Coding and Decoding

The coding and decoding test is designed to test the candidate's ability.The term Coding and Decoding relates message. Coding is method of transmitting a message between sender and receiver that no third person can't understand it. Coding, therefore, means rule or method used to hide the actual meaning of a ward or group of wards and Decoding means the methods making out the actual message that is disguised in coding.
Based on various type of questions asked in different examinations, it is divided into 4 types of categories.
1. Letter Coding
2. Number Coding
3. Substitution Coding
4. Mixed Coding and Mixed Number Coding
To solve the questions of this section,the candidate has an idea about the Alphabet letter series. In the below has been given a forword letter series, reverse letter series and opposite letter series.  
Alphabet Numbering:      
1   2    3   4    5    6    7     8    9   10  11  12   13
A   B   C   D   E    F    G    H    I     J    K     L   M 
N   O    P    Q    R    S    T    U    V   W   X    Y    Z
14  15 16  17   18  19  20  21  22  23  24   25  26

Alphabet second half Reverse Order:
A   B   C   D   E   F   G   H   I    J   K   L   M
Z   Y   X  W   V   U   T   S   R   Q   P   O  N

Alphabet forward order:
A    B   C   D   E   F   G   H   I    J   K    L   M
N   O   P   Q   R   S   T   U   V   W  X   Y   Z

Some examples to under stand coding and decoding:
1.Interchanging of positions
Example:In a certain code IMTITJU is written as TMIIUJT.How is TEMREMP written in that code?
Explanation:The given code contain 7 letters.In the given code, the letters of even numbered position have been left as they are while the first and third letters have been interchanged.similarly,the fifth and seventh letters have been interchanged.similarly,for TEMREMP solution is METRPME.
2. Addition/Substraction of Alphabet numeric position value
Example:In certain code of MTUXTRVN is written as NUVXTQUM.how is ASUMNJKL written in that code ?
Explanation: There are 8 letters in the word.the codes for first three letters can be obtained by ( taking followin letters )adding +1 to the position of alphabet numeric value.the fourth and fifth letters are written as they are in the word and the last three letters have by taking preceding letters.so,the solution become's NUVXTQUM.
3. Number coding
Example:if PRIVATE is coded as 1234567 and RISK is coded as 2398,how RIVETS coded ?
Explanation: By comparing PRIVATE and RISK codes R=2,I=3....they code numbers in serial to PRIVATE. So,solution we get 234769.
4. Substitution Coding
Example: In a code language ' We Me Ye' means "Tell Them Young" and 'Me Yo Na Ye' means 'Wise Young Sharp Tell'.which code represents 'Them' in the given code language ?
Explanation: By Comparing two codes Me and Ye are seems in two codes.where,Them is not there in second code.so,Them in code language is 'We'.
In some rare number coding problems coding requires squares or cones of alphabate position numeric value.example for this case is: if a certain code Z=2197 and R=729 how would J be written in that code.
For this we may go in different trials or ways.but,the correct procedure is The position value Z is 26 and half of 26 is 13,qube of 13 I'd 2197.similarly, J position value 10.half of 10 and qube is 125.so,solution is 125.
Upto now I have gone through so many coding and decoding problems.but,I felt some difficulty to get answer to the following question.
Problem:In certain code language COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that code language ?
Note:First try it on your own and then see the explanation
Explanation:There are 8 letters in the word.the coded word can be obtained by taking the immediately following letters of the word,but in reverse order.that means,in coded form the first and the last letters have been interchanged while the remaining letters coded by taking their immediate next letters in the reverse order.
So solution we get RFUVQNPC.

Coding and decoding problems are seems to easy.but,if you practice more and more you may get answers in fraction seconds.here given some questions to practice:
1. In a certain code EVEREST is coded as TSEREVE then EDUCATION will be:
a) EVEREST       b) TSEREVE
c) EDUCATION d) NOITACUDE
2.If DEMOCRACY is coded EDOMCARYC then POLITICAL will be :
a) OPILTCILA.   b) EDOMCARYS
c) POLITICAL.   d) DEMOCRACY
3. If AUTHORITY is coded YTIROHTUA then DESIGNATE is coded :
a) AUTHORITY.  b) YTIROHTUA
c) DESIGNATE.  d) ESENGITAD
4.In a certain code RENOWNED is coded DEENNORW then INFORMATION is coded :
a) RENOWNED   b) DEENNORW
c) INFORMATION d) AFIIMNNOORT
5. In a certain code PRIVATE is coded IAEPRVT then SECTION will be :
a) PRIVATE        b) IAEPRVT
c) EIOSCTN.      d) SECTION
6. In a certain code, PAPER is written as RCRGT How is MOTHER written in that code?
a) MOTHER       b) OQVJGT
c) REHTOM       d) OMHTRE
7. If in a certain language COMPUTER is coded as FRPSXWHU. Which word would be coded as VLOHQFH
a) SILENCE       b) SCIENCE
c) ECNEICS.      d) ECNELIS
8. If C = 3 and LOVER = 72 then BEHIND = ?
a) 32.  b) 53.  c) 43.  d) 42
9. In a certain code, 2568 written as CFNV and 14739 is written as BSLDE. How is 2834 written in that code?
a) CNFE b) LOVE c) CVDS d) CDEF
10. If SKY is called CLOUD, CLOUD is called RAIN, RAIN is called AIR, AIR is called SUNLIGHT, SUNLIGHT is called POWER. Where will a bird fly?
a) AIR b) RAIN c) SUNLIGHT d) POWER
11. If LOSE is coded as 1357 and GAIN is coded as 2468, what do the figures 84615 stand for?
a) NAILS b) SNAIL c) LANES d) SLAIN e) None
12. If CASE is coded as 5231, CHAIR is coded as 58206, and TEACH is coded as 71258, what does 586037 stands for?
a) CHASTE b) CHRIST c) STREET d) CHEESE e) None
13. If QUICK is written as JVRDPO How will PANEL be written as?
a) KBMFO b) KBMUO c) QBMUP d) QZLFP
14. If HUNCH is written as NUHCH How will SQUAD be written as?
a) UQSAD b) QUADS c) UQDAS d) UQSDA
15. If GRIM is written as PIKK, Which word is written as GYUW?
a) EVEN b) EASE c) EAST d) EASY
16. If LUCKY is written as YKLUC How will POWER be written as?
a) REPOW b) ERPOQ c) ERWOP d) WERPO
17. If TEAR is written as UGBT, Which word is written as QQTV
a) POST b) PONY c) PORT d) PORE
18. If WASH is written asVZRG, Which word is written as RGNV
a) SHOW b) WISH c) SHEW d) STEW
19. If MOUTH is written as NNVSI How is CLAIM written as?
a) BMZHL          b)DMBJN   
c) DKBHN         d) BKZJL
20. If DRAFT is written as AFYDR How is SLING written as?
a) LINGS          b) INGLS
c) LNIGS    d) INGSL      e) None
Direction: The group of letters in each question from 21 to 25 is to be codified in the following code.
Letters D I N E S H K U M
Digits  8 2 5 1 7 4  9 3  6
21. D E S H M U N
a) 2174672           b) 8175346
c) 1356984           d) 8174635
e) 8176453
22. S H K N U D I
a) 7453298      b) 7495238
c) 7495382      d) 4579283
23. N I S U D I M
a) 3598762             b) 527862
c) 5273826            d) 5273628
e) 8723569
24. D I N E S H
a) 821574               b) 821475
c) 217485                d) 528135
e) 825174
25. S I M U K I
a) 7639522        b) 726923
c) 726392.         d) 632793
e) 237693

