GMAT data sufficiency tips Save precious minutes…HOW?

Save precious minutes…HOW?

Don’t calculate exact answer.

Ask: “can I find the answer?” instead of “what is the value of the unknown variable?”

Data sufficiency is a test of mathematical reasoning.  It tests your ability to evaluate the adequacy of given data in answering a question in the mathematical setting. This involves verifying the sufficiency of data to solve a problem, distinguishing between relevant and irrelevant data, and establishing relationship between variables.

Here’s how the directions for data sufficiency problems appear in the exam

A given question is followed by two statements. You are required to determine whether the statements can be used to answer the question.

Mark (A) if statement I alone is sufficient but statement II alone is not sufficient to answer the question

Mark (B) if statement II alone is sufficient but statement I alone is not sufficient to answer the question

Mark (C) if both statements I and II together are sufficient to answer the question

Mark (D) if each statement alone is sufficient to answer the question

Mark (E) if statement I and II together are not sufficient to answer the question

Let’s take a problem

In the figure above, the points A,B,C,D  and E lie on the a line. A is on both circles, B is the centre of the smaller circle, C is the centre of          the larger circle, D is on the smaller circle and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?
(I) AB=3 and BC=2
(2)CD=1 and DE=4

To find the area of a circle the radius of the circle is required. The area of the circle = (pi)*radius*radius.
AB = is the radius of the inner circle
AC = is the radius of the inner circle
The required area= (area of the outer circle)-(area of the inner circle)

Lets take statement (I)
AB= 3 and BC =2. The area of the outer circle can be computed as the radius of the outer circle is AC(AB+BC).The radius of the inner circle is AB. The difference in the two areas will give the numerical answer.
It is not necessary to calculate the exact numerical value. It is just enough to know that the answer can be determined with the data given. Time can be saved.
Statement(I) alone is sufficient.

Let’s take statement (II)
CD+DE=CE=CA which is the diameter of the bigger circle.
The diameter of the smaller circle is CA+CD. The radius of the smaller circle is half the diameter. Hence the radius and the diameter of the inner circle can be computed.  As the radii of the bigger and inner circle are computed, the required area can be determined.

Statement (II) alone is sufficient.

Hence answer is D.

Questions such as “what is the value of ...?” , “determine the value of ...?“ can be attacked in this manner.

Data sufficiency understanding the directions

Data sufficiency is designed to measure your ability to

• Analyse a quantitative problem
•  Recognize which information is relevant
• Synthesize data
• Determine at which point there is sufficient information to solve a problem.

Data sufficiency questions contains a question statement, followed by two sub statements labeled (1) and (2). Do not waste valuable time  solving a problem.  Only determine the statements sufficient to solve a problem. Follow the flow chart presented below.

The order of preference while answering a question is

1. D
2. A/B
3. C
4. E

Scenario 1:

Check question statement and statement (1) first. If you get an answer, wait

Then

Check question statement and statement (2)alone. If you get an answer now mark D

Scenario 2:

Check question statement and statement (1) first. If you get an answer, wait

Then

Check question statement and statement (2)alone. If you do not get an answer now mark A

Scenario 3:

Check question statement and statement (1) first. If you do not get an answer

Then

Check question statement and statement (2)alone. If you do get an answer now mark B

Scenario 3:

Combine question statement ,statement (1) and statement (2).

 If you get an answer now mark C

Scenario 4:

Combine question statement ,statement (1) and statement (2).

 If you do not get an answer now mark E

5 tips to crack the GMAT data sufficiency section

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Essentials for GMAT data sufficiency.. Must read

What is Data Sufficiency?

Data sufficiency is designed to measure your ability to

1. Analyse a quantitative problem
2. Recognize which information is relevant
3. Synthesize data
4. Determine at which point there is sufficient information to solve a problem.

Data sufficiency questions contains a question statement, followed by two sub statements labeled (1) and (2). Do not waste valuable time solving a problem. Only determine the statements sufficient to solve a problem.

Follow the flow chart presented below.

 The order of preference while answering a question is

• D
• A/B
• C
• E

There are 5 possible scenario's while answering questions. They are:

Scenario 1:

Check question statement and statement (1) first. If you get an answer, wait
Then
Check question statement and statement (2)alone. If you get an answer now mark D

Scenario 2:

Check question statement and statement (1) first. If you get an answer, wait
Then
Check question statement and statement (2)alone. If you do not get an answer now mark A

Scenario 3:

Check question statement and statement (1) first. If you do not get an answer
Then
Check question statement and statement (2)alone. If you do get an answer now mark B

Scenario 4:

Combine question statement ,statement (1) and statement (2).
If you get an answer now mark C

Scenario 5:

Combine question statement ,statement (1) and statement (2).
If you do not get an answer now mark E

I hope you get your DS sums right now. Mail me at george@semanticslearning.com for your GMAT doubts...:-)



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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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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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5 crucial points to keep in mind while attempting a Data sufficiency problem

of the equation don’t match. Hence x only has to be 0.

4. Do not make any assumptions of the figure drawn. If a four sided figure is drawn with straight line, do not assume it’s a square or if a point is marked in the middle of a circular region, don’t assume it’s the centre of the circle.

5. Although Data sufficiency tests your decision making skills (choosing which statement is sufficient) it is advisable to spend some time arriving at an answer and checking whether the answer derived is always true or always false.



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5 crucial points to keep in mind while attempting a Data sufficiency problem

of the equation don’t match. Hence x only has to be 0.

4. Do not make any assumptions of the figure drawn. If a four sided figure is drawn with straight line, do not assume it’s a square or if a point is marked in the middle of a circular region, don’t assume it’s the centre of the circle.

5. Although Data sufficiency tests your decision making skills (choosing which statement is sufficient) it is advisable to spend some time arriving at an answer and checking whether the answer derived is always true or always false.



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5 crucial points to keep in mind while attempting a Data sufficiency problem

of the equation don’t match. Hence x only has to be 0.

4. Do not make any assumptions of the figure drawn. If a four sided figure is drawn with straight line, do not assume it’s a square or if a point is marked in the middle of a circular region, don’t assume it’s the centre of the circle.

5. Although Data sufficiency tests your decision making skills (choosing which statement is sufficient) it is advisable to spend some time arriving at an answer and checking whether the answer derived is always true or always false.



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5 crucial points to be kept in mind while solving a probability based problem in GMAT

1.    Calculate the numerator {Number of favourable terms} and the denominator {Total number of terms}     separately using the concepts of arrangement, permutation and combination.

2.    Be part of the problem : Imagine you are arranging / selecting the items. The action of taking     the object and placing it in the relevant position is the key.

If you have to arrange 10 rings in 4 fingers, you have to imagine yourself picking a ring and placing it on a finger instead of computing the number of rings each finger has.

3.    When two or more items are picked it is easier to compute the probability of picking one     element at a time than computing the probability of picking many items at a time.

4.    When A and B are selected relate the respective probabilities with multiplication. When either     A or B is selected relate the respective probabilities with addition.

5.    When there are multiple outcomes possible the probability of at-least one of them happening is     computed by calculating the reverse probability
 = 1 – probability of event not happening.


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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

http://www.semanticslearning.com/beta/gmat-l3-method.asp

Download the math concept book for SAT,GMAT,GRE at

http://www.semanticslearning.com/beta/downloads/GMAT-Math.zip

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