Monday, November 22, 2021

GRE math thinking skills 4

                         

GRE tests your logical skills as well as your knowledge of math concepts. To score high, you need to remember various formulas, theorems. Also you need to master critical problem-solving skills.

Today I am going to  take you through one problem -solving skill – Diagramming


 Students with a non-math background usually.. do this

  1. Read the complete math problem
  2. Write equations.

Solving equations is time consuming.  You can make mistakes too..if your are not careful.

 

Students who are fairly proficient in quantitative reasoning..do this

  1. Break the problem into parts. (they don't read the whole question in one assay)
  2. Analyze each part, and represent that part visually
Rarely do they write equations. 

Then  they do mental calculations

This approach saves time...


Lets take this math problem

Observe the problem solving process…

If the average number of 8 terms is given to be 40 and the average of first 6 terms is given to be 35. What is the average of the remaining 2 terms?


Method 1:Conventional approach




Average = sum of numbers/ number of items

Average of 8 terms = 40

So let the 8 terms be a,b,c,d,e,f,g,h

(a+b+c+d+e+f+g+h)/8 = 40

(a+b+c+d+e+f+g+h) = 40*8 = 320…..equation (i)

(a+b+c+d+e+f)/6 = 35

(a+b+c+d+e+f) =  35*6 = 210…..equation (ii)

Subtract both equations to get g+h

g+h= 320-210= 110

Average = 110/2 = 55

 

Method 2: Visualization 



Let's visually represent the sum

Let's take 8 terms as 8 dashes.


The sum of the 8 terms = 8 x 40=320.  The sum of the first six terms is 6 x 35=210.

Subtract both sums to get the sum of the remaining terms = 320 - 210= 110

Hence average =110/2=55

The second method takes less time too.


So even if you have non math background, you can ace the math section by writing less equations and drawing more diagrams.

Feel free to contact me if you want to ace the math section by using simple strategies like this. 

My contact link is here:



 

Let's try another sum

Solution is here

http://letsgre.blogspot.com/2021/07/gre-math-thinking-skills-3.html

Saturday, July 10, 2021

GRE math thinking skills - 3

 GRE tests your logical skills as well as your knowledge of math concepts.  To score high, you need to remember various formulas, theorems. Also you need to master critical problem-solving skills.

Today I am going to  take you through one problem -solving skill –

Counting skills

Take this problem .

This sum requires higher order thinking


There are two ways to solve this question

 

Method 1:Using pattern recognition





 Lets say,  you didn’t know the concept of counting and permutation and combination

First focus on the 8x8 grid...

Take the smallest unit of chessboard. It’s a 2x2 grid

How many rectangles can you count?

All the squares are rectangles too.

First count squares  there are 5

How many rectangles can you count? There are 4.

In total there are 9 . 

If you observe........ 9  = 1+8

these numbers follow the cube series

 

Now take a  3x3 grid

How many rectangles can you count?

First count squares  there are 14

How many rectangles can you count? There are 22

In total there are 36 . 

If you observe ..........36  = 1+8+27

these numbers follow the cube series

 

Always remember 

the number of rectangles in a grid follow the cubic series 13 23 …33

So in a chess board.. the number of rectangles is the  sum of the cubes from 13 to 83

 Hence 13 +23 + 33+43 +53 +63 +73 +83 =1296

  

 

 

Method 2:Using principles of counting



The chess board has 8 rows and 8 columns. a 8x8 grid.


All squares are rectangles. So you need to count the squares also.



 

Okay.. First look at the gird..

Can you observe the number of horizontal lines? There are 9 lines

Similarly

Can you observe the number of vertical lines? There are 9 lines

 

If you observe… to draw a rectangle. You need to select two horizontal lines and two vertical lines.


The point of intersection of these lines form a rectangle.


So how do we choose two lines out of 9. 

Use combination.

To select 2 horizontal lines = 9C2

To select 2 vertical lines = 9C2

Now as per the rules of counting…you need to multiply

9C2 x 9C2 = ((9x8)/ (1x2) ) x ((9x8)/ (1x2) ) = 1296

There are 1296 rectangles in a chessboard.

 

To know more about Math problem solving skills.. Feel free to contact me


 My contact link is here:


Thursday, April 29, 2021

3 ways to improve your math skills - GRE math tips

 


Math is tough for some of us.

The reason - The way, math was taught to us in school or college.

Can it be mastered now?

Yes, you can...


GRE  mainly tests your mathematical reasoning.

Your ability to 

  • reason with numbers and symbols.
  • apply principles/formula and solve questions
  • evaluate cases or arguments
  • strategize for a solution
  • identify patterns and use logic
  • check data efficacy and more.

So if you are taught skills ( Skills are different from math concepts), you will be fine.

