GMAT math concept - difficulty level - hard

Difficulty level - hard
Concept - Maxima - minima of functions

In GMAT, you will encounter problems based on functions.

These questions require higher order reasoning skills.

Ideally, you need to know calculus  to solve. But, it is not necessary. 

Some of you don't have a math background, don't worry. 

This tip can help you crack questions from this chapter.


Remember to : 

Develop math reasoning skills. The math section test you on reasoning 
  
This video will give you insights into the reasoning skills required..




Now lets take a problem

A and B can complete a work in x and y days respectively. Working together they can complete the same work in 15 days. If X and Y are integers, what can be the maximum difference between x and y? 

This problem is from the concept of time and work.

As you know. You will have to represent the equation wrt the amount of work done in a day.

Hence A will complete the job in 1/x days

B will complete the job in 1/y days.

As they together take 15 days to complete the work.

We need to calculate the maximum value of (x - y)
that means x should be the largest possible number and y should be lowest number

TIP: to calculate the maximum value of x- y  or maximum value of x+y, always factorize the equation 

15y+15x= xy

15y-xy +15x = 0

y(15-x) + 15x = 0

To factorize the equation i need to reduce the above equation in this format

(x+a)(y+b) = constant

I need (15-x) so lets add 225 which is 15²

i need to add +225 and -225

y(15-x)  +15x +225 -225 =0

y(15-x)  +15x -225 +225 =0

y(15-x) -15(15- x) +225 =0

(15-x) (y-15) = -225

(x-15)(y-15) = 225 or

(x-15)(y-15) = (225)(1)

Which is

x-15 =225 and y-15 =1

X = 240 and y = 16

Hence maximum difference is 224

Hope you understood this sum.. 

You can reach me if you are targeting Q51 in the math section. There are few skills you need to master. 

my linkedin profile - https://www.linkedin.com/in/georgeanand

My facebook learning community - https://www.facebook.com/groups/semanticsGMAT

What next

You can try this problem and check your reasoning skills.

solution here:

http://letsgmat.blogspot.com/2020/07/gmat-math-thinking-skills-4.html

GMAT math program for beginners

If you 

1. are touching math after a long break

2. scared of math

3. know math but you want to ace the math section

we got a math program for you..

Remember that 

GMAT tests you on math reasoning and not math ability

Its possible to 

• brush up your basics

• learn to apply the basics on math questions

• solve questions in less than 20- 30 seconds 

within a month

Get live classes, study books, progressive section tests,tips/strategies and more..

Check this video to understand better. 

You can opt for 

1. 30 hr program

2. 50 hr program

Lets chat up and work together 

Contact me - whatsapp - 9884123808
Catch me on linkedin - https://www.linkedin.com//in/georgeanand
Join our facebook community - https://www.facebook.com/groups/semanticsGMAT/

The Top Executive MBA programs in the world

If you  

• have more than 3 years of relevant work experience
• want to take a 1 year sabbatical 
• desire a career shift
• want to up-skill

Then opt for an executive MBA program


. 

Feel free to message me, I can evaluate your profile and offer guidance on how to build  a strong profile... 

Here is my linkedin profile…

These colleges require a GMAT score of 680+ / 800

These are the top colleges in the world

Ranking   School                           Location
1              HEC Paris                        France/Qatar/China
2              Kellogg/HKUST               China
3              TRIUM                             France/UK/US/China
4              Columbia/HKU/LBS         US/China/UK
5              CEIBS                              China/Switzerland/Ghana
6              Columbia/LBS                  US/UK
7              Washington: Olin              US/China
8              LBS                                  UK/UAE
9              Tsinghua/INSEAD            China/Singapore/France/UAE
10            Oxford: Saïd                     UK
11            Jiao Tong: Antai                China
12            IESE                                 Spain/US
13            Arizona: Carey                  China
14            ESCP                                France/UK/Germany/Spain/Italy/Lebanon
15            MIT: Sloan                         US

Source: FT.com (Based on the Return on investments (ROI))

How to train your brain to focus - Tedx talk

GMAT preparation requires you to
1. focus continuously for 3hrs+ during the exam
2. Study extensively for a long duration
3. Remove the chatter in your brain, while preparing.

