Wednesday, November 18, 2009

Pattern recognition as a skill to solve GMAT math problems

Many math problems are based on patterns. These problems may involve a set of numbers or a set of alphabets or maybe even a set of figures.

The skill is in
  • Identifying patterns
  • Taking a sample and deriving meaning full relationships between the various elements in the pattern
  • Expostulating the pattern to encompass the entire series
  • Use this new knowledge to arrive at an answer
Lets take a problem

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then what is the value of n?

This sum involves a set of even numbers from 1 to n.(n is an odd number)
Lets derive the pattern
First let n =5
Then the even numbers involved are 2,4
Hence, Sum = 2+4 = 6
6 can be written as 2 *3( Same pattern as 79*80)

Now let n =7
The even numbers are 2,4,6
Sum = 2+4+6 = 12 i.e 3*4

So you get a pattern 2*3, 3*4…………………….79*80, when n = 5,7……n
Do you observe that 2+3 =5 and 4+3 =7, 4+5 =9

This leads to the answer.

In a nutshell: when you encounter problems which ask you to compute the value for n terms
Take a small sample and analyze.(Relate the analysis to the answer)
Take another sample and analyze
Write the result together and derive a relationship among the numbers
This leads to the answer.

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1 comment:

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