Basics of Speedy Calculation (Quantitative Aptitude: Speed Maths/Vedic Maths)

Here, we are providing basic concepts to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some values can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam.

1. Faster way of Calculations: We all know a lot about addition, subtraction, multiplication, divisions. While solving questions of Quantitative Aptitude/Numerical Ability, candidates should learn to perform these calculations mentally rather than following conventional methods. There are specific approaches one can follow to do this.

2. Multiplication tables up to 20: It is not just enough to know what the multiple figures are. It should be a two way thoroughness i.e., it is not sufficient to know that 17 x 8 is 136, it is also very important that when you see 136, the factors 17 and 8 (or 34 and 4 for that matter) should come to your mind.

3. Squares up to 25: Candidates should be thorough with squares up to 25. Any higher square can be calculated relatively easily.

4. Cubes upto 12: It is used widely in calculations.

5. Powers of 2 upto 12:It is widely used in the questions relating to Number System.

6. Powers of 3 upto 6: It is widely used in the questions relating to Number System.

7. Reciprocals of integers upto 12: These should be learn' by heart. These will also be useful in Data Interpretation calculations.

8. 100s complements: (For any number less than 100, the number that should be added to make it 100).

9. Vedic Maths : Vedic Maths can be widely used for calculations in Quantitative Aptitude.
In due course of time, 

(jagranjosh.com)

Usefulness of Powers of 2 (Quantitative Aptitude: Speed Maths /Vedic Maths)

important concept i.e. is power of 2 to help the aspirants in attempting all the questions speedily. Here, we are providing basic concepts to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some values can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam.

A useful property for the powers of 2: Powers of 2 are very helpful in calculations. Candidates should memorise powers of 2 upto 12 so that it can be used in the questions.
2⁰=1 ; 2¹=2 ; 2²=4 ; 2³=8 ; 2⁴=16 ; 2⁵=32 ; 2⁶=64
2⁷=128 ; 2⁸=256 ; 2⁹=512 ; 2¹⁰=1024 ; 2¹¹=2048 ;2¹²=4096

1. The sum of powers of 2 from 0 to any number n will be equal to 2ⁿ⁺¹ – 1.
If a number is written from 1 to N as a sum of one or more of the integers of a given set of integers, then it can easily be done from powers of 2. The set of integers used by us comprise of all the powers of 2 starting form 1 (i.e. 2⁰) to the largest power of 2 less than or equal to N.

For example: If you want to build all the integers upto 255, the numbers 1, 2, 4, 8, 16, 32, 64, 128 are sufficient as 255=1+2+4+8+16+32+64+128.
2. Differently, if we have one weight each of 1, 2, 4, 8, 16, 32, 64 and 128 kg, then all the items would be measured from 1 kg to 255 kg using one or more of the given weights (the weights used only in one pan of the weighing scales).

Example: How much minimum number of weights are required to weigh all possible weights upto 512 Kg (Putting all the weights only in one side of pan)

Solution: 512=2⁹. Minimum Number of weights required=9+1=10. The weights will be 1,2, 4, 8, 16, 32, 64,128, 256 kg

(jagranjosh.com)

Usefulness of powers of 3 (Quantitative Aptitude: Speed Maths|Vedic Maths)

 Important concept i.e. power of 3 to help the aspirants in attempting all the questions speedily. Here, we are providing basic concepts to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some values can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam.
3⁰ = 1
3² = 9
3³ = 27
3⁴ = 81
3 ⁵ = 243
3 ⁶ = 729
First have a look at the powers of 3 upto 6 given above
The sum of the numbers 3⁰, 3^-1, 3² and 3³ (i.e. 1, 3, 9 and 27) is 40. Using a combination of these numbers we can obtain any number from 1 to 40.
For Example:
2=3-1;
4=1+3;
5=1+1+3; and so on.. 40=1+3+9+27

• Each occurring at the most once we can obtain all the numbers from 1 to 40 by using the operations of only addition and/or subtraction.
• In other words if you have one each of the weights of 1 kg, 3 kg, 9 kg and 27 kg, by using a combination of these weights in EITHER one of the two pans of a weighing scale, we can weigh all weights from 1 kg to 40 kg. You are using the weights in 2 pans.
• The above usefulness of the powers of 3 can be widely used in the questions of Quantitative Aptitude/Numerical Ability.

