NUMBERS AND THEIR PRINCIPLES

Hello Amazing People!
So who out there hates maths? Lol yeh me too! But it becomes interesting the second you start getting answers, Don't it?! So, I don't have a special book for IBPS but these days I'm preparing for SSC CGL 2014, and the book I'm following for that is simply great. For DI I can help y'all with whatever experience I've gained so far by writing and clearing SBI PO phase I.
Let's start with Numbers!

Face Value : Of any digit is the value of the digit itself irrespective of its place in the number. eg in 4387236 face value of 7 is 7

Place Value : is the place at which digit is present. eg. in 3238741 Place value of 8 = 8x1000 = 8000

TYPES OF NUMERALS

1. Natural Nos :  Starting from 1 --->> 1,2,3,4........ Denoted by 'N'

• Zero is not a natural no
• All natural nos are positive

2. Whole Nos :  Natural nos + Zero. Denoted by 'W'

3. Integers :  Whole nos + Negative nos.

• 1,2,3,5,7,99,18459 - Positive Integers
• -1 , -33, -349823874 - Negative Integers

4. Even Nos : These are divisible by 2. Zero is an even no.

5. Odd Nos. : Not divisible by 2

6. Prime Nos. : These are divisible by only 1 and itself. eg. 2,3,5,7,11,13.....

• 2 is the only prime no that is even
• 1 is not a prime no

7. Coprimes :  2 nos are coprimes if their HCF is 1. eg (7,9) (15,16) ----> matlab inme 1 k alawa koi common factor nahi hota. Coprimes may or may not prime nos.

8. Composite nos : All non-prime nos.

• They must have 1 factor other than 1 and itself.
• 1 is not a composite no

10. Rational Numbers : are in the form of p/q where q is not equal to zero. eg. 3/5, 7/9, 1889/100 ....

11. Irrational Numbers : These cannot be expressed in p/q form. eg √2 , √3, √5 ....

12. Real Nos : include both rational and irrational nos. Denoted by 'R'


DIVISIBILITY TEST

1. By 2 : If last 1 digit is even
2. By 4 : If last 2 digits are divisible by 4
3. By 8 : If last 3 digits are divisible by8
4. By 3 : If sum of digits is divisible by 3
5. By 9 : If sum of digits is divisible by 9
6. By 6 : If number is divisible by both 2 & 3
7. By 12 : If number is divisible by both 3 & 4
8. By 5 : If last digit is 0 or 5
9. By 10 : If last digit is 0
10. By 25 : If last 2 digits are divisible by 25 or if they are both 0
11. By 7 : If difference b/w 2 times the last digit and the no formed by rest of digits is 0 or divisible by 7. eg. 581 ----> 58 - (2x1) = 58 - 2 = 56 which is divisible by 7 , so 581 is also divisible
12. By 11 : Find the sum of digits at odd places and then even places separately. If the difference of the 2 sums is 0 or divisible by 11 then no is also divisible by 11. Remember - Count from right to left!

         eg. 57945822 --> At odd places sum = 2+8+4+7 = 21
                                      At even places sum = 2+5+9+5=21
                                      Difference = 21-21 = 0 ----->> Divisible by 11

TRICKS??
I'll be blunt! Tricks don't work! Not for me at least. I've wasted hours on cramming all kinds of fancy formulae - be it digital sum, fast addition subtraction methods, Vedic maths. I've gone through the first 3 chapters of M Tyra word by word after someone recommended it for Bank PO. But when I was there, staring at my Computer in the examination hall ---- Not even a single formula hit me. So if ur a math genius - good for u, but if ur an average kid like me, my advice to you my friend is - Stop googling "maths tricks and shortcuts for IBPS".
I'm sure the noobs must have heard all sorts of horror stories about SBI's DI this year- well they are true! So to help, I will share with you , what actually did help me in the exam!

• Rattafy the tables up to 20
• Rattafy squares up to 30, cubes up to 15 and prime numbers up to 100
• While practising at home, try to use as little pen & paper as possible (I started this by putting a few maths pdfs in my phone. I used to solve 3-4 questions at a time while travelling, and made sure I was not carrying a pen with me) 
• The last one is the only shortcut I use. It is a little difficult to explain but I'm doing the best I can :

MULTIPLICATION SHORTCUT

MULTIPLYING Two Digit Numbers
Eg. 43 x 58

This works only for 2 digit numbers. It also helps in calculating squares. There's another for 3 digit numbers as well, but I'll have to go through my notes and add it later.

That's it for now! I'm attaching 2 images which have helped me, hope they do the same for you. Just take a print and put it on your cupboard :))