Watch this video to hone your focusing skills

How you can jump 100+ points in the GMAT, in one month?

I trained a student for GMAT. Let me share my experiences with you:

He had written GMAT and got a score of 500. He had prepared for 2 months. This was his preparation

1. He had 2 GB of downloaded material- different books/different videos. He went through them once.
2. He studied GMAT official guide twice.
3. He went through different forums. And collected strategies from different answers posted there

This is my observation:

His knowledge of mathematical formula was strong.

He could remember the formula for area of the equilateral triangle, formulae in trigonometry and other conceptual formulae. He could also remember intricate details like the height of the equilateral triangle, the formula to arrive at the in-centre of the circle….

However. when he saw tough problems he couldn’t proceed beyond the first stage in the problem solving process (identifying what formula to use). He knew which formula to apply but he didn’t know how to apply the formula.

In verbal his vocabulary was strong.

He knew some grammar concepts like subject verb agreement, errors due to misplaced modifier, pronoun errors, ambiguous use of ‘which’ and ‘it’ and few more error types.

In critical reasoning he went by his gut feeling to get his answers.

He could eliminate 3 options, but two options were very close. He guessed the answer.

Extra reading

He briefly dilly dallied by reading the local newspaper.

Here is a typical case of GMAT student who presume he/she can prepare for GMAT in less than a month.

I suggested the following things and I closely monitored his training

• I selected (edited obviously) GMAT like passages from various sources in the net, the topics covered business, philosophy, anthropology, science….

• I exposed him to 25 different errors commonly asked in GMAT sentence correction. I didn’t go back to high school grammar. I found that, the knowledge in high school grammar is too elementary to teach sophisticated error identification.

• For critical reasoning, I took him through a course in logic. I taught him how to identify arguments, how to identify fallacies in the argument. I designed an algorithm (a step by step process) to arrive at an answer for critical reasoning questions. There are 10 different types of CR questions. Hence 10 different algorithms.

• For math I taught him how to critically analyze mathematical problem, how to determine the variables in a problem, how to define relationships in the variables, how to derive hidden relationships. How to diagram the problem.

• Further I taught him faster means of solving equations, working backwards with the answer options and also how to effectively eliminate answers by using deductive reasoning.

• I taught him for 3 weeks and then I gave him problems to practice on and told him to classify problems in the OG.

• I told him to take 4 full tests. He was averaging around 620 in them.

He eventually got 660.

I wish he had met me earlier, he could have saved one GMAT attempt .

For him 650 was his target score.

For a person to reach 720+, a different strategy is employed.  More on that in my next post.

GMAT sentence correction - online live classes

Contact me  @ 9884123808.. (This is also  my Whatsapp number)

"Purposeful" practice vs "just" practice..

"Purposeful" practice vs "just" practice.. I read this book before. I feel like sharing this page A GMAT coach will work on making a better you... A coach will

• teach you the basic skills
• reinforce the basic skills through drills
• re-orient your path, if the current path is not working
• motivate you to achieve high performance
• help you maximize your performance in minimum time using time-tested approaches.

Feel free to chat and lets work on a study plan together... George.. GMAT coach(since 2008)
My linkedin profile: https://www.linkedin.com/in/georgeanand

GMAT math thinking skills 4

Topic: Number system

Difficulty level: Average

You will get word problems like this in your exams.

The concepts involved in this problem are

1. Equations

Method 1:

This method will take time as you need to read the question,  write equations, and solve them. Time consuming!!

First let us assume variable x

Method 2:

The previous approach involves equations. Some of us

• don’t like solving equations
• tend to make errors while solving equations..

