Trachtenberg Speed Maths - Pdf

Friends, today we are giving you one of the useful books on mathematics. That is The Trachetenberg System of Speed Maths. And before going to download and read the book, lets read a small story of our hero Jakow Trachtenberg (The inventor of a system of rapid mental Calculation known as The Trachtenberg System). He created the Trachtenberg system of mathematics, whilst a political prisoner in Hilter's concentration camps during the second world War. To keep himself sane whilst living in an extremely brutal and harsh environment, Trachtenberg immersed his mind in a world of mathematics and calculations. As concentration camps do not provide books, paper, pen or pencils nearly all of his calculations had to be performed mentally. This forced Trachtenberg to develop methods and shortcuts for performing calculations mentally. Trachtenberg developed his discoveries into a complete system of mathematics.

After the second world war, Trachtenberg started teaching his system of mathematics. He started teaching the more backward children to prove that anyone could learn his system. In 1950 he founded the Mathematical Institute in Zurich, where both children and adults were taught the system.

The system has been thoroughly tested in Switzerland and is found to produce an increase in self confidence and general aptitude to study, as the students prove to themselves what they are capable of, by their accomplishments in calculating results to computations.

The Trachtenberg system is based on a series of keys which must be memorized. There is no need for multiplication tables or division as the system only relies on the ability to count. The system also places an emphasis on getting the right answer and provides a number of methods for checking the answers achieved by the system.

Research on the system, indicates that the system shortens time for mathematical computations by twenty percent and produces correct results, ninety nine percent of the time, due to the checking method used as part of the system. Ok, now lets see the Pdf format of theTrachtenbergSystemof Speed Maths. You can get more shortcuts Here. Like our Facebook Page for frequent updates. Good day and Happy Reading :)


Download the pdf file of Trachternberg Speed Mathematics from here 

01:07 - By Unknown 0

 Math Tables in Audio (Mp3) format

First time in the history, Guide4BankExams is proudly presenting Math tables in audio (Mp3) format. The concept behind this post is very simple. Its an open secret that most of us don’t know the answer of “What is Seventeen eights are!!!”. Ofcourse we do have some techniques to calculate the answer in our minds, but my question is “Why to waste those few seconds during the time of exam???”. We are posting the tables in audio format because It has been known for years that our brains can continue to take in and learn new information even while we are asleep. So why not use this to help those people who have great difficulty in learning their 'times tables'. These  files are numbered the same as the tables. i.e. the Ten’s times table is track 10; the Thirteen’s times table is track 13 etc. The tables cover the numbers from 1 to 20! You can use the files in two different ways : 

1. Conscious Learning : Play the files using  your CD Player or Mobile’s autorepeat. The table will be read to you and then read again in a different order. Try to beat the second version by giving the answer before the end of the pause. 
2. Sleep Learning : Select one or two tracks to learn. Set your CD Player or Mobile to repeat these tracks continously. Set the volume fairly low but loud enough so that you can make it out. Play the track while you are sleeping. Repeat the process the next night. You will be surprized how quickly you will learn the tables.  For better results, use this sleep method with short sessions of conscious learning. Happy Listening :)

Guide4BankExams'   Multiplication Tables in Audio Format
Multiplication Table 1	Multiplication Table 11
Multiplication Table 2	Multiplication Table 12
Multiplication Table 3	Multiplication Table 13
Multiplication Table 4	Multiplication Table 14
Multiplication Table 5	Multiplication Table 15
Multiplication Table 6	Multiplication Table 16
Multiplication Table 7	Multiplication Table 17
Multiplication Table 8	Multiplication Table 18
Multiplication Table 9	Multiplication Table 19
Multiplication Table 10	Multiplication Table 20

And please keep in mind this caution message too… “If you use the headphones, then just avoid using the inside ear versions. Ofcourse they are fine for using during the day, but using them overnight can lead to a painful ear infection espicially if your ear is damp after bathing. And also keep in mind that too much hearing may lead to hearing problems.

Hope you will like our idea, if you found this post useful then please feel free to tell us… Good Day :)

Note : If you are unable to download the above Mp3 files then please mail us to Guide4BankExams@gmail.com with the subject line "Mp3 Tables". We will send all the files to your mail Address.