Ping me if you would like to know more about the math skill-development course .

My contact details are here:

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


So how we do work on our math skills. Here are 3 ways, which can help you hone your general math skills


1.Make math part of your daily life... practice it without even thinking


For example, if a dress that’s regularly $50 is on sale for 30% off, what is the sale price?  

Do simple calculation.

Or if you have to travel 20 miles. You are going at a speed of 20 miles per hour. How long will you take?


2.Use mental math everyday

20+30+45+60 = ??? don’t use calculator.

What is 15 squared or what is 20 squared…

Everyday spend 5 - 10 minutes working on basic computation


 

3.Practice diagramming

Always picture a math problem.

Make few circles/ draw connections/ some stick figures….

Here are sample images for math problems



If you have any queries regarding math preparation.. ping me

Happy learning... 


Monday, February 22, 2021

10 must not do's for GRE reading comprehension

  



10 must NOT DOs for GRE reading comprehension


1.Reading only for the topic

Read for the author’s opinions running parallel to the topic as well

2.Concentrating on the specific details

Higher weight-age questions demand overall intent, flow and tone of the passage.

3.Choosing a stated idea for inference question

The answer to an inference question is never explicitly stated in the passage; it is implied

4.Taking the notes too far

One way to keep track of a long passage is by making thought flow chart; use symbols arrows to show relationships

5.Losing track of ‘who says what’

The passage may present multiple perspectives- of the author’s, someone else’s ( being quoted)..

6.Overlooking the question stem.

Some question stems are simple, yet others roundabout. ensure that you are clear what the question asks.

7.Undermining the need to build vocabulary

One third of the RC questions demand word knowledge…. Skepticism, laudatory, archaic, condescending…these all appear

8.Over reading

Skip, examples, specific details, long parenthetical statements….

9.‘ NOT SEEing crucial words- Only, except, not in the question stem


10. First reading- a slow ‘thorough’ reading

The first reading can be a faster skimming, for the main points of discussion.

If you need help in GMAT verbal preparation, Feel free to ping me..

My contact link is here:



Happy learning

 



Sunday, January 31, 2021

GRE math thinking skills - 2

GRE tests your logical skills as well as your knowledge of math concepts.  To score high, you need to remember various formulas, theorems. Also you need to master critical problem-solving skills.

Today I am going to  take you through one problem -solving skill –

Attention to detail

Take this problem .

    

I am going to show you, two ways to solve this sum

Method 1 :  The traditional approach


You need to choose the numbers which negate each other

For example Row 6 column 6 = 36.

Row 5 column 6 = -30 and  Row 1 column 6 is -6

So 36+ (-30-6) =0.

You need to choose the right numbers

 Add the remaining numbers you will get the answer


I have highlighted the different combinations with letters

1J

-2I

3H

-4J

5D

-6A

-2

4G

-6C

8G

-10I

12I

3J

-6B

9H

-12H

15E

-18B

-4F

8G

-12F

16F

-20E

24B

5E

-10

15

-20G

25D

-30D

-6

12

-18C

24C

-30A

36A

 

Numbers left =  12 15  -6 -10 -2

Sum = 9

This method takes a long time

Method 2: Pattern recognition


This approach is a lot faster.

If you look at the numbers column-wise can you see a pattern(ignore signs)

column 1: 1 2,3,4,5,6

column 2: 2x1,2x2,2x3,2x4,2x5,2x6 

.

.

column 6: 6x1,6x2,6x3………..6x6

When the signs are inserted, then a pattern emerges  i.e. = 1-2+3-4+5-6

lets calculate the sum of the repeating pattern 1-2+3-4+5-6 = -3


Hence column 1 adds upto -3

Next column will be -2+4-6+8-10+12 = -2 x(1-2+3-4+5-6)= -2x-3 = 6

Next column will be 3 x(1-2+3-4+5-6)= 3 x-3 = -9

Next column will be -4 x(1-2+3-4+5-6)= -4 x-3 = 12

Next column will be 5 x(1-2+3-4+5-6)= 5 x-3 = -15

Next column will be -6 x(1-2+3-4+5-6)= -6 x-3 = +18

Answer = -3+6-9 +12-15+18 = 9

If you want to maximize your math scores in the GRE.. Lets have a chat...




Thursday, January 28, 2021

3 essential skills to ace GRE verbal

 



If you are starting your GRE preparation, then you need to work on concepts and develop skills.

So, what are the skills?

Here are 3 essential skills ,which are required to ace the GRE verbal

 1. Writing a summary – rewording a paragraph in your own words

 2. Observing the structure of the passage

 3. Identifying clue words.

 

These are 3 of the 10 major skills, you need to hone during GRE preparation.

 If you need any help in GRE preparation. Ping me.

