations is to eliminate the need of 
calculations. 
 
Most problems in CAT/GMAT are actually meant to test your ability to look at a 
complex scenario and find simple solutions to it. You are wannabe managers, right ? A 
manager is not somebody who is a mathematical genius, but somebody who is proficient 
at efficient utilization of resources.  
 
In most problems, a bulk of calculation can be avoided by using logical arguments.  
 
This is the best way to speed up calculations – avoid the need for calculations. Before 
rushing on to make a calculation – stop to see if there are logical explanations that can 
resolve things to a great degree ? You will be surprised, that in most cases, this actually 
turns out to be so. The questions for these examinations are carefully crafted not to test 
whether you can find a cube-root, but to find out whether you can find the inherent 
patterns in the problem and reveal the underlying simplicity. 
 
Consider the following problem : 
 
S is a 6-digit number that begins with 1. When the digit “1” is moved from the left-most 
to the right-most place, the resultant number is three times the original number. The sum 
of the digits of S is : 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
(i) 6    (ii) 15  (iii) 24 (iv) 27 
 
Try it out for a while before you proceed. 
 
There are several ways to solve this problem – some involving some trial-and-error, some 
involving some solid calculations. Most of them involve finding the value of S and then 
adding the digits to find the sum. 
 
Now read through the problem statement again thoroughly – s l o o o o w w w l y and 
mark all the important points in the problem statements. 
 
What we have to find is the sum of the digits of S. Can we do something directly about 
the sum of the digits of S ? 
 
Note that the digits of S remains the same, only the order changes. Therefore, the sum of 
the digits of S and the second number (which is 3S) are the same. 
 
Now, since 3S is a multiple of 3, what can you say about the sum of digits of S ? 
 
It has to be a multiple of 3. 
 
What can you say about the sum of digits of S ? It is the same as the sum of digits of 3S, 
isn’t it ?  
 
Therefore, the sum of digits of S is a multiple of 3. 
 
Therefore, S is a multiple of 3. 
 
Therefore, 3S is a multiple of 9. 
 
Therefore, the sum of digits of 3S is a multiple of 9. 
 
Therefore, the sum of digits of S is a multiple of 9. 
 
Can you find the answer now ? 
 
Although this argument takes a lot of space to write and a lot of time to read, it would 
take a few seconds for you to go through the entire argument and get to the right answer. 
 
What does it take to come up with solutions like these ? The answer is 
extreeeeeeeeeeemely simple – and is disclosed in the next tip. 
 
 
 
 
Page 3


The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
Five Ways To Drastically Improve Your 
Quant Skills 
 
 
 
Most of the MBA entrance examinations require you to be extremely quick, agile and 
efficient a problem-solving. The MBA aspirants spend several hours mastering the ways 
to speed up their problem-solving abilities. 
 
The usual tools for speeding up problem-solving are : finding short-cuts, memorizing all 
the formula, learning tricks to compute faster, etc. 
 
These tools do have a role to play, but they do nothing to enhance your problem-solving 
abilities.  
 
 
Try out these tips and see your problem-solving abilities soar up instantly. 
 
 
Tip No. 1  
The best way to speed up calculations is to eliminate the need of 
calculations. 
 
Most problems in CAT/GMAT are actually meant to test your ability to look at a 
complex scenario and find simple solutions to it. You are wannabe managers, right ? A 
manager is not somebody who is a mathematical genius, but somebody who is proficient 
at efficient utilization of resources.  
 
In most problems, a bulk of calculation can be avoided by using logical arguments.  
 
This is the best way to speed up calculations – avoid the need for calculations. Before 
rushing on to make a calculation – stop to see if there are logical explanations that can 
resolve things to a great degree ? You will be surprised, that in most cases, this actually 
turns out to be so. The questions for these examinations are carefully crafted not to test 
whether you can find a cube-root, but to find out whether you can find the inherent 
patterns in the problem and reveal the underlying simplicity. 
 
Consider the following problem : 
 
S is a 6-digit number that begins with 1. When the digit “1” is moved from the left-most 
to the right-most place, the resultant number is three times the original number. The sum 
of the digits of S is : 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
(i) 6    (ii) 15  (iii) 24 (iv) 27 
 
Try it out for a while before you proceed. 
 