01:05 - By Unknown 1

 Squares, Square Roots and Cube Roots Shortcuts Free Download

Friends, we have already given shortcut methods for finding Squares and Cubes. You can read those shortcuts Here. In today's post we are going to give you some traditional techniques to find the Squares, Square Roots and Cube Roots of the given numbers. That too in pdf format. So that you can download this pdf version and read when ever you are free. Just understand the concept well and try to solve all the 35 problems given there. And latter check with the key given at the last page. Hope you will like this post. If you like this post... and want more, you can download some more pdf materials Here. We are presently working on even more easiest ways to find Square Roots and Cube Roots of the given numbers. You can get those posts within a week. Please like our Facebook page here for frequent updates of the shortcuts via Facebook. Good day and Happy Reading.
Squares, Square Roots and Cube Roots

01:04 - By Unknown 0

 Speed Maths shortcuts - Pdf version

Friends, we've got tremendous response to our previous pdf post of the shortcuts about Squares, Square roots and Cube roots. First of all thanks for the support. So many of our users have asked to upload the shortcuts for doing basic maths like additions, subtractions, multiplications and divisions etc.   So for you we are posting the shortcut tricks for mental maths. In this post you will get the shortcuts for finding almost all the mathematical problems (including square roots and cube roots). Hope this post will help you in improving your problem solving skills. You can get more downloads here. Please LIKE our facebook page here for frequent updates. Happy Reading :).

Download Speed Math Shortcuts Pdf File from Here (Mediafire Link)

Speedmaths Shortcuts

01:03 - By Unknown 0

R. S. Aggrawal's Quantitative Aptitude

 R. S. Aggrawal's Quantitative Aptitude - Pdf

Thanks for the response to our previous post, the pdf version of R.S. Aggrawal's Verbal Reasoning. As number of our friends here are asking us to post the pdf version of R. S. Aggrawal's Quantitative Aptitude, so in this post we are updating the pdf version of the Quantitative Aptitude. This will help you preparing for the Aptitude section of Any competitive Exam in India. And friends, plz remember that just saving this file in your system wont help you. Do practice daily. Here is the Download Link (Click on the slow download button and wait). Please Like us at Facebook for frequent updates. You can get more downloads Here. All The best and Happy Reading.

01:02 - By Unknown 0

 Shortcut for finding Cubes

Attention Friends... we've came to know that this method is not working for some numbers... So presently we are working on more efficient method than this... We advise you to avoid this method....

In our last posts we've discussed the method of finding Squares (read that post Here). In this post we shall discuss the method of finding cubes. This is very easy and simple method. You just have to put little concentration while learning and should do little practice so that you can do the process in a easy way mentally. And another thing you should keep in mind is, we are posting the step by stem inorder to make you understand the process in detail, but you SHOULD do most of these steps MENTALLY and only should put some important final results on paper. Now lets have a look at the method. In earlier method of finding squares we'd discussed finding the squares with the formula (a+b)² , here we shall use the formula (a+b)³. 

Lets start with an example. Assume that you should find out the cube of 18. The general process is multiplying 18 to itself for 2 times (18 x 18 x 18). This process is time consuming and often people end up with the wrong answer caused by confusion and hurry. 

Ok, now lets use our method. here you should use the formula  (a+b)³  = a³ +b³+ 3a²b +3ab². But here you should be little tricky. Have a look.........

Note : Here a or b should contain 3 digits. Or else, just put zeroes to fill the gaps so that you can avoid confusion while doing additions. So, the calculation will look like this.....

Here, please note that you are placing 0s to avoid confusion and to fill the GAPS. If you have some 2 digit number (say 25)  instead of that 1 in the above example, you should write that as 025.

Some Points to Remember : 

• You should write a³  and b³ Side by side (no need to add them)
• You should start writing the 3a²b term exactly below from the  a³  term.  
• The 3ab² term should end one number before the  b³ term.

Lets see another example,

Liked this Post ?? Read more Shortcuts Here >>

Thats all for now friends. This method may look little confusing initially. Please do practice well so that you can understand the advantage of this method. Happy reading :) 

01:00 - By Unknown 0

 Shortcut for Square - A Simple Method

We have already discussed a method for finding the squares of the given number (check that method Here). Now we shall discuss another simplest method to calculate square of the given number. First of all one thing you should keep in mind, for you r convinience we've mentioned each and every step in detail. But You should do all these calculations MENTALLY. I mean without using pen or pencil. So practice well to do these problems orally. Now lets go to the topic, Finding the square of a number ending in 5 is very simple. If the last digit of the number is 5, then the last two digits of the square will be 25.What ever is the earlier part of the number multiply it with one more than itself and that will be the first part of the answer. (The second part of the answer will be 25 only).