This approach is faster, involves using answer options as an additional tool to arrive at the answer

First you need to arrive at the equation as described earlier

Hence option D should be the correct answer

Take-away:

Use the answer options . substitute them in the equation and check if  the Left hand side of the equation  = right hand side of the equation)

Watch this tutorial video and understand mathematical reasoning skills..

You can excel in math once you learn these skills.

Ready for more

Try another sum

Solution here

http://letsgmat.blogspot.com/2020/08/gmat-math-thinking-skills-5.html

GMAT critical reasoning - Weaken the argument - Difficulty level hard

In Kravonia, the average salary for jobs requiring a college degree has always been higher than the average salary for jobs that do not require a degree. Over the last few years, the number of Kravonians enrolled in college has been growing steadily. Therefore, the number of Kravonians entering the job market who have at least the qualification of a college degree will eventually be significantly higher than it has been over the last few years.

Which of the following, if true, most seriously weakens the argument?

(A) Kravonians with more than one college degree earn little more, on average, than do Kravonians with only one college degree

(B) The average number of years Kravonian college students remain enrolled before completing a degree has been increasing over the past several years.

(C) Despite the increase in the number of Kravonians attending college, the percentage of the population attending college is lower in Kravonia than in most other countries.

(D) In recent years, employers have been requiring college degrees for workers in jobs t hat were previously performed successfully by Kravonians who did not have college degrees.

(E) For many years, employers in Kravonia have had difficulty finding enough college graduates to fill the high-paying jobs that were available.

Weaken the argument.
Broad steps.

1. Identify the conclusion
2. Identify the logic. The argument uses a certain logic to arrive at the conclusion.
3. Choose an answer option which weakens the arguments. 

Let’s break down the argument.

• average salary for jobs requiring a degree  is greater than average salary for jobs without a degree 
• Number of people joining college has grown steadily
• Therefore, number of people entering the job market will be higher this year than the number earlier 

What is the conclusion?

Tip: The conclusion indicator word is “Therefore”  
number of people entering the job market will be higher than the number earlier

What is the premise (reason/evidence for this claim)?

Number of people joining college has grown steadily

Lets link it up

Number of people joining college has grown steadily
                     *Therefore*
number of people entering the job market this year will be higher than the number earlier.

The logic used in this argument is causal.

Cause …. Therefore… effect

It is necessary to identify the logic used in the argument. There are 5 of them. Learn more about them in the critical reasoning course. More details here….
https://letsgmat.blogspot.com/2020/07/gmat-live-online-verbal-classes_5.html

Now lets look at the answer options. 

We need to choose an answer option which weakens the conclusion. The answer option should undermine the fact that the number of people entering the job market will increase when compared to the number earlier

Option A:
(A) Kravonians with more than one college degree earn little more, on average, than do Kravonians with only one college degree

Does  the number of  college degrees relate to the conclusion
Does it undermine the conclusion that more people will enter the job market. 
No.

The statement regarding salary is irrelevant.

In-fact the premise
average salary for jobs requiring a degree is greater than the  average salary for jobs without a degree
is unnecessary. This premise can be ignored as it is not linked to the conclusion

Option B
(B) The average number of years Kravonian college students remain enrolled before completing a degree has been increasing over the past several years.

If the duration of the program has increased over the past years, then more students will still be in college. They wouldn’t have graduated college. Hence the number of people entering the job market will not be “significantly higher”

This option weakens the conclusion

Tip: Always look out for “other” factors which rebuts the claim. Here duration of the program is the other factor.

Longer the duration of  the program ……*therefore*.....   fewer people enter the job market.

Option B is the answer

Option C
(C)Despite the increase in the number of Kravonians attending college, the percentage of the population attending college is lower in Kravonia than in most other countries.
Comparison of data from other countries is irrelevant.
Option C is ruled out.