There are several ways to solve this problem – some involving some trial-and-error, some 
involving some solid calculations. Most of them involve finding the value of S and then 
adding the digits to find the sum. 
 
Now read through the problem statement again thoroughly – s l o o o o w w w l y and 
mark all the important points in the problem statements. 
 
What we have to find is the sum of the digits of S. Can we do something directly about 
the sum of the digits of S ? 
 
Note that the digits of S remains the same, only the order changes. Therefore, the sum of 
the digits of S and the second number (which is 3S) are the same. 
 
Now, since 3S is a multiple of 3, what can you say about the sum of digits of S ? 
 
It has to be a multiple of 3. 
 
What can you say about the sum of digits of S ? It is the same as the sum of digits of 3S, 
isn’t it ?  
 
Therefore, the sum of digits of S is a multiple of 3. 
 
Therefore, S is a multiple of 3. 
 
Therefore, 3S is a multiple of 9. 
 
Therefore, the sum of digits of 3S is a multiple of 9. 
 
Therefore, the sum of digits of S is a multiple of 9. 
 
Can you find the answer now ? 
 
Although this argument takes a lot of space to write and a lot of time to read, it would 
take a few seconds for you to go through the entire argument and get to the right answer. 
 
What does it take to come up with solutions like these ? The answer is 
extreeeeeeeeeeemely simple – and is disclosed in the next tip. 
 
 
 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
 
 
Tip No. 2  
The most important step in solving a problem is to “study” the problem 
statement - NOT read it , NOT skim through it, but study it thoroughly 
– chew it, digest it, assimilate it.  
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Most of the time we just read through a problem and rush through to the solution. The 
biggest excuse for this approach is – the lack of time. We just have seconds to solve each 
problem, right ? 
 
Ironically, this would be your biggest undoing. 
 
A skillful, efficient problem-solver follows an entirely different approach. He enjoys 
exploring the problem, looking at it through different perspectives, and while doing so – 
an interesting, elegant solution emerges which saves him several minutes of hard-work in 
getting the answer. 
 
Yes, yes, I can hear you scream – Where is the time ? We have to solve the problems in 
seconds.  
 
I know. Read the following statement again : 
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Consider the following problem : 
 
Ram and Shyam start from a point A, move to B which is  5 Kms away from A, and then 
travels back to A. Ram starts at 9 AM, traveling at 5 Km/hr while Shyam starts at 9:45 
AM, traveling at 10 Km/hr. When do they meet first ? 
 
Try the problem for a while before proceeding further. 
 
There is a general tendency to start forming equations about the problem statement and 
trying to solve them. If you followed that approach, you would realize the complexity 
with the problem – you don’t know whether they were moving in the same direction or in 
the opposite direction when they meet first, and because of this, you cannot really form a 
simple equation to represent the above problem. 
 
Let us dig into the problem further. 
Page 4


The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
Five Ways To Drastically Improve Your 
Quant Skills 
 
 
 
Most of the MBA entrance examinations require you to be extremely quick, agile and 
efficient a problem-solving. The MBA aspirants spend several hours mastering the ways 
to speed up their problem-solving abilities. 
 
The usual tools for speeding up problem-solving are : finding short-cuts, memorizing all 
the formula, learning tricks to compute faster, etc. 
 
These tools do have a role to play, but they do nothing to enhance your problem-solving 
abilities.  
 
 
Try out these tips and see your problem-solving abilities soar up instantly. 
 
 
Tip No. 1  
The best way to speed up calculations is to eliminate the need of 
calculations. 
 
Most problems in CAT/GMAT are actually meant to test your ability to look at a 
complex scenario and find simple solutions to it. You are wannabe managers, right ? A 
manager is not somebody who is a mathematical genius, but somebody who is proficient 
at efficient utilization of resources.  
 
In most problems, a bulk of calculation can be avoided by using logical arguments.  
 
This is the best way to speed up calculations – avoid the need for calculations. Before 
rushing on to make a calculation – stop to see if there are logical explanations that can 
resolve things to a great degree ? You will be surprised, that in most cases, this actually 
turns out to be so. The questions for these examinations are carefully crafted not to test 
whether you can find a cube-root, but to find out whether you can find the inherent 
patterns in the problem and reveal the underlying simplicity. 
 
