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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