35² = 1225  Here 3 x 4 = 12 so the answer is 1225

45²   = 2025

55²   = 3025

75²   = 5625

95²   = 9025

125²   = 15625

175²   = 30625

235²  = 55225

195²   = 38025

245²   = 60025

Well friends, now we know the squares of numbers 25, 30, 35, 40, 45, 50, 55 etc. If we want to find the squares of any other number, we find it using these squares which we already know.

For 262 we will go from 252, for 322 we go from 30 2 and so on.

One way is writing 262 = (25+1)2. But we need not even calculate (a+b)2 by adopting the following method.

262  = 252 + 26th odd number. i.e., 625 + 51 = 676

(a+b)2   = a2 + 2ab + b2

262   = (25 + 1 )2

           = 252  + 2 x 25 x 1 + 12

        = 625 + 50 + 1

       = 625 + 51 

        = 676

So, the answer is same. Now we shall look at an easiest method which will help you to calculate Squares Mentally. 

12   = 1 = 1

2 2  = 4 = 1+3

32   = 9 = 1+ 3 + 5

42   = 16 = 1 + 3 + 5 + 7

52   = 25 = 1 + 3 + 5 + 7 + 9

I mean, to get n2, you should add the FIRST n odd numbers. If we want 172, it will be the sum of the FIRST 17 odd numbers. 

n^th odd number is equal to (2n - 1)

Suppose you want to find out 62 knowing what 52 is, we can move from 52 to 62.

62 will be the sum of 1st 6 odd numbers. But the sum of the first 6 odd numbers can be written as " Sum of the first 5 odd numbers" + "Sixth odd number". Since we already know that the sum of the FIRST 5 odd numbers is 52 , i.e., 25, we need to add the sixth odd number, i mean (2x 6-1) = 11 to 25 to give us 62 = 36.

Similarly

312 = 900 + 31st Odd number = 900 + 61 = 961

362 = 1225 + 36th odd number = 1225 + 71 

                = 1296 (remember that 352 = 1225)

412 =  1600 + 81 = 1681

462 =  2025 + 91 = 2116

1262 = 15625 + 251 = 15876

1962 =  38025 + 391 = 38416

2162 =  46225 + 461 = 46656      Read More ☛

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00:59 - By Unknown 0

 Finding the Square of the given Number

In this post we shall discuss about the Shortcut of finding the Square of the Given Number. This is very easy and Simple method. All the you need to learn this method is little concentration and little patience. Remember friends, To make you understand the process clearly, we are posting the process in Step by Step process. But you have to do all these steps Mentally and you should Only write the Answer on Paper... 

Lets start with an example. Assume that you have to find the Square of the number 38.

So, the general process is 38²  multiplying 38 with itself. But this process take much time and effort. So, instead of calculating 38 X 38, just use the formula a² + 2ab + b²

But here you should apply a little trick. If you apply the above formula as it is... you cant get the answer... Just do as mentioned below.

Now, follow the below mentioned steps

Thats it... The answer is 1444.

Now lets have a look at another example. Lets see how to find out the square of 56. I mean 56².

Now treat 6 as a, and 5 as b and apply the a² + 2ab + b² formula as explained above.

• First of all, find the a ² i.e., 6 ² = 36. 

• Now find 2ab i.e., 2 X 6 X 5 = 60

• Now find the b ² i.e.,  5 ²  =  25, now  add this 25 to 6 = 31. And put this before the numbers 3 6. So it will become 3 1 3 6
• This is our answer 56 ² = 3136

Advantages of this Method :

• We are dividing the given number into two small numbers and then performing calculations on those smaller numbers. So that you can do calculations Mentally in very easy way. 
• Initially you may think that this method is little confusing. Just do 3 or 4 problems, so that you can find the advantage of this method.

If you have any Comments, please use the comments box below. Please tell your friends about us if you like this Post.. Good Day and Happy Reading :)

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00:58 - By Unknown 0

 Aptitude Shortcuts - Average

Aptitude Questions with Answers - Average

Before going to solve the below problems, first read the basics of Average here. 