Consider the following problem : 
 
S is a 6-digit number that begins with 1. When the digit “1” is moved from the left-most 
to the right-most place, the resultant number is three times the original number. The sum 
of the digits of S is : 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
(i) 6    (ii) 15  (iii) 24 (iv) 27 
 
Try it out for a while before you proceed. 
 
There are several ways to solve this problem – some involving some trial-and-error, some 
involving some solid calculations. Most of them involve finding the value of S and then 
adding the digits to find the sum. 
 
Now read through the problem statement again thoroughly – s l o o o o w w w l y and 
mark all the important points in the problem statements. 
 
What we have to find is the sum of the digits of S. Can we do something directly about 
the sum of the digits of S ? 
 
Note that the digits of S remains the same, only the order changes. Therefore, the sum of 
the digits of S and the second number (which is 3S) are the same. 
 
Now, since 3S is a multiple of 3, what can you say about the sum of digits of S ? 
 
It has to be a multiple of 3. 
 
What can you say about the sum of digits of S ? It is the same as the sum of digits of 3S, 
isn’t it ?  
 
Therefore, the sum of digits of S is a multiple of 3. 
 
Therefore, S is a multiple of 3. 
 
Therefore, 3S is a multiple of 9. 
 
Therefore, the sum of digits of 3S is a multiple of 9. 
 
Therefore, the sum of digits of S is a multiple of 9. 
 
Can you find the answer now ? 
 
Although this argument takes a lot of space to write and a lot of time to read, it would 
take a few seconds for you to go through the entire argument and get to the right answer. 
 
What does it take to come up with solutions like these ? The answer is 
extreeeeeeeeeeemely simple – and is disclosed in the next tip. 
 
 
 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
 
 
Tip No. 2  
The most important step in solving a problem is to “study” the problem 
statement - NOT read it , NOT skim through it, but study it thoroughly 
– chew it, digest it, assimilate it.  
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Most of the time we just read through a problem and rush through to the solution. The 
biggest excuse for this approach is – the lack of time. We just have seconds to solve each 
problem, right ? 
 
Ironically, this would be your biggest undoing. 
 
A skillful, efficient problem-solver follows an entirely different approach. He enjoys 
exploring the problem, looking at it through different perspectives, and while doing so – 
an interesting, elegant solution emerges which saves him several minutes of hard-work in 
getting the answer. 
 
Yes, yes, I can hear you scream – Where is the time ? We have to solve the problems in 
seconds.  
 
I know. Read the following statement again : 
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Consider the following problem : 
 
Ram and Shyam start from a point A, move to B which is  5 Kms away from A, and then 
travels back to A. Ram starts at 9 AM, traveling at 5 Km/hr while Shyam starts at 9:45 
AM, traveling at 10 Km/hr. When do they meet first ? 
 
Try the problem for a while before proceeding further. 
 
There is a general tendency to start forming equations about the problem statement and 
trying to solve them. If you followed that approach, you would realize the complexity 
with the problem – you don’t know whether they were moving in the same direction or in 
the opposite direction when they meet first, and because of this, you cannot really form a 
simple equation to represent the above problem. 
 
Let us dig into the problem further. 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
Let us explore what Ram does. He starts from the point A at 9 AM at 5 Km/Hr.  
 
Therefore, he reaches B at 10 AM and back to A at 11 AM. 
 
What about Mr Shyam ?  He starts from the point A at 9:45 AM at 10 Km/Hr. 
 
Therefore, he reaches B at 10:15 AM and back to A at 10:45 AM. 
 
What happens at 10 AM ? 
 
At 10 AM, Ram has started moving from point B back to point A at 5 Km/Hr 
 
At 10 AM, Shyam is 2.5 Kms away from B and is moving towards it at 10 Km/Hr 
 
Now we have a new problem to solve : 
 
At 10 AM, A and B are 2.5 Kms apart, they are moving in the opposite directions at 5 
Km/Hr and 10 Km/Hr respectively. When do they meet ? 
 
 
Did the original problem really have so much information in it ? Yeeeeesssssss --- only if 
you go down deep enough. 
 
 
As an exercise, try finding the time when Ram and Shyam meet for the second time.  
 
 
 
It is IMPOSSIBLE to get to solutions like these, if you tend to rush through to the 
solution using the most familiar ways known to you. 
 
 
Similarly, it is POSSIBLE for EVERYONE (yes, and that includes YOU) to be able to 
come up with solutions like these, provided you spend sufficient time with the problem 
statement, the options given. 
 