 My contact link is here:

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

Facebook learning group: https://www.facebook.com/groups/semanticsgre

Now, let us understand each skill in detail.

 

Skill 1: Write a summary

This skill involves rewording the paragraph in your own words.

 While reading a paragraph, you need to observe

  • the main points of the paragraph.
  • an “opinion” or a “feeling” statement (for example: Author's opinion)

A summary should be 1 or 2 lines long.

 Lets take an example

 

Example 1

 There are times when the night sky glows with bands of color. The bands may begin as cloud shapes and then spread into a great arc across the entire sky. They may fall in folds like a curtain drawn across the heavens. The lights usually grow brighter, then suddenly dim. During this time the sky glows with pale yellow, pink, green, violet, blue, and red. These lights are called the Aurora Borealis. Some people call them the Northern Lights. Scientists have been watching them for hundreds of years. They are not quite sure what causes them. In ancient times people were afraid of the Lights. They imagined that they saw fiery dragons in the sky. Some even concluded that the heavens were on fire.

 Summary:

 The Aurora Borealis, or Northern Lights, are bands of color in the night sky. Ancient people thought that these lights were dragon on fire, and even modern scientists are not sure what they are.

 Note:

 There are times when the night sky glows with bands of color. The bands may begin as cloud shapes and then spread into a great arc across the entire sky. They may fall in folds like a curtain drawn across the heavens. The lights usually grow brighter, then suddenly dim. During this time the sky glows with pale yellow, pink, green, violet, blue, and red. These lights are called the Aurora Borealis. Some people call them the Northern Lights.Scientists have been watching them for hundreds of years. They are not quite sure what causes them. In ancient times people were afraid of the Lights. They imagined that they saw fiery dragons in the sky. Some even concluded that the heavens were on fire.

 

1. The lines in blue is factual information.

 In GRE they rarely ask you questions based on  factual information. So this part can be ignored.

 2. The line in red is the main idea.

 The whole paragraph talks about Aurora Borealis. So main idea can be “description of Auora Borealis”

 

Further

 3. You can notice two opinion statements. These lines are underlined.

 Opinion 1: Scientists are not sure, what causes them

 Opinion 2: Ancient people are afraid.

 So the summary of this paragraph has two components:  main idea+ opinions.

 Some paragraphs may not have opinions.

 Note*

 In your preparatory phase, take notes. Write down the summary of each paragraph. When you start taking computer adaptive tests, you wont have time to jot down the summaries on paper. Instead, you will be able to frame the summaries in your mind.(To reach this stage, you need to do extensive practice though.)

 

Skill 2: Observe the structure of the passage

It is imperative you observe the structure/layout of the passage.

 You need to identify the link/relationships that connect the lines in the paragraph.

 For example a paragraph may follow this structure

 

Line 1: Conclusion (main point, author is trying to prove)

Line 2: Reason 1

Line 3: Reason 2

Line 4: Example

Or

 

Line 1: Claim ( a view without evidence)

Line 2: Counter conclusion (main point, author is trying to prove)

Line 3: Reason 1 for the counter conclusion

Line 4: Example for the counter conclusion

So on and so forth

 

This skill(identifying the layout) is essential to ace the critical reasoning and the reading comprehension section of the exam

 

Let us take an example and observe the layout

 

Read the passage and write the layout

 

Purebred cows native to Mongolia produce, on average, 400 liters of milk per year; if Mongolian cattle are crossbred with European breeds, the crossbred cows can produce, on average, 2,700 liters per year. An international agency plans to increase the profitability of Mongolia’s dairy sector by encouraging widespread crossbreeding of native Mongolian cattle with European breeds.

 

The layout of the passage is as follows:

 

Purebred cows native to Mongolia produce, on average, 400 liters of milk per year; if Mongolian cattle are crossbred with European breeds, the crossbred cows can produce, on average, 2,700 liters per year. An international agency plans to increase the profitability of Mongolia’s dairy sector by encouraging widespread crossbreeding of native Mongolian cattle with European breeds.

   

1. Underlined line in brown is the objective /conclusion

 2. Line in red is the plan/ reason which leads to the conclusion

 3. Line is green is a hypothetical opinion

  Note*

 To tackle a Short passage(critical reasoning) question, you need to identify the conclusion first.

  

So layout here is

 Line 1: claim

Line 2: conclusion

Line 3: plan

Lets take a complex passage

 

Rain-soaked soil contains less oxygen than does drier soil. The roots of melon plants perform less efficiently under the low-oxygen conditions present in rain-soaked soil. When the efficiency of melon roots is impaired, the roots do not supply sufficient amounts of the proper nutrients for the plants to perform photosynthesis at their usual levels. It follows that melon plants have a lower-than-usual rate of photosynthesis when their roots are in rain-soaked soil. When the photosynthesis of the plants slows, sugar stored in the fruits is drawn off to supply the plants with energy. Therefore, ripe melons harvested after a prolonged period of heavy rain should be less sweet than other ripe melons.

