Problem Solving

Let start with a show of hands

How many of us go blank when we see a math sum?

I can see that most of you are raising your hands, the others must be one of lucky 2%.

Now the big question.
Why some of us go blank and others seem to have the knack of solving math sums?

Well you can blame it on your mathematics teacher @ school or on your genes. But nevertheless while preparing for GMAT or in fact while doing an MBA, you will encounter lot of math.
I can hear lots of groans.

Few years back I read this book 'How to solve it' by George Polya. I modified my teaching style from just teaching question answers, question answers, question answers, question answers......to question logic answers, question logic answers, question logic answers.....

I found that I could tutor a person to achieve 45+(raw score in GMAT) within few weeks as instead of few months. Wow!!

The best part of it I could see that students are able to solve math problems independently without me intervening.

In the book, Polya gives a detailed step by step process on how to approach math problems in general
I will modify the process and present it to you in context with GMAT math
Keep these steps in mind when you approach a math problem in the future.

Step 1: Understanding the problem
Answer the following questions first

• Do you understand all the words used in stating the problem?
  What are you asked to find or show?
  Can you think of a picture or diagram that might help you understand the problem?
  Is there enough information to find the solution?
  What information, if any, is missing?

The answer to these questions will channelize your thinking towards the answer.

Step 2: Devise a plan

Answer these questions now

What will be the best approach to address the problem?

Approaches can only be devised. If a tutor explains a sum to you, then you will be able to understand only that problem. But when you encounter a new problem, you will go blank again.
Ideally when you encounter a new problem, you will have to use the existing ideas plus any new ideas you can conjure up. These process are mostly done mentally and involve little computation/calculation.

To get an idea, do any/all of the following.

• Make a systematic list/table
  Write an equation
  Consider special cases
  Use direct reasoning- for example If A>B and B>C then A>C.
  Use indirect reasoning.-Think of an earlier sum where you encountered a similar problem
  Look for a pattern
  Draw a picture
  Solve a simpler problem- break the problem into small parts and solve each part.
  Use a model- Make a general assumption and solve by guessing.
  Work backwards. -work with answer options

Now that you have got an idea. Put pen on paper and solve to get an answer

Stage 3: Carry out the plan

• Solve the problem with great care and patience
  Discard the plan if it does not work and devise a new plan
  Record what you have done to avoid repetitive work - For future use.

While attempting Data sufficiency questions, it is imperative you check your results. So

Stage 4: Looking back or checking

• Have you addressed the problem?
  Is your answer reasonable?
  Can the method applied to other similar problems?
  Is It consistent.

Now go ahead and repeat this thought process on different math problem and the next time when you see a math problem you will not go blank.

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