Being inefficient and ineffective at problem-solving is a simple 3-step process : 
 
1) Read through the problem fast 
2) Start solving the problem 
3) Congratulations if you still got a great solution. Otherwise, happy merry-go-rounding. 
 
 
Being efficient and effective at problem-solving is even simpler : 
Page 5


The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
Five Ways To Drastically Improve Your 
Quant Skills 
 
 
 
Most of the MBA entrance examinations require you to be extremely quick, agile and 
efficient a problem-solving. The MBA aspirants spend several hours mastering the ways 
to speed up their problem-solving abilities. 
 
The usual tools for speeding up problem-solving are : finding short-cuts, memorizing all 
the formula, learning tricks to compute faster, etc. 
 
These tools do have a role to play, but they do nothing to enhance your problem-solving 
abilities.  
 
 
Try out these tips and see your problem-solving abilities soar up instantly. 
 
 
Tip No. 1  
The best way to speed up calculations is to eliminate the need of 
calculations. 
 
Most problems in CAT/GMAT are actually meant to test your ability to look at a 
complex scenario and find simple solutions to it. You are wannabe managers, right ? A 
manager is not somebody who is a mathematical genius, but somebody who is proficient 
at efficient utilization of resources.  
 
In most problems, a bulk of calculation can be avoided by using logical arguments.  
 
This is the best way to speed up calculations – avoid the need for calculations. Before 
rushing on to make a calculation – stop to see if there are logical explanations that can 
resolve things to a great degree ? You will be surprised, that in most cases, this actually 
turns out to be so. The questions for these examinations are carefully crafted not to test 
whether you can find a cube-root, but to find out whether you can find the inherent 
patterns in the problem and reveal the underlying simplicity. 
 
Consider the following problem : 
 
S is a 6-digit number that begins with 1. When the digit “1” is moved from the left-most 
to the right-most place, the resultant number is three times the original number. The sum 
of the digits of S is : 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
(i) 6    (ii) 15  (iii) 24 (iv) 27 
 
Try it out for a while before you proceed. 
 
There are several ways to solve this problem – some involving some trial-and-error, some 
involving some solid calculations. Most of them involve finding the value of S and then 
adding the digits to find the sum. 
 
Now read through the problem statement again thoroughly – s l o o o o w w w l y and 
mark all the important points in the problem statements. 
 
What we have to find is the sum of the digits of S. Can we do something directly about 
the sum of the digits of S ? 
 
Note that the digits of S remains the same, only the order changes. Therefore, the sum of 
the digits of S and the second number (which is 3S) are the same. 
 
Now, since 3S is a multiple of 3, what can you say about the sum of digits of S ? 
 
It has to be a multiple of 3. 
 
What can you say about the sum of digits of S ? It is the same as the sum of digits of 3S, 
isn’t it ?  
 
Therefore, the sum of digits of S is a multiple of 3. 
 
Therefore, S is a multiple of 3. 
 
Therefore, 3S is a multiple of 9. 
 
Therefore, the sum of digits of 3S is a multiple of 9. 
 
Therefore, the sum of digits of S is a multiple of 9. 
 
Can you find the answer now ? 
 
Although this argument takes a lot of space to write and a lot of time to read, it would 
take a few seconds for you to go through the entire argument and get to the right answer. 
 
What does it take to come up with solutions like these ? The answer is 
extreeeeeeeeeeemely simple – and is disclosed in the next tip. 
 
 
 
 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
 
 
Tip No. 2  
The most important step in solving a problem is to “study” the problem 
statement - NOT read it , NOT skim through it, but study it thoroughly 
– chew it, digest it, assimilate it.  
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Most of the time we just read through a problem and rush through to the solution. The 
biggest excuse for this approach is – the lack of time. We just have seconds to solve each 
problem, right ? 
 
Ironically, this would be your biggest undoing. 
 
A skillful, efficient problem-solver follows an entirely different approach. He enjoys 
exploring the problem, looking at it through different perspectives, and while doing so – 
an interesting, elegant solution emerges which saves him several minutes of hard-work in 
getting the answer. 
 
Yes, yes, I can hear you scream – Where is the time ? We have to solve the problems in 
seconds.  
 
I know. Read the following statement again : 
 
Every second that you spend assimilating the problem statement will save you minutes 
when you start solving it. 
 