 Option D
(D) In recent years, employers have been requiring college degrees for workers in jobs that were previously performed successfully by Kravonians who did not have college degrees
Employers prefer graduates over employees who don’t have college degree. This statement doesn’t weaken the conclusion that more people will enter the job market. Option D is ruled out.

(E) For many years, employers in Kravonia have had difficulty finding enough college graduates to fill the high-paying jobs that were available.


This statement is irrelevant to the conclusion. High paying jobs is not connected to the number of people entering the job market.

Hence Option B weakens the claim

10 must NOT DOs for GMAT math Data sufficiency questions

The directions: 
(some tips below may require you to revisit these directions)

This problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether:

A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

D EACH statement ALONE is sufficient to answer the question asked;

E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

To understand the directions better,watch this video


Now here are some simple not do's

1. Assume that a given number is positive only

The numbers can be zero, negative fractions or decimals.
Sample question

 Is the modulus of X less than 3?
(1)  X(X+3) is lesser than 0
(2)  X(X-3) is greater than 0 When you substitute values for x, some of you usually use positive integers. you must also substitute other types of numbers like  zero, negative, fraction or decimal...

2. Assume that in a ‘Is...( refer main statement in point 1 above ) question type, no is an invalid answer. 

‘yes,’ can be a valid answer; no can be a valid answer.
You can mark A or B or C or D. 

 ‘sometimes yes and sometimes no’ are invalid.

You should mark E.

3. Ignore minimum factors required (that can be gauged from the main statement) to answer the question,

if either of the sub statements do not have the minimum factors, the answers cannot be A or B.

for example

 Is X greater than Y?
(1) X is greater than Z
(2) Y is lower than Z
We need information on X,Y to compare
Here as per directions, the answer cannot be A or B.

4. Conclude based on the outcome, while substituting a positive number to arrive at the answer.

 Check the outcome while substituting varied numbers i.e. zero,+ve integer,-ve integer,+ve fraction and –ve fraction

5. Hurriedly mark either A (or B) as the answer option when statement 1(or 2) yields an answer.

 Study statement 2(or 1)also . If this also leads to answer mark D, else mark A(or B)

6. Spend time deriving absolute values when approximation is sufficient in arriving at a decision.

You can save time by arriving at a range of possible answers than by arriving at an absolute answer

Use approximation

7. Arriving at numerical values when the question requires only counting the occurrences.

Most test takers focus on solving the equation when they see an equation. 

For example:

How many values can satisfy the equation x^2 +3x +5=0 ?

You should know that x^2 +3x + 5=0 will have two values for x (as the power of x is 2)  You need not  spend time solving this equation.  

8. Attempt a complex combinatorics problem by attempting to pick/select many objects at a time. pick/select one object at a time. This doesn’t change the final outcome.

In probability, test takers find it difficult to approach a question

For example.

what is probability of picking 3 red balls out of 10 balls in from a bag ?

You can either pick 3 balls in one go

or

you can pick one ball at a time

Either way the answer remains same.

If you focus on picking one item at a time, you will be able to arrive at a solution easily.  

9. Follow faulty logic.

i.e. A sample sum

main statement: Is the modulus of X less than 3?
sub statements:
(1) X(X+3) greater than 0
(2) X(X-3) lesser than 0

While substituting number to check the inequality always use the correct logic
Correct logic
Determine the range of numbers which satisfy the sub statements
Check whether these numbers satisfy the main statement.
Wrong logic
Determine the range of numbers which satisfy the main statement
Check whether these numbers satisfy the sub statements.

10. Ignoring additional information required to solve the problem

Sample problem
A and B takes x and y days respectively to complete a work. How many days will A and B together take to complete it?
(1) x=5
(2) B alone takes twice as many days as A alone to complete the work
additional information on the efficiency of each person’s work per day is a factor needed. If A works at 50% efficiency, A will take 10 days to complete the work.