Time Saving Methods in Multiplications (Quantitative Aptitude: Speed Maths/Vedic Maths)

 We are trying to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some values can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam.
We have come up with some Time Saving Methods in Multiplications, which will make your calculations more speedy and faster.

Multiplication by 5, 25 & 125
1. For multiplication by 5
As we know that 5=10/2. Multiply the figure given by 10 and then divide it by 2.
For example: 3568 x 5 = 35680/2 = 17840.
It is considered as a very simple method. The adoption of this method saves 5 seconds. If one adopts such methods at a number of places in the entire exam. It will save even 4 to 5 minutes that helps you attempt at least 115 more questions. This itself may make all the difference to your chances of selection.

2. For multiplication by 25
Similarly, We know 25=100/4. So multiply the figure given by 100 and divide it by 4.
For Example 3568 x 25 = 356800/4=89200.

3. For multiplication by 125
We know 125=1000/8. So multiply the figure given by 1000 and divide it by 8.
For Example 3568 x 125 = 3568000/8 = 446000. Alternatively, if we write 125 as 100 + 25, it is correct. So, multiplication by 125 can be treated as multiplication by 100 and add to this figure one- fourth of itself (because 25 is one-fourth of 100).

4. For multiplication by 11, 21, 31 etc
It can be treated as multiplication by 10+1, 20+1, 30+1, etc..
For Example 3568 × 11 3568 X (10+1) = 39248

5. Multiplication by 19, 29, 39 etc
It can be treated as multiplication by (20 - 1), (30-1), (40-1) etc...
For Example 3568 x 19 = 3568 x 20 – 3568 = 67792

(jagranjosh.com)

Quantitative Aptitude: Speed Maths\Vedic Maths: Squaring by Vedic Nikhilam Method

Important concept i.e. Squaring by Vedic Nikhilam Method  to help the aspirants in attempting all the questions speedily. Here, we are providing basic concepts to make the calculation faster than doing from long and traditional ones. Practice and thorough learning of some values can help the candidates in cracking Quantitative Aptitude/Numerical Ability Section in Bank Exam, SSC Exam, Railway and Other Exam
 •Here, we are introducing the Squaring of numbers closer to 100, 1000, 10000, etc in very speedy manner.

 •Vedic Nikhilam Method is explained for squaring which is found in Atharva Veda. Here squaring is explained with the help of Yavadunam Formula.

Method

a) Finding out the Square of 99 or (99)2

Step 1. Decide the base: Base is some power of 10 nearest to the given number. In this example, (10)2 i.e.100 is the nearest number to 99. So we will take 100 as our base.

Deviation from base 100-99=01

Step 2. Squaring: We can directly write the answer in Two Parts one after another-

Part A   Part B

Part A : It is a number obtained from subtracting deviation from the given number. Part A = 99-1= 98

Part B : It is a two digit number(for base 100, 3 digit number for base 1000 and so on..) and can be obtained by squaring the deviation. So, Part B = (01)2= 01

So, (99)2 = 9801

b) Finding out the Square of (102)2 : When the number is more than base, the deviation to be added to the number to get Part A.

Part A : Deviation=102-100=2

Part B : (02)2=04

So, (102)2=10404

Number      Base       Deviation         Part A         Part B      Answer

c) (94)2        100         100-94=6         94-6=88     62=36       8836

d) (92) 2       100         100-92=8         92-8=84      82=64      8464

e) (104)2    100         104-100=04    104+4=108  42=16    10816

f) (994)2      1000     1000-994=6   994-6=988   62=036     988036

g)  (992)2   1000     1000-992=8   992-8=984   82=064     984064

h) (9992)2 10000  10000-9992=8 9992-8=9984 82=0064 99840064

i)  (1006)2   1000     1006-1000=6    1006+6=1012 62=036  1012036

By regular practicing this method, one can easily find out square of nearest number of 10, 100, 1000, 1000 and so on.
(jagranjosh.com)