  

Now draw a layout

 Check your answer here

 


 Can you see how the lines are inter-connected?

 Line 1 leads to line 2… which leads to line 3…and so on.

 The last line is the conclusion.

 So focus on the layout of the paragraph

 

 

Skill 3: Identify clue words

  

There are clue words which are strategically placed in the given paragraph.  These words can help you identify the relationships between lines.

 Some of the clue words are

  And,because,hence,thus,therefore, yet….

  Lets take an example

   I got fever because I ate ice cream.

  Here “because” indicates a cause and an effect.

  I ate ice cream is the reason ..I got fever is the effect

  Now lets take this question

 A peculiar feature of the embryonic mammalian circulatory system is that in the area of the heart the cells adhere to one another, beating in unison yet adopting specialized orientations exclusive of one another.

 

 Here the clue word is “yet”

 “beating in unison” yet “ adopting specialized”

  Here “yet” is used as a conjunction . It means but or nevertheless.

 In-spite of beating together the heart cells adopt different orientations which are not related


  These are 3 of the 10 major skills you need to hone while preparing.

 If you need any help in GRE preparation. Ping me.

 Happy learning!.

Wednesday, January 6, 2021

How to overcome GRE math anxiety?


Do you have a non-math background?

 Has it been a long time since you touched your math books?

 Feeling math-anxious?

 

Many students ask me this question.

 "Can I ace the GRE math, if I have a non-math background?"   Yes, you can.


Remember GRE tests you on math reasoning...

 To overcome anxiety, You need to learn math concepts.+ You need to develop math skill-sets too.

 Formula/theorems (Area of the circle, HCF and LCM of numbers...)  are the math concepts.


 So what are the math skill-sets?

 Definition of a skill-set: A skill-set is the combination of knowledge and abilities that you've developed through your life and work. You use these skills-sets to tackle problems.

 We, at semantics, have developed modules, which can hone a students math and verbal skill sets.

 Let me take you through one math skill-set.

 Problem Decomposition  

Definition: Decomposition is  the process of breaking a problem down into smaller parts to make it easier to tackle.

  

If you have a non- math background, you might find it difficult to comprehend word problems.

 One way to analyze word problems is - break problems into meaning-full chunks.  

 You need to

 1. break the problem into  2 or more segments.

 2. Analyse each segment.

 3. Infer data (if necessary)

 4. Diagram information…

 Only after all this, you write equations and solve..


 Let me demonstrate the above process via a math question 


Lets take this problem and break it into segments.

 Segment 1: "Each machine produces 1 toy every 3 minutes"

 Segment 2: "After replacement : 40% of machines  produce 1 toy every 2 minutes"

When you process segment 2, you should also infer additional information.

 This information is not explicitly mentioned.

 Inference:  If 40% of the machines produce 1 toy every 2 minutes, then 60% of the machines produce 1 toy every 3 minutes

 

Segment 3: "Percentage increase in the number of toys produced in 60 minutes."

 After breaking the problems into segments, you should use one of the many problem solving approaches.

 Lets use this approach:  substitution of numbers.

 Assume 100 machines are there initially


 Segment 1:

 Total time is 60 mins.

 1 machine produces a toy every 3 minutes . Hence 20 toys are produced by 1 machine in 60 mins.

 There are totally 100 machines.. Hence number of toys produced = 100 x 20=  2000 toys

  

Segment 2:

 Total number of machines = 100

  type 1: 40% of the machines (i.e. 40 machines) produce 1 toy every 2 minutes,

 type 2: 60% of the machines (i.e. 60 machines)  produce 1 toy every 3 minutes

 Lets calculate number of machines produced by  type 2 first..

 1 machine produces a toy every 3 minutes . Hence 20 toys are produced by 1 machine in 60 mins. Totally 60 machines.. Hence 60x20= 1200 toys  

 Let us calculate number of machines produced by type 1.

 1 machine produces a toy every 2 minutes . Hence 30 toys are produced by 1 machine in 60 mins. Totally 40 machines.. Hence 40x30= 1200 toys

 so totally 1200+1200 = 2400 toys are produced.

 

 Segment 3:

 Percentage change =  (2400-2000)/2000 x 100 = 20%

  Hope you have understood this problem solving process.

 Even if you have a non-math background, you can learn these processes and apply them on a wide genre of questions.

 If you need help in GRE math or verbal..

 Feel free to reach out:

 My contact link is here:

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

 Facebook learning group: https://www.facebook.com/groups/semanticsgre

 

Happy learning.