Most of the MBA entrance examinations require you to be extremely quick, agile and efficient at 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, memorising 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 utilisation 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 :
(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 remain 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 only 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.
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 travel back to A. Ram starts at 9 am, travelling at 5 km/hr while Shyam starts at 9:45 am, travelling 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 realise 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.
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 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 :
Read through the problem fast
Start solving the problem
Congratulations if you still got a great solution. Otherwise, happy going round in circles.
Being efficient and effective at problem-solving is even simpler :
Chew, Digest and Assimilate the problem statement entirely.
Watch the solution emerge. These tips, however simple or obvious they look, can help you increase your problem-solving abilities many many times. Each tip would make your problem-solving much easier and exciting. As you master these, you would start to enjoy quant and develop a natural flair for problem-solving.
Watch this space for more tips.
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