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 :))

 

BANK LICENSING & NATIONALISATION

I'm sure y'all know there are 2 kinds of commercial banks - Public (SBI, PNB etc.) and Private (HDFC , Axis etc.). These banks cannot operate in India unless they get a license from RBI which is India's Central Bank. [There's a commercial bank with the name "Central Bank of India" but wo sirf uska naam h, don't mix the 2!!] But public sector banks me toh already maximum stake Govt ka hi hota h, therefore license sirf private & foreign banks ko required hota h; Public sector banks ka "Nationalisation" hota h!
There are 2 terms which you surely must have read/heard somewhere - Nationalisation & Liberalisation. For easy learning ---->> remember : Nationalisation = Public Sector Banks and Liberalisation = Private Banks.
To clear this concept, Let's go to the beginning!

1. LIBERALISATION    - How private banks got their licenses!!
In general, liberalization refers to a relaxation of previous government restrictions, usually in such areas of social, political and economic policy.

(A) Narsimhan Committee I (1991) -->> Lets look at the recommendations made by this committee and the actions taken based on them :

• Govt./RBI shouldn't regulate Bank's loan interests --> BPLR (Benchmark Prime lending rate)  system came , nowadays called Bank Rate
• Setup Debt recovery tribunals --> Done!
• Liberate branch expansion policy --> Banks can open branches anywhere but 25% branches must be opened in rural areas (every year)
• Reduce SLR & CRR --> from 15 , 40 it was reduced to 4,23
• NBFC (Non Banking Financial Company) regulatory framework --> done!
• Govt should reduce shareholding of banks --> SBI shares sold, Govt now owns 60%
• Allow entry of private sector & foreign banks ---> This lead to 1st round of private Bank licenses

And thus RBI released its guidelines for licensing of new banks in private sector and in 1993 - 10 new private banks were formed :-
1. ICICI
2. HDFC
3. Times Bank (later merged with HDFC)
4. Global Trust Bank (later merged with OBC bank)
5. Centurion Bank (later merged with HDFC)
6. Bank of Punjab (later merged with HDFC)
7. UTI (now renamed as Axis Bank)
8. IDBI (Not exactly private, it's public now)
9. Indus Bank
10. DCB
*Merging aka Amalgamation.

(B) Narsimhan Committee II (1998) -->> Recommendation & action taken :

• Introduce voluntary retirement scheme (VRS) in Public sector banks - done!
• Legal Reforms for Loan recovery - SARFAESI act 2002
• Computerisation, EFT (Electronic Funds Transfer) - done!
• Payment & Settlement Act - Retail (ECS, NEFT, Cards) + Wholesale (RTGS) --- I'll discuss these in the future in detail
• Continue allowing entry of private & Foreign banks - 2001 More applications were invited by RBI

And again in 2001 - RBI revised guidelines for licenses and then in 2003-04 licenses were given to 2 new banks - Kotak Mahindra & Yes Bank.

(C) 2013 - 2014 --->> Then Finance Minister P. Chidambaram recommended more private banks - A total of 26 applicants including Anil Ambani, Birla, Bajaj, Tata, Muthoot, India Post were there. But later 2 withdrew their applications and left the race - Tata & Videocon ; And new applicant - KC Land & Finance joined in. Therefore, total of 25 were there in the end.

Bimal Jalan Committee (2013) ---> Set up to decide the winners and they were announced in April 2014 - only 2 - IDFC (Infrastructure Development & Financial Corporation) and Bandhan Microfinance. Both of them were given in principle approval.

*  In principle approval - Within 18 months, they must get net worth to Rs. 1000 crore, open 25% branches in unbanked rural areas --> only then RBI will give them license under Banking Regulation Act, 1949 and only then public will be able to open Current & Savings Account.

 

2. NATIONALISATION - Means govt. becomes majority shareholder in those bank and govt. can pick board of directors of it's choice for these banks.

 

Timeline :

• Creation of RBI - 1935
• Nationalisation of RBI - 1949
• Enactment of Banking Regulation Act - 1949
• Creation of SBI - 1955
• Creation of SBI Subsidiaries - 1969
• Nationalisation of 14 major Public Sector Banks - 1971
• Creation of RRBs (Regional Rural Banks) - 1971
• Nationalisation of 6 more banks with deposits > 200 crores - 1980

(A) Creation of RBI : RBI Act was passed in 1934 and Bank was established in 1935 on recommendation of Hilton-Young Commission.

• Initially Head Office was in Calcutta, moved to Mumbai in 1937 where Governor sat and formed policies. At that time, RBI was privately owned and Sir Osborne Smith was 1st governor of RBI till 1937
• C D Deshmukh - 1st Indian governor of RBI till 1949. He was a member of Indian Civil Services. He represented India at Bretton Woods Negotiations in 1949.
• In 1949, RBI was nationalised - i.e. fully owned by Govt.

