Divisibility Rules



Divisibility by 2 Rule


Almost everyone is familiar with this rule which states that any even number can be divided by 2. Even numbers are multiples of 2. A number is even if ends in 0,2,4,6, or 8.
Ex.
  • 2
  • 0
  • 4
  • -2
  • -312
  • 31,102

Divisibility by 3 Rule


Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 3, so is the number
Ex.
12→1 + 2 = 3 And 3 is divisible by 3 so the number 12 is also divisible by 3.

Divisibility by 4 Rule


A number is divisible by 4 if the number's last two digits are divisible by 4.
Ex.
358912 ends in 12 which is divisible by 4, thus so is 358912

Divisibility by 5 Rule


A number is divisible by 5 if the its last digit is a 0 or 5.
Ex.
  • 10 → since the last digit is 0, 10 satisfies this rule and is divisible by 5
  • 15 → since the last digit is 5, 15 satisfies this rule and is divisible by 5
  • 45
  • -30
  • 55
  • -105

Divisibility by 6 Rule


If the Number is divisible by 2 and 3 it is divisible by 6 also.
Ex
 114 → satisfies both conditions
  • 1) 1+1+4 = 6 which is divisible by 3
  • 2) 114 is even so divisible by 2
  • Hence 114 is divisible by 6


Divisibility by 7 Rule


Test - 1
Take the last digit in a number. Double and subtract the last digit in your number from the rest of the digits. Repeat the process for larger numbers.
Ex
357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

Test - 2
Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary Add the products. If the sum is divisible by 7 - so is your number.
Ex
Example: Is 2016 divisible by 7? 6(1) + 1(3) + 0(2) + 2(6) = 21 21 is divisible by 7 and we can now say that 2016 is also divisible by 7

Divisibility by 8 Rule


A number passes the test for 8 if the last three digits form a number is divisible 8.
Ex.
6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

Divisibility by 9 Rule


A number is divisible by 9 if the sum of the digits are evenly divisible 9.
Ex.
43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

Divisibility by 10 Rule


A number passes the test for 10 if its final digit is 0.
Ex.
  • 100
  • 110
  • -110
  • 1,320,320.

Divisibility by 11 Rule


A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.
Ex.
  • 682 → (6+2) - 8 = 0 which is, of course, evenly divided by 11 so 682 passes this divisibility test
  • 10,813 → (1+8+3) - (0+1) = 12-1 =11. Yes, this satisfies the rule for 11!
  • 25, 784 = → (2+ 7 + 4) - (5+8) = 13 - 13 =0 . Yes this also satisfies the rule for 11!



Mixture and Alligation questions concept with tricks


Mixture and Alligation based Questions



Question Type -1


In X gram mixture of milk and water, milk is P %. To make the quantity of milk in the mixture to be Q %, the quantity of milk added to the mixture will be.

Trick: X{(Q-P)/(100-Q)}

Ex. In a 60 liters mixture of milk and water, the quantity of milk is 5 %. In how much quantity, should milk be added to this mixture so that the quantity of milk in the mixture becomes 15 % ?

Ans. Use trick-
60*{(15-5)/(100-15)
60*(10/85)
120/17 liters


Question Type -2


In what ratio must a grocer mix two varieties of things costing Rs. C (Cheaper) and Rs. D(Costlier/Dearer) per kg respectively so as to get a mixture worth Rs. M kg?

Trick: (Cheaper quantity) : (Dearer quantity) = (D - M) : (M - C)



Ex. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

Ans. Use trick-
(Cheaper quantity) : (Dearer quantity) = (20-16.50):(16.50-15)
(Cheaper quantity) : (Dearer quantity) = (3.50):(1.50)
(Cheaper quantity) : (Dearer quantity) = 35:15
(Cheaper quantity) : (Dearer quantity) = 7:3




Trick to remember Nationalization Date of Banks


Nationalization Date of Banks


Trick 

a PUNJABI boy of name VIJAYA is studying COMMERCE in a CORPORATE college of ANDHARA PARDESH

  1. PUNJABI - Punjab and Sindh Bank (Don’t be confuse with Punjab National Bank)
  2. VIJAYA - Vijaya Bank
  3. COMMERCE - Oriental Bank of Commerce
  4. CORPORATE - Corporation Bank
  5. ANDHARA PARDESH - Andhra Bank
  6. Dena Bank - Mumbai (This bank don't have 'of india' at last but its Headquarter is in Mumbai)

    These 5 banks nationalization date is : Aril 15, 1980.
    Except these 5 banks (also except SBI group and IDBI) all other 14 banks were nationalized on July 19, 1969.

