Saturday, November 21, 2009

Science of high performance in the GMAT -1 : Is GMAT Official guide sufficient?

Official guide- published by the GMAC has a list of 800+ questions (11th edition). There are around 230 problem solving (math) questions.. However I feel that this list represents the easier problems in the GMAT.

To break into the 720+ it is imperative that you have to solve tougher higher difficulty problems. (This is true for the verbal section also)

What is a higher order problem?
A higher order problem is problem which has
• A situation which can otherwise be solved by identifying the concept/formula and applying the same directly
• A complexity present in the problem which acts as a stumbling block, thereby preventing you from getting an answer directly.

When approaching a higher problem first
  1. Identify the concept involved
  2. Identify the complexity in the problem
  3. Remove the complexity and if possible arrive at a result
  4. Modify the complexity in such a manner the complexity gets integrated into the problem and this results in  a   newer problem
  5. Solve the new problem by directly applying the concept.
Let me highlight a higher order problem. Watch how I analyzed the problem and how I solved.

A car moving at 45 kmph and is chasing a two wheeler that is moving at 30 kmph. The distance between the car and the two wheeler at 10:00 am is 48 kms. The car stops at 11:30 am for 15 mins to fill fuel and moves at 45 kmph. When will the car meet the two-wheeler?

1.12.42 pm      2.1:42 pm           3.1:57 pm          4. 1:47 pm  5. 1:30pm

Try this problem independently first, then read further.
Let me take you through the problem in the science of thinking* approach toward higher order problem solving.

The concept – Time, speed and distance, Relative velocity involving two bodies moving towards each other.
The complexity – The stoppage time of the car. At 11:30 am the car stops for 15 mins.

Eliminate the complexity first
If the car didn’t stop at 11:30 then the time taken by both the bodies to meet is determined using the relationship
Time taken to meet = Initial distance between the bodies/ relative velocity
= 48/(45 -30) { Relative velocity when two bodies move in the same direction = difference of their speeds, hence 45-30 =15)
= 48/15= 3.2hrs

Modification of the complexity
As you would have observed if the complexity is eliminated the problem can be solved directly. As per the problem. The car travels till 11:30 and then stops for 15mins. So you might calculate the distance travelled by each body from 10:00 till 11:30 and then calculate the distance travelled by the two wheeler for that extra 15mins and then proceed. This complicates the problem.
Instead you can restructure the problem in such a way that the complexity gets integrated into the problem and doesn’t get noticed.

Here you can shift the 15min time interval from 11:30 to 10:00 such that the car starts only at 10:15 instead of 10:00. Hence the initial distance increases from 48 to 48 + (distance travelled by two wheeler for 15mins) = 48 + 7.5 =55.5kms

Hence now there is no stoppage time at 11:30.
Time taken to meet = Initial distance between the bodies/ relative velocity
= 55.5/(45 -30) = 55.5/15= 3.7hrs = 3hrs 42minutes
Meeting time =10:15 + 3 : 42 = 13: 57
You would get higher order problems only if the adaptive algorithm decides that you deserve questions of this difficulty.
So for those of you who aim to crack the 720+ barrier. Practice on higher order problems.

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