Consider the following problem : 
 
Ram and Shyam start from a point A, move to B which is  5 Kms away from A, and then 
travels back to A. Ram starts at 9 AM, traveling at 5 Km/hr while Shyam starts at 9:45 
AM, traveling at 10 Km/hr. When do they meet first ? 
 
Try the problem for a while before proceeding further. 
 
There is a general tendency to start forming equations about the problem statement and 
trying to solve them. If you followed that approach, you would realize the complexity 
with the problem – you don’t know whether they were moving in the same direction or in 
the opposite direction when they meet first, and because of this, you cannot really form a 
simple equation to represent the above problem. 
 
Let us dig into the problem further. 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
Let us explore what Ram does. He starts from the point A at 9 AM at 5 Km/Hr.  
 
Therefore, he reaches B at 10 AM and back to A at 11 AM. 
 
What about Mr Shyam ?  He starts from the point A at 9:45 AM at 10 Km/Hr. 
 
Therefore, he reaches B at 10:15 AM and back to A at 10:45 AM. 
 
What happens at 10 AM ? 
 
At 10 AM, Ram has started moving from point B back to point A at 5 Km/Hr 
 
At 10 AM, Shyam is 2.5 Kms away from B and is moving towards it at 10 Km/Hr 
 
Now we have a new problem to solve : 
 
At 10 AM, A and B are 2.5 Kms apart, they are moving in the opposite directions at 5 
Km/Hr and 10 Km/Hr respectively. When do they meet ? 
 
 
Did the original problem really have so much information in it ? Yeeeeesssssss --- only if 
you go down deep enough. 
 
 
As an exercise, try finding the time when Ram and Shyam meet for the second time.  
 
 
 
It is IMPOSSIBLE to get to solutions like these, if you tend to rush through to the 
solution using the most familiar ways known to you. 
 
 
Similarly, it is POSSIBLE for EVERYONE (yes, and that includes YOU) to be able to 
come up with solutions like these, provided you spend sufficient time with the problem 
statement, the options given. 
 
Being inefficient and ineffective at problem-solving is a simple 3-step process : 
 
1) Read through the problem fast 
2) Start solving the problem 
3) Congratulations if you still got a great solution. Otherwise, happy merry-go-rounding. 
 
 
Being efficient and effective at problem-solving is even simpler : 
The CAT Lounge                                                           Creating INDIA with ATTITUDE 
 
 
ReInvent Software Solutions (India) Pvt Ltd,                                                          info@thecatlounge.com 
#12, 1
st
 Floor, 1
st
 Cross, 5
th
 A Block,                                                                        91-80-41303230    
Koramangala, Bangalore – 560034 
 
1) Chew, Digest and Assimilate the problem statement entirely. 
2) Watch the solution emerge. 
 
 
 
 
 
 
Tip No 3.   
Do not carry all the luggage on your head. 
 
Imagine if you were traveling in a train with your suitcase on your head, move to your 
seat and sit down comfortably. Now it feels so lazy to take off that damn suitcase off your 
head. So, you leave it right there – anyway what harm is it going to do ?  
 
Funny, isn’t it ? But that’s exactly what most of us do while solving a problem !!! storing 
every single piece of information in our heads is more painful (and ridiculous) than 
traveling on a train with the luggage on our heads.  
 
We tend to keep the problem statement in mind, all the data for the problem in the mind, 
we perform the steps mentally and store the intermediate results in the mind – every bit of 
data that you are “trying” to “remember” is hindering your thought process. Any extra 
luggage on your head is going to make your journey that much uncomfortable. 
 
Well, the solution is easy. Do not be lazy and do not be presumptuous (O, I can 
remember all that !!!) . Write down all the bit of information in front of you with 
sufficient clarify. Represent the problem well. Draw diagrams if necessary. Mark 
everything that you know on the diagram. If you make any inferences, mark that too.  
 
At any point, whatever you have known so far about the problem – transfer that out of 
your head to a piece of paper in front on you. 
 
Keep your mind FREE – FREE, so that it can think, be creative and solve the problem, 
rather than working hard at just keeping a tab on all the darn data. 
 
Consider the following problem : 
 
An equilateral triangle ABE is drawn inside the square ABCD. Find the angle CED. 
 
 
Now suppose we have drawn the following diagram : 
 
 
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