GMAT live online verbal classes

Course starts on Sunday 12th July 2020

Class timings: 9:00 pm to 11:00 pm (IST) saturday and sunday
Duration : 30hrs

Classes are 2 way interactive sessions. Study books will be provided

Topics covered:

• Sentence correction.. all error types
• Reading comprehension....critical reading -tips/strategies
• Critical reasoning - exhaustive discussion of all CR question

If you would like to schedule a counselling session. call or message me whatsapp @ 9884123808

5 Tips to crack the sentence correction section of the GMAT.

Here are some of the GMAT sentence corrections tips i compiled.  I have added examples for each tip.

1.Check pronouns:their,his,her…..

Wrong sentence: The instructor asked everyone of the trainees to remain in their respective seat.
Correct sentence: The instructor asked everyone of the trainees to remain in his respective seat.

2. Check for pronoun omission:

Wrong sentence: In Japan elderly people are treated with far greater respect than most Western countries.

Elderly people in japan vs western countries?????

Correct sentence: In Japan elderly people are treated with far greater respect than those in most Western countries.

3. Check subject verb

Wrong sentence: A slowdown becomes useful only when the opportunity to both reorient as well as innovate are used for further growth.
Slowdown …………………………..are???

Correct sentence: A slowdown becomes useful only when the opportunity to both reorient as well as innovate is used for further growth.

4. Watch for incomplete comparisons

Wrong sentences: California’s child-support payments are as high or higher than other states.
As high…..as…..

Correct sentences: California’s child-support payments are as high as or higher than other states.

5.Watch for descriptions in the beginning

Wrong sentences: Disturbed by the media’s relentless criticism, it was decided by Gupta to resign as the chairman of TERI.
What does it refer to…….medias criticism or the disturbances

Correct sentences: Disturbed by the media’s relentless criticism, Gupta decided to resign as the chairman of TERI.


Struggling with sentence correction.. watch this video tutorial


These are some of the three dozen tips..

Click here for another sentence question with in-depth analysis
http://letsgmat.blogspot.com/2020/06/gmat-sentence-correction-question_28.html

How to prepare for GMAT critical reasoning?

Let’s face reality. Few college books prepare you to think critically. But critical thinking skills are extensively tested in both  GMAT. 

Critical reasoning (referred to also as logical reasoning or analytical reasoning) constitute an array of thinking skills that 

• involve
• analysis 
• synthesis 
• evaluation 

of numerical, verbal or non-verbal data. 

Numerical reasoning questions measures your ability to apply reasoning in a math setting whereas non-verbal reasoning involves interpreting symbols and pictures, the latter skills hardly tested in higher order aptitude tests. A majority of reasoning questions tested in these exams are text-based

(verbal reasoning).

Logic is the science of correct reasoning. It is integral to mathematics and philosophy. There are many logic concepts that originate from the above disciplines and applied in GMAT tests. 

The common test areas, viz.  critical reasoning (short passages that present arguments), argument essay and integrated reasoning draw immensely from philosophy and logic. These questions requires you to analyze issues, reason logically, and argue effectively. These skills are essential to succeed in higher studies as well as in careers.

How to build reasoning skills

1.    Using test prep resources

A common practice among test aspirants is to seek help from coaches, preparatory test guides and online discussion forums in order to learn tips and strategies to crack reasoning questions. No doubt some of these are useful sources to make you motivated and test ready. However exercise caution; desist from using these indiscriminately; do quality check.

2.    Reading varied texts

Those who are habituated to reading will over time become critical thinkers, and thereby succeed in many areas of aptitude tests. It is to be noted that the question stimulus in reasoning tests are drawn from everyday knowledge rather than from academic disciplines. Being well-read will make you familiar with the content of these problems.

3.     From principles of  logic

A third and highly productive way to build your logical reasoning is to master elementary logic theory. What is logic theory?

 Here’s a basic concept in logic.

Statement : Whenever Sara goes to the supermarket, she buys cookies.

You saw Sara this morning carrying a jar of cookies. Can you then infer that Sara has gone to the super market?