(B) Banking Regulation Act  1949 : 
This act empowers Union govt. in consultation with RBI Governor to issue directions to banks as necessary. This act governs all public & private sector banks & other banks in India. RBI can even remove the entire board of a bank. RBI prevents connected lending [some bank lending to a connected corporation at low rates causing loss in the end]. RBI can check accounts and of those connected corporations as well!! RBI can conduct special audits of co-operative banks and implement penalty on any bank not maintaining cash reserves. Approval of RBI is needed to buy > 5% shares of a bank.
All these powers were granted to RBI by this Act.

(C) Nationalisation of SBI : Earlier k/a Imperial Bank of India, acquired by Govt. in 1955. Remember : SBI is NOT a nationalised bank. It's a public sector bank which is regulated by SBI Act 1955. SBI was already under govt. control in 1969 & 1980 , so there was no need of Nationalisation of SBI. In 1959, 8 banks were converted into SBI subsidiaries - Bikaner , Jaipur, Hyderabad, Indore, Mysore, Patiala, Travancore & Saurashtra. Bikaner & Jaipur were merged to form 1 bank. Saurashtra & Indore were merged with SBI.

(D) Nationalisation of Major Banks :  Banks that were nationalised were either privately owned by companies or individual investors. In 1969 14 banks were nationalised and then in 2nd round in 1980 6 more were nationalised. But later, in 1993 New Bank of India was merged with PNB. This left us with 19 nationalised banks until 2013.

(E) Bharatiya Mahila Bank : 3rd round of Bank Nationalisation! In budget 2013, Fin Min P Chidambaram announced to open this bank with Rs1000 crore = 100% State (Govt.) owned.
In November 2013, BMB was inaugurated on Indira Gandhi's B'day.

• It's an all women bank
• Board of directors = females
• Staff = male + female
• Customers = male + female -->> no distinction
• But loans given predominantly to women. Through BMB, women entrepreneurs can get loans up to Rs1 crore without putting any collateral with the bank.

That's all folks!! :)) Here check out my next article Numbers and their Principles 

SYLLOGISM

Before you proceed, make sure you have read my article on Venn Diagrams.

Now Syllogism! I have seen 90% students 100% confused when it comes to Syllogism. I'll try to make this post as self-explanatory as possible, but for this to be effective you'll have to forget everything that you've read or learnt so far on this topic. Make a note of few points first :

1. We are going to use Venn diagrams to solve the questions but I won't be taking the usual "AEIO - universal particular" and what not route, because honestly Mujhe bhi nai aata wo samajh! And how does it matter what method you're using if you're getting the correct answer.
2. Don't solve any complicated faltu questions from 100 different websites, you're bound to get confused. For this particular topic, only & only solve from either an error-free book or past years' papers.
3. Don't get nervous if you're required to solve 4-statement or 1000-statement syllogisms. Sabme same Funda lagega!
4. My way of solving is not the conventional way, I use my own symbols while drawing Venn, but you can get used to them in 1 session, so no biggie!

 

Case - 1 & 2: These should be clear from the Venn.
Case - 3 : In the 2nd possibility, you can see that Venn is the same as for "All S are P". And you might be thinking that I'm wrong here - but I am not. Remember - "All" can be converted to "some" but "Some" cannot be converted to "All".
Case - 4 : Again this one is easy. Only thing is you have to rattafy all the 3 possibilities.

Now, the symbol that I was talking about. If you have to represent a "NOT" anywhere in syllogism you can do it as :

 

That little cross would help you in a big way. Here, it's evident that there's nothing common between Black and Green, and this also includes the area which is common between Black and White. What does that tell us?
That ---->> Some White are NOT green.
Also, there's no cross linking White and Green. And what does that tell us?
That ---->> Some whites are green is a possibility. Isn't it? Yes it is.

See? The 4 cases that we discussed and this little cross : That covers all of syllogism! Now we have to apply these and some brains and we can solve any question on this topic. But again, I'm warning you - Don't go solving faltu questions which are extremely twisted! Neither any Bank nor SSC is looking for Einsteins!

EXAMPLES

1. Statements - Some dews are drops.
                         All drops are stones.
    Conclusions - At least some dews are stones.
                           At least some stones are drops.
Solution : Don't get anxious if you see unexpected words like "at least" , "maybe" , "possibility" in these questions. Whatever be the variation in the question, we have to apply the same rules and answer as per the basic English meanings of these words. So here, the answer would be : Both conclusions follow.
You can very well see in the diagram, that wherever we place drops, it will be inside stones (as per 2nd statement) ---->> This  explains Conclusion 1.
Conclusion 2 is directly derived from Statement 2.

2. Statements - Some squares are Circles.
                        No circle is a triangle.
                        No line is a square.
    Conclusions -  All squares can never be circles.
                            Some lines are circles.
Solution : Conclusion 1 follows because there is some part of squares that's common with triangles. And considering statement 2 , that cannot happen.
Conclusion 2 doesn't follow because it's not definite. If the statement would have been "some lines may be circles" then it would have followed.