Tricks to remember Bank Headquarters in India




Public Sector Bank Headquarters in India


Trick : 1
Banks having "OF INDIA" at their Last except UBI : Headquarters - Mumbai

  1. State Bank of India - Mumbai
  2. Bank of India - Mumbai
  3. Central Bank of India - Mumbai
  4. Union Bank of India - Mumbai
  5. IDBI (Industrial Development bank of India) - Mumbai
  6. Dena Bank - Mumbai (This bank don't have 'of india' at last but its Headquarter is in Mumbai)
  • Reserve of India - Mumbai
  • Security & Exchange Board of India - Mumbai

Trick : 2
Banks having "INDIAN" at their starting: Headquarters - Chennai

  1. Indian overseas Bank - Chennai
  2. Indian Bank - Chennai

Trick : 3
Vajay Can Bang - Bangalore

  1. Vijaya Bank - Bangalore
  2. Canara Bank - Bangalore

Trick : 4
Bank having HQ in their own cities

  1. State Bank of Bikaner and Jaipur -- Jaipur
  2. State Bank of Hyderabad -- Hyderabad
  3. State Bank of Mysore -- Bengalooru
  4. State Bank of Patiala -- Patiala
  5. State Bank of Travancore -- Thiruvananthapuram
  6. Bank of Baroda - Baroda
  7. Bank of Maharashtra - Pune
  8. Andhra Bank - Hyderabad

Trick : 5
Delhi & Punjabi Girls(Mahila) are good in Commerce

  1. Punjab National Bank - New Delhi
  2. Punjab & Sindh Bank - New Delhi
  3. Bharitya MAHILA Bank - New Delhi
  4. Oriental Bank of commerce - New Delhi

Trick : 6
Allahabad & Kolkata's People are Unite

  1. UCO (United Commercial Bank) - Kolkata
  2. United Bank of India - Kolkata
  3. Allahabad - Kolkata

Trick : #
Two banks which have very uniqueheadquarters

  1. Syndicate Bank - Manipal
  2. Corporation Bank - Mangalore


At the present time there are 27 Public Sector Banks in India which includes 19 Nationalized banks also.
List is as follows :

[1] Public sector bank which are nationalized -
Allahabad Bank
Andhra Bank
Bank of Baroda
Bank of India
Bank of Maharashtra
Canara Bank
Central Bank of India
Corporation Bank
Dena Bank
Indian Bank
Indian Overseas Bank
Oriental Bank of Commerce
Punjab & Sind Bank
Punjab National Bank
Syndicate Bank
UCO Bank
Union Bank of India
United Bank of India
Vijaya Bank

[2] Public sector bank which are not nationalized -
State Bank and its associate
State Bank of India
State Bank of Bikaner and Jaipur
State Bank of Hyderabad
State Bank of Mysore
State Bank of Travancore
State Bank of Patiala
And
IDBI
Bhartiya Mahila Bank


Why State Bank and its associate are not nationalized ?

People often get confused about whether SBI is a nationalized bank or not.
SBI is NOT a Nationalized bank. It is a Public Sector Bank. Actually, SBI draws power from State Bank of India Act, 1955. Nationalized banks are the banks which were nationalized in two phases – in 1969 and 1980. These banks were established under Banking Companies (Acquisition and Transfer of Undertakings) Acts, 1970 and 1980. So, these banks are governed by their respective statutes. In 1969, 14 Commercial banks were nationalized and in 1980, 6 more banks were nationalized. But, later in 1993, PNB and New India bank got merged taking the figure of nationalized banks to 19.
Now, couple of interesting question comes to our mind while we talk about nationalization of Banks, we’ll try and answer these questions.

1). Why Nationalization of Banks was done by the Government?
  • To raise public confidence in Banking system
  • Expansion of banking facilities in a uniform manner
  • Provide banking facility in rural and sub-urban areas
  • Sought to end the monopoly control of big industrialists upon the banking system
  • Aimed at giving more credit to priority sectors
  • To reduce regional economic inequalities
  • To ensure enough development funds for the planned growth of the country


2). Why SBI was not nationalized during the waves of Nationalization of Banks in 1969 and 1980?
SBI was already under State control in 1969/1980, vide SBI Act, 1955. So, there was no need of Nationalization of State Bank of India. Banks which were nationalized in 1969/1980 were either owned by private business groups or individual investors.