1.  What is the average of first 21 multiples of 7 ?

1.  49
2. 147
3. 77
4. Cant be determined
5. None of these

2.  In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?

1. 12.5 Yrs
2. 14.2 Yrs
3. 12.3 Yrs
4. 12.6 Yrs
5. None of these

3.  The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?

1. 42
2. 57
3. 27
4. Cant be determined
5. None of these

4.  The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher

1. 49
2. 46
3. 48
4. Cant say
5. NOne of these

5.  The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?

1. 67.4kg
2. 58.85kg
3. 57.75kg
4. 49.4kg
5. None of these

6.  The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?

1. 53kg
2. 58.85kg
3. 75kg
4. 77kg
5. None of these

7.  The average temperature for Monday, Tuesday and Wednsday is 36.3 degrees C. The average temperature for Tuesday, Wednesday and Thursday is 36.7 degrees C. if Monday's temperature recorded as 39 degrees c, find the Thursday's temperature ?

1. 40.2 degrees C
2. 39.2 degrees C
3. 41.4 degrees C
4. 40.4 degrees C
5. None of these

8.  A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?

1. Rs. 2050
2. Rs. 210
3. Rs. 1950
4. Rs. 2200
5. None of these

9.  There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess?

1. Rs. 624
2. Rs. 562
3. Rs. 585
4. Rs. 598
5. None of these

10.  The average age of father and his two sons is 27 Years. Five years ago, the average age of the two sons was 12 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?

1. 42
2. 48
3. 44
4. 47
5. None of these

Answers :

1.  Required average  = 7(1+2+....+21) / 21

                 =  (7/21)X ( (21x22) / 2 )  (because sum of first 21 natural numbers)

                  =  77

2.  Total age of 50 students 

                             =  (30X 13+20 X 12) = 630

                          Average =  630/50 = 12.6 Years

3.  The total of seven numbers = 7X18 = 126

          The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99

          So, the middle number is (126 - 99 ) = 27

4.  Total age of students is 32X16 = 512 Years

     Total age inclusive of teacher = 33X (16+1) = 561

      So, Teacher's age is 561-512 = 49 Yrs

                               There is a shortcut for these type of problems :

                                                    Teacher's age is 16+(33X1) = 49 Years :)

5.  Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs

          Actual average weight is 1177/20 = 58.85kgs

6.  Let the average weight of 8 persons be 'x'

      years and the age of the new person be 'y'   years

                         so, (8x - 65 + y) / 8  = x+1.5

                          so, y = 77kgs                   Shortcut : 65 + 8X1.5 = 77kgs

7.  MOn + Tue + wed Temperature  =  3X36.3 = 108.9

        Tue + wed Temperature = 108.9 - 39 = 69.9

         Tue + wed + Thu temperature = 3X36.7 = 110.1

           So, Thursday's temperature = 110.1 - 69.9 = 40.2 degrees C

8.  Total expenditure for the first 3 months = 3X1600 = 4800

      Total expenditure for 4 months = 4X1550 = 6200

           Total expenditure for 5 months = 5X1800 = 9000

           Total expenditure and saving (which is income for one year)

               = 4800 + 6200 + 9000 + 5200 = Rs. 25200

              So, Average monthly income = 25200/12  =  Rs. 2100

9.  Let the original expenditure be Rs.x

     Original average expenditure = X/45

            New average expenditure = (x+39)/52

            So (x/45) - ((x+39) / 52) = 1  so x = 585

               so, original expenditure is Rs 585

10.  The total present age of father and two sons is 3S27 = 81 yrs

           The total present age of sons is (12+5) X 2 = 34Years

           so, present age of father is 81 - 34 = 47 yrs

                                                               

Liked this Post? Read more Shortcut Techniques of Aptitude Here

Math Trick Speed Math Math Shortcuts Aptitude Shortcut Tricks for Bank Exams ssc

00:56 - By Unknown 0

 Average

• Average of Given Items :
  
  

Average =		Sum of the given Items
		Number of those Items




• Average Speed :
  
  
  Suppose a Person covers a certain distance at X kmph and an equal distance at Ykmph.
  
  Then, the average speed for the whole journey will be (2XY)/(X+Y) Kmph

✒ Lets do some problems on Average (Click Here)

00:54 - By Unknown 0

 Mathematical Operations

Friends, today we shall discuss another important model of Reasoning Section Mathematical Operations. Of course, even these questions are asked under reasoning section these are mainly dependent on mathematical operations. All calculations will be performed using BODMAS Rule. We can divide these problems in three types.Those are,

1. Symbol Substitution
2. Mathematical Logic
3. Interchange of Signs & Numbers

Now lets discuss these types with detailed examples.