3. Statements - Some leaves are skies.
                        Some skies are clouds.
                        No cloud is a boat.
   Conclusions  -I. Some boats are definitely leaves.
                          II. At least some clouds are leaves.
                         III. All skies being leaves is a possibility.
                         IV. No leaf is a boat.
   Options : a) I, II and III follow
                   b) II, III and IV follow
                   c) Either I or IV and II follow
                   d) Either I or IV and III follow
 Solution : D is the correct answer. All skies can be inside the leaves circle, this will not contradict with any of the other statements, It is a possibility!! Therefore, conclusion III follows. As for I & IV --->> Dono me se ek to hoga hi na! Either leaf & boat don't have common area ya fir they do.
Conclusion II will not follow because again, it's not definite that some clouds are leaves. If there was a "maybe" or a "possibility" used here, then it would have followed. But the conclusion uses -->> At least some clouds ARE leaves.

That's all for now, since Syllogism has a lot of variations , I'll try to generalise them and post another article with examples from each variation with explanation. Until then, try solving questions (only from reliable sources) and you can leave your doubts in the comments!!

VENN DIAGRAMS

My general awareness was somewhat poor and so to maintain the balance I worked really hard on Reasoning. I attempted 44/50 questions in SBI PO with 90% accuracy in a span of 35minutes. Now before you get any ideas, there's simply no tricks or shortcuts in Reasoning, there's only practise. Even so, I'm going to share how I handle each and every topic when it comes to Reasoning. Let's start with Venn Diagrams.


What are Venn Diagrams?
They are figures representing group of items in the form of circles (mostly).

Can I expect these questions?
Direct questions on Venn diagrams won't be asked in any of the SBI exams. You might find them in IBPS or SSC CGL. But we will be using these to solve syllogism questions in the next article, and questions on syllogism are asked in every exam, that too worth atleast 5 marks.

Situation - 1
When 1 group is completely included in the 2nd and 2nd is completely included in the 3rd. For eg. Guitarists, instrumentalists, musicians

Situation - 2
When 2 groups are unrelated to each other but are completely included in the 3rd. For eg. carrot, pumpkin, vegetable

Situation - 3
When 2 groups have something in common and both are completely included in the 3rd. For eg. Mothers, sisters, females. Some mothers can be sisters too and vice versa.

Situation - 4
When 1 group is completely included in another, while 3rd group is unrelated to both of them. For eg. Indians, Asians, Europeans

Situation - 5
When all 3 groups are related in some way but cannot be completely included in each other. For eg. Illiterate people, unemployed people, poor people. We can have a combination of any 2, and we can even have a combination of all 3.

Situation - 6
When 2 groups are unrelated to each other but they are both somewhat related to the 3rd. For eg. Police, Doctor, Female. We can have Female policemen and female doctors but police and doctors don't have anything in common.

Situation - 7
When 1 is completely included in the 2nd and both of them are party related to the 3rd. For eg. Females, Nieces, cousins. All nieces can only be females, but there can be female cousins and some female cousins can also be somebody's niece.

Situation - 8
If 1 group is partly related to the 2nd group and 3rd is completely unrelated to both of them. For eg. Students, scholars , books. Some students can be scholars but neither of them can be a book!

Situation - 9
When all 3 are completely unrelated. For eg. Sun, Pluto, Earth. Now, if there was another group "Planets" then Pluto and Earth would fit in there, but we can't add things of our own will, right?!

That's all the possibilities there can be while using Venn Diagrams. In case you're confused, just refer to the picture posted above, I'm sure it will clarify things for you.

QUESTIONAIRE
There's mainly 3 kinds of questions on Venn diagrams. I am posting sample questions on each of the 3. The answer keys have been added. Happy solving! :))


                                  

 

ANSWERS

21-C 22-A 23-C 24-B 25-C 26-C
31-E 32-D 33-E 34-C 35-A 36-B 37-C 38-E 39-D
9-B 10-D 11-D 12-A

Check out my article on Syllogism  

What is a Bank? SCHEDULED & COMMERCIAL BANKS

What is a Bank?
It's a financial institution authorized by the government to receive deposits, pay interest, clear cheques, serve loans, act as an intermediary in financial transactions and provide other such financial services to customers.

SCHEDULED BANKS

These are included in the 2nd schedule of RBI Act, 1934. RBI includes only those banks that satisfy section 42 (6)(a) of the act. Two conditions to be fulfilled are :
1. Paid Capital & collected funds of the bank should be >= 5 lakhs
2. any activity of the bank should not adversely affect interests of depositors

Every Scheduled bank :
A. Becomes eligible for debt/loans on bank rate from RBI
B. Automatically acquire membership of clearing house

COMMERCIAL BANKS
These may be defined as institutions that deal with deposits & advances of a business organisation. Remember!!! RBI is NOT a commercial bank! These can be classified into :
1. Public Sector Banks : All government of India undertakings + IDBI + SBI & Assoc.
2. Private Sector Banks : ICICI, YES, HDFC, Axis etc etc ... whose head offices are in India (GoI does not have stakes in these)
3. Foreign Banks : HSBC, Bank of America etc. whose Head offices are not in India
4. Regional Rural Banks - These will be discussed in details in an upcoming article.


That's for today aspirants!! Hang on until 2moro!
P.S. If there's any terms you don't get, don't go digging, try to memorise what I've provided as much as possible and after I'm done posting all my articles, you'll feel differently!! Later!!