Tricks for Percentage Questions


Percentage based Questions



Question Type -1


If there is increase of X% and subsequently X% decrease then there is always loss / decrease in the condition.

Trick: (X*X)/100

Ex. If Ruhan salary is increase by 50% and subsequently decrease by 50%. How much percentage loss?

Ans. Use trick: 50x50/100= 25% decrease/loss

Question Type -2

(Two Successive Discounts)


What single discount is equivalent to two successive discounts of X% and Y%

Trick: (X+Y)-{(X*Y)/100}

Ex.What single discount is equivalent to two successive discounts of 10% and 20% ?

Ans. Use trick: (10+20)-(10*20)/100= 28%

Question Type -3

(Two Successive Increases)


What single Increase is equivalent to two successive Increases of X% and Y%

Trick: (X+Y)+{(X*Y)/100}

Ex.What single Increase is equivalent to two successive Increases of 10% and 20% ?

Ans. Use trick: (10+20)+(10*20)/100= 32%



Trick to remember Aluminium Ores




Trick: Alu in Box

  1. Alu- Alumina
  2. Box- Bauxite

Trick to remember Type of Coal in order of Quality





Type of Coal in order of Quality

(Trick)

 Remember 1st Alphabet of Coal Type

A > B > L > P (in English Alphabet)

 

  1. A- Anthracite (93% Carbon)
  2. B- Bituminous (84% Carbon)
  3. L- Lignite (64% Carbon)
  4. P- Peat (54% Carbon)

Trick to remember borrowed features of Indian Constitution





Borrowed features of Indian Constitution

(Trick: Read bellow conversation )



एक बार कुछ लोग बैठकर आपस मे बाते कर रहे थे और भारत के " डॉ. भीम राव अम्बेदकर" चुप चाप सुन रहे थे। बाते कुछ इस प्रकार हो रही थी...


ब्रिटेन :- पूरे भारत देश पर मेरा कब्जा था इस लिये `संसद का निर्माण अकेले करेँगे (संसदिये , विधि निर्माण , एकल)

अमेरीका :- नही, मेरे पास संयुक्त राष्ट्र संघ है। इसलिए लोगो को न्याय और स्वतंत्रता दिलाना मेरा अधीकार है (न्यायिक , स्वतंत्रता का अधिकार और मौलिक अधीकार)

जर्मनी :- तुम लोगो ने हमे विश्व युद्ध में हराया है इसलिये अब मै आपातकाल घोषित करुंगा (आपातकाल)

फ्रांस :- मै तो पहले से ही गणतंत्रता वाला देश हूँ ये तुम सब जानते हो|  (गंतत्रतात्मक शासन)

कनाडा :- तुम लोग को जो करनी हो करो। मै ऐक शक्तिशाली देश हूँ शक्ति का बँटवारा कर अपनी सुरक्षा कर लुंगा (राज्यो मे शक्ति का विभाजन)

आयरलैँड :- अरे यार। तुम लोग कि निती निर्देश हमे कुछ समझ नही आ रही (नीति निर्देशक तत्व)

ऑस्ट्रेलिया :- मै विश्व कप क्रिकेट मे हमेशा सूची नं 1 पर रहता हूँ | (समवर्ती सूची)

दक्षिण अफ्रिका :- पर हम इतना अच्छा खेलने के बाद भी आज तक सेमी फाइनल तक भी नही पहचे सायद अपने खेल मे कुछ संसोधन करना पङेगा (संविधान संसोधन की प्रक्रिया)

रुस : भारत मेरा दोस्त है और उसकी मदद करना हमारा मूल कर्तव्य है (मूल कर्तव्य)


Trick to remember Hydroelectric Dam of Uttar Pradesh






Hydroelectric Dam of Uttar Pradesh

(Trick: Ri O Ma Ra)

  1. Ri- Rihand Dam (1962- Sonbhadra at 'Ganga' )
  2. O- Obra Dam (1970- Sonbhadra at 'Ganga' )
  3. Ma- Matatila Dam (1958- Lalitpur at 'Ganga' )
  4. Ra- Rajghat Dam (2000- Lalitpur at 'Ganga' )

Trick to remember Inscriptions where Ashoka name is mentioned






Places of inscriptions where Ashoka name is mentioned

(Trick: नीतू मास्को से उड़कर गुजरी)

  1. नीतू- नेत्तूर(Nittur)- Karnataka
  2. मास्को- मास्की(Maski)- Karnataka
  3. उड़कर- उद्गोलन(Udgolan)- Karnataka
  4. गुजरी- गुर्जरा(Gurjara)- M.P.