Tuesday, June 19, 2012

June 20 , 2012 – The dilemma : Quick maths or the traditional quantitative approach?

Hello there, it has been a month since my last post. Somehow work always seems to increase when you least want it to grow on you. L These are the few petty matters in the life of an B-School applicant after all J

With respect to the quantitative problem solving questions, this dilemma has been testing my nerve for quite some time now. The basis of this issue rises from the way one’s approach is conditioned to approaching the problem solving quant problems. Being from an engineering background with plenty of exposure to mathematics, the natural approach for problem solving is to take the mathematical way. Believe me this approach will rarely fail. The trick however on the GMAT questions is most importantly there are only 2 minutes per problem and secondly that the questions are not actually meant to test the depth of the quant skills of the test-taker but instead the application of the basic math concepts. Following the natural mathematical approach gets really tough on the harder quant questions since the wording of the problem gets really tricky.

With this in mind, I have consciously decided to try the smarter way of solving the quant problems. This is a very demanding approach and needs immense practice. The end result should possibly result in relative improvement in time taken to solve the problems and also in making informed guesses on the harder problems. Now, a rather straight forward question is that why is this approach so demanding, if one decides on following this approach shouldn’t it be easy enough?

Let me try to explain this with a simple example. The below question is one of the easier questions in OG 12 problem solving quant section. Please take your time in trying to solve it.
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82% of the total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? 
A. 9 
B. 14 
C. 25 
D. 30 
E. 44 

Ok, so since you now have attempted to solve this problem it is time to move on to checking the answer. But hold on for a second, the example was not for evaluating the answer but rather for evaluating the approach.

So, when I first looked at this problem, my natural instinct told me that form the equation and solve for the unknown variable. If (82/100) = 138 then x% = 124. Find the value of x and solve up for the total of 100% and subtract 124 from it to get the answer. Voila!

Some potential drawbacks here are that the calculations involved are slightly tedious and can take a significant amount of time. So then how can this be solved using another approach? The answer choices are close enough. So even though this is an easy question they answer choices do not scream out on the correct answer. Notice the word “approximately” in the question stem. So the approach that I now intend to take for such problems is as below.

138 billion = 82%
13.8 billion = 8.2% i.e. ~ 14 billion = 8%.
Now, remaining % in tank is 100 – 82 = 18%.

This can be loosely translated to ( 8% + 8% + 2% ) i.e. 14 + 14 + ~3.5 which gives us 31.5 billion. Now a very important point to take note of is that this is NOT our final answer. We want to find originally (before the rain) how much short of capacity was the reservoir? So we need to keep in mind that something (138-124 = 14 billion) needs to be added to 31.5 to get the desired answer. Now look at the answers, only 44 is greater than 31.5. Our answer is hence E.

To sum it up, as per my personal observation, very seldom will the test the core of your mathematical skills. The second approach, which I by now have thoroughly realized, is not straight forward to apply. It needs quite a lot of practice but the rewards will be good. So, I intend to work out on applying this approach more. Let us see how it goes.

But the bottom line is that one should take the approach one is most comfortable with. There are no extra points for the approach taken hence the approach which suits one best should be used. Hopefully this post has been of some help and has made you think again.

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