Showing posts with label GMAT PS. Show all posts
Showing posts with label GMAT PS. Show all posts

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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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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Thursday, November 5, 2009

Math Problem solved using ScoT

I got a query from a in this problem. I solved using Science of Thinking(ScoT) approach.Observe the problem solving process.

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

These type of sums can be solved using my thinking skills – “pattern recognition” and “hypothesis testing”


Take sum of even numbers when n =5( N has to be an odd number)
Sum = 2+4 = 6 i.e 2 *3( Same pattern as 79*80 i.e n*(n-1))
Now take sum of even numbers when n = 7
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.

So our hypothesis is that n should be sum of the product of the numbers(in the form n*(n-1) which yields the sum of the even numbers.
Now lets check our hypothesis
When n =9
Sum = 2+4+6+8 = 20 = 4*5
4+5 is equal to n
Hence n can be concluded as 79+80=159

For more details visit http://www.semanticslearning.com/gmat-l3-method.asp
My math Ebook has all the thinking skills tested in GMAT.You can access the demo at
http://www.semanticslearning.com/gmat-home.asp Title GMAT higher order problem solving.

Cheers




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Wednesday, October 28, 2009

Analyzing GMAT math problems using the Science of Thinking(ScoT) approach

The first step in the problem solving process is problem analysis. Problem analysis comprises
  • Problem Definition
  • Solution length
  • Problem length
  • Constraints and conditions

Let me explain the process of classification of problem based on their definition now.

Problems can be classified as a poorly defined or a well defined problem.

A well defined problem everything relevant and required is clearly specified, without any ambiguity or uncertainty, such that a solution, even if it involves complex calculations can be arrived at with accuracy. You can predict the path to take or steps required to solve the problem.

A poorly defined problem much of the data & relationships are hidden or not clear.

Lets take a poorly defined problem.

A says to B: I will be three times as old as you were when I was five years older than you are. I am 5/4th as old as you will be and then you will realize that you will be double the age you were. If the sum of the future ages of A and B is 50, what are their present ages?

The data present in the above question is cryptic. The interpretation of this problem lies in your ability to attach meaning to the verb tense.

To analyze the above problem you have to represent the problem diagrammatically to understand the relationship between the variables.

Try creating a table with the past ages, present ages and future ages as the columns. Given below is a simplified version of the table.






More ScoT approaches follow this link..
http://www.semanticslearning.com/gmat-l3-method.asp


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Monday, September 28, 2009

How to take charge of you GMAT math section?


To get a high score in the GMAT, you must be familiar with the relevant concept/formula as well as the hidden relationships accompanying the concept/formula.  Many of us attempt to crack the math section of the GMAT by solving problems from sources such as the official guide.
This strategy works for people who have a strong mathematical background. For the rest of us, we have to first understand the concepts, then we have to derive relationships from the existing concepts.

Concept learning is an art. We look at a math text book and we get overwhelmed by the size. 20 odd chapters!! How am I going to master all of them? Each topic looks menacing.

But if you observe closely not all the concepts are abstract, a time speed distance problems is related to a problem based on similar triangles(geometry), a problem on roots of an equations is based on factor theorem in number system. The concepts required to crack GMAT math are inter- related.

 The quantitative section is primarily focussed on number system, ratios proportion and percentages.  Majority of the other concepts are based on these concepts. Focus on these areas first, then apply these concepts to study other concepts like Time and work, Geometry, Profit, loss and discount,.

So from 20 odd chapters the area of focus boils down to 3 or 4 chapters.

Also:  Make derivations

While working out practice problems at the conceptual level, derive notes on where you can apply the concepts. Some of these derivations are highlighted below.

Presented below are some of the hidden relationship accompanying the concept/formula. These relationships are termed ScOT bytes which are the present through out our course material.

1. Let A and B be two numbers, then Product of A and B = HCF (A, B) × LCM (A, B)


2. (Even number)4x  will always end in the digit: ‘6’,(Odd number)4x  will always end in the digit:  ‘1’

3. Let a × b = c.  The remainder obtained when you divide c by d is equal to the product of the remainders obtained when you divide a by d and b by d.






5. If a is increased/decreased by b%, then the new value calculated after the increase is new value = a ± b% of a  ±  (b/100) x a








7. If a same positive number is added to both the terms of ratio (of lesser inequality), then the ratio is increased.

8. If a same positive number is added to both the terms of ratio (of greater inequality), then the ratio is diminished.
9. The number of factors for a square number is always odd. For 4 there are 3 odd factors(1,2,4), for 9 there are 3 odd factors(1,3,9)...
10. Discount percentage is always calculated on  list price/marked price and not on selling price.
11.If a:b = 3:4 then a and b are not equal to 3 and 4 respectively. a = 3x and b = 4xwhere x is any constant.
12. The Simple and compound interest is the same after 1 year. The amount as well as the compound interest increases by r% every year.








Where r1,r2,r3 are interests and n1,n2 
and n3 are the years.
14. To convert km/hr into m/sec multiply the number by 5/18
15.Average speed can be calculated by 2ab/(a+b) where a and b are the two speeds. This formula is only applicable when the distance travelled is constant.
For more math tips and details browse
Download the math concept book for SAT,GMAT,GRE at


Tuesday, September 1, 2009

Are you a quant person?

Are you a quant person?
Quantitative thinking ( thinking with numbers) is integral to corporate business careers. Hence MBA entrance tests contain a generous dose of quantitative problems. One’s performance in such problem solving is a manifestation of his overall problem solving ability. 
Business Schools perceive quantitative scores as indicative of higher order thinking and decision making skills. They believe that quant thinkers can handle diverse business challenges. They can analyse, diagram, hypothesise, set goals, try permutations and combinations, perceive probabilistic outcomes and synthesis a possible outcome.

Quantitative personality is not necessarily a hardcore math person

For a quantitative thinker, math knowledge is one of the many tools in his quest for excellence in problem solving. It is also possible that one is a good quantitative person but not a math person.
By and large, a quant person is someone who can look at independent ideas and facts, look at a situation and be able to come up with a response irrespective the accuracy of the approach and thereby the solution.  It also means looking at a situation and draw up on one’s own repertoire of tactics for a possible way forward…. a possible answer... In short, a quant person  might have a great memory but is rather someone who reasons very well.

A quant person uses thinking skills approach to problems
So when a quant person looks at a math problem with varied factors, and probably requiring more than one mathematical concept, he  doesn’t get confused; he will pull the question apart and can see where one step leads into the other and can merge and manipulate the combinations to get the final answer. He goes beyond the given data, creates a problem field, assumes himself to be part of the problem, takes various experiences and knowledge points to extrapolate a position and direction. In other words, a quant person is empowered to handle problem situations well; one who says no ‘can’t’, until he has exhausted all possible knowledge, theories, and experiences before asking for help.
 
A quant person ‘transfers learning’
For a quant person, the idea of doing a lot of problems stems from the need to see the various possibilities of solving problems rather than an expectation of chancing upon an exam like problem. For effective ‘transfer of learning’ making observations while attempting a problem is the key.

The quant person in a nut shell should be inquisitive, innovative, fearless, flexible and an inherent risk taker. “the Science of Thinking” methodology attempts to inculcate quantitative reasoning in addition to quantitative aptitude in test aspirants. Visit www.semanticslearning.com for more details.
Read http://www.semanticslearning.com/beta/gmat-science-of-thinking.asp of thinking for more details