 No. this is wrong reasoning, because the supermarket is not the only place where Sara buys cookies from.

Let’s consider the scenario:  Sara did not buy cookies, can we infer that she did not go to the supermarket? Yes, we can.

In logic theory terms, the original statement can be expressed as,

If A, then B; If not B, then not A. This expression can be applied to a class of problems. Many such formulae  can be learnt and applied to logical reasoning. Merely common sense will not work.

There are many books on elementary logic suitable for beginners  that can give you solid foundation in  critical thinking. You may make use of such sources for your test preparation.

A good book on critical reasoning

One book I would recommend is Critical thinking: A Student’s Introduction by  Gregory Basham, William Irwin et al.  Online edition of this book is also available.

This book provides all basics consistent with the reasoning historically assessed in tests of reasoning and aligned with the content areas covered in  global admission examinations. Hence a good reference source for aptitude trainers too. The real-world examples and proven step- by- step approach to answering questions that this book provides can significantly improve the way you look at reasoning  problems.  The concepts that you need are; structure  and components of arguments, inductive and deductive arguments, method of evaluating arguments and  ways to spot common errors in arguments.

Let your preparation involve understanding the logic behind problems and not merely seeking solutions.

Becoming a critical thinker is both an adventure and  hard work.   Practice. Make mistakes. Learn from them. Improve. In the coming  test season, be equipped with a workable set of thinking tools.

GMAT math thinking skills 3

Topic: Number system

Difficulty level: Average

You will get word problems like this in your exams.

The concepts involved in this problem are

1. Equations

2. Numbers system

Method 1:

This method will take time as you need to read the question,  write equations, and solve them. Time consuming!!

First: assume variables

Let John’s age (at the time of the wedding) be J and Mary’s age (at the time of the wedding) be M. 

Second : write equations

The condition relating their ages is

Hence Mary was 18 and John was 24, when they got married 

That was long and time consuming.

Now let us  try approach 2

Method 2:

The previous approach involves equations. Some of us

• don’t like solving equations
• tend to make errors while solving equations..

There is an easier and faster approach  

Lets observe equation 1

M =(3/4)J                      Re-arranging ............(M/3) = (J/4)

we can observe that ages are integers. 

We can say that M is divisible by 3 and J is divisible by 4.

Similarly   

Lets observe equation 2

12 years hence

(M+12)/5 =(J+12)/6

(M+12) is divisible by 5 and (J+12) is divisible by 6

Let us use the answer options and eliminate the wrong options

Mary’s age when she got married should be one of the 5 options

(A) 24       (B) 26         (C) 18        (D) 30          (E) 22  

Mary’s age,when she got married, should be divisible by 3

Hence we can eliminate option B,E as these numbers are not divisible by 3

Further 

Mary’s age, after 12 years, should be divisible by 5

Let us take each option

 Option A: Mary’s age initially 24……after 12 years………. Mary’s age = 36

 Option C: Mary’s age initially 18……after 12 years ………Mary’s age = 30

 Option D: Mary’s age initially 30……after 12 years …….. Mary’s age = 42

Only 30 is divisible by 5

Hence option C should be the correct answer

Therefore, Mary’s age at the time of her wedding should be 18.

Isn't the second method easy and fast… However many test aspirants don’t observe these subtleties.

Most of us start writing equations when we see word problems.

Take-away:

observe the numbers, check the nature of the numbers( prime/odd/even/ divisible by x numbers….)

Watch this tutorial video and understand mathematical reasoning skills..

You can excel in math once you learn these skills.

Need math help: Get in touch with me:

My linkedin profile: https://www.linkedin.com/in/georgeanand

My facebook learning group:  https://www.facebook.com/groups/semanticsGMAT

My company: http://www.semanticslearning.com/

Want to explore math reasoning skills further try another problem

Click here

Solution here:

https://letsgmat.blogspot.com/2020/06/gmat-math-thinking-skills-1.html