1st Type : Symbol Substitution

In this type, to find the value of the given expression you should replace the symbols by mathematical operations. Then apply the BODMAS Rule (i.e., Brackets, of, Division, Multiplication, Addition, Subtraction).

For the detailed understanding, lets have a look at an example

Example : 42% (9-2) + 6 x 3 - 4

Solution :
42 % (9-2) + 6 x 3 - 4
= 42 % 7 + 6 x 3 - 4
= 6 + 6 x 3 - 4
= 6 + 18 - 4
= 24 - 4 = 20


2nd Type : Mathematical Logic

In this type, they just give you some logical statements followed by some mathematical operations. You should solve the given mathematical operations with the help of given logical statements.

Example : If % stands for greater than, x stands for addition, + stands for division, - stands for equal to, > stands for multiplication, = stands for less than, < stands for minus, then which of the following alternatives is correct ?

1. 3 + 2 < 4 % 6 > 3 x 2 
2. 3 x 2 < 4 % 6 + 3 < 2
3. 3 > 2 < 4 - 6 x 3 x 2 
4. 3 x 2 x 4 = 6 + 3 < 2 

Usually for these type of questions people tend to make direct decisions with the help of given statements. But confusion arises when you tried to  coordinate given mathematical symbols with the logical statements mentioned above. It is because lack of coordination between eyes and brain. So, to avoid confusion you just should make a note of given logical statements in simple mathematical equations format. So that it will be easier for your eye to pick the correct operation.

by using above logical statements, you can use a rough sketch like this,

now you can calculate the values of given operations mentally by picking the right hand side symbols instead of left hand side. Or you just can replace the symbols by taking the reference of above rough sketch.

Solution : Using the symbols correctly as given in the above operations, for the option (2) you will get, 3+2-4>6%3-2. Using BODMAS rule in this inequality, we will get 5-4>2-2 or, 1>0, which is correct.

3rd Type : Interchange of Signs & Numbers

In this type they just give you some random set of numbers and mathematical symbols. And then ask you to choose the correct of symbols to fit the given equation.

Example : Select the correct set of symbols which will fit in the given equation 5  0  3  5  = 20

1. x, x, x
2. =, +, x
3. x, +, x
4. +, -, x

Solution : Using the set of symbols given in options, you will get the Option 2 as the correct answer.

Using the set of symbols given in option 2, you will get the equation,

5-0+3x5 = 20

Using BODMAS rule you will get,

5-0+15=20 or 20-0 = 20 which is correct

Now lets have a look at some examples,

1. '<' means subtraction, '>' means Addition, '+' means Multiplication and '$' means Division. Then what will be the value of 27 > 81 $ 9 < 6 ?

Solution :

27+81%9-6 = 27+9-6 = 36-6 = 30

2. If % means +, - means x, x means -, + means %, then what will be the value of 15 - 2 % 900 + 90 x 100 ?

Solution :

15x2+900%90-100 = 30 + 10 - 100 = -60

3. Q means Addition, J means Multiplication, T means Subtraction, K means Division then what is the value of 30K2Q3J6T5 ?

Solution :

3%2+3x6-5  =  15 + 18 - 5 = 28

4. P means x, R means +, T means %, S means -, then what will be the value of 18T3P9S8R6 ?

Solution :

By substituting the given symbols, you will get the answer 52

5. P means Multiplication, T means Subtraction, M means Addition, B means Division then what will be the value of 28B7P8T6M4 ?

Solution :

28 % 7 x8 - 6 + 4 

= 4 x 8 - 6 + 4 

= 32 - 6 + 4 

= 36 - 6 = 30

Thats all for now friends. In our next post we shall discuss some more problems of Mathematical Operations with higher difficulty level. Happy Reading :)

03:11 - By Unknown 0

 BODMAS

• In The simplifications of numerical questions, the order of mathematical operations to be followed is given in the abbreviated form : "BODMAS", where

• B stands for 'Bracket'
• O stands for 'Of'
• D stands for 'Division'
• M stands for 'Multiplication'
• A stands for 'Addition' and
• S stands for 'Subtraction'.
• Order to be followed by in case of brackets is as follows :
• (   )  : Small Brackets,
• {  } : Curly Brackets   and
• [  ]  : Square Brackets

00:53 - By Unknown 0