Direction Sense

Direction Sense - Verbal Reasoning
Direction Sense Test in Verbal Reasoning is the most important part to achieve marks in any competitive exams, most exams contains atlest 2 to 3 questions of Direction Sense which in keen area to score, Direction Sense is nothing but just a ascertain the sense of direction. Candidates are required to use their sense about direction and answer the given questions correctly. The following examples and images will clarify exactly.
Example 1 :
A man Started to walk in West. After moving a distance he turned to his right. After moving a distance he turned To his right. After moving a little he turned in the end to his left. Now in which direction was he going?
(A) North (B) South (C) East (D) West
Answer With Explanation : (A) The man started to walk from A towards West and reached to B after moving a little distance. Then From B he turned to his right (C) From (C) he turned to his right and reached at (D). at D he turned to his left. So, he Was going in the north direction.
Direction Sense Test Tips image
Here is a tricky image to remember which direction would be face goes and went while solving Direction Sense questions. This image will help you to answer quickly of any Direction Sense test.

Practice Questions : 1. Going 50 m to the south of her house, Radhika turns left and goes another 20 m. Then, turning to the north, she goes 30 m and then starts walking to her house. In which direction is she walking now? (1) North-west (2) North (3) South-east (4) East 2. A watch reads 4.30 if the minute hand points east, in what direction does the hour hand point? (1)North (2)North-west (3)South-east (4)North-east
3. One morning after sunrise, Sumesh and Ratheesh were standing on a lawn with their backs towards each other. Sumesh’s shadow fell exactly towards his left hand side. Which direction was Ratheesh facing?
(1) East (2) West (3) North (4) South
4. Shailesh and Mohan start from a fixed point. Shailesh moves 3 km. northward, turns right and then covers 4 km. Mohan moves 5 km westwards, turns right and walks 3 km. The distance between Shailesh and Mohan now is
(1) 10 km (2) 9 km (3) 8 km (4) 6 km (5) 4 km
5. A man walks 10 km towards north. From there he walks 6 km towards south. Then he walks 3 km towards east. How far and in which direction is he with reference to his starting point?
(1)7 km east (2) 5 km west (3)5 km north-east (4) 7 km west

Ratio

If the values of two quantities A and B are 4 and 6 respectively, then we say that they are in the ratio 4:6 (read as "four is to six"). Ratio is the relation which one quantity bears another of the same kind, the comparison being made by considering what multiple, part or parts, one quantity is of the other. The ratio of two quantities "a" and "b" is represented as a:b and reads as "a is to b". here, "a" is called antecedent, "b" is the consequent. since the ratio express the number of times one quantity contains the other, it's an abstract quantity.
Ratio of any number of quantities is expressed after removing any common factors that all the terms of the ratio have. For example, if there are two quantities having values of 4 and 6, their ratio is 4:6, i.e., 2:3 after taking the common factor 2 between them out. similarly, if there are three quantities 6,8 and 18, there is a common factor among all three of them. so, dividing each of the term by 2, we get the ratio ass 3:4:9.
If two quantities whose values are A and B respectively are the in the ratio a:b, since we know that some common factor k(>0) would have been removed from A and B to get the ratio a:b, we can write the original values of the two quantities (i.e., A and B) as ak and bk respectively.For example, if the salaries of two persons are in the ratio 7:5, we can write their individual salaries as 7k and 5k respectively.
A ratio a:b can also be expressed as a/b. so if two items are in the ratio 2:3, we can say that their ratio is 2/3. if two terms are in the ratio 2, it means that they are in the ratio of 2, it means that they are in the ratio of 2/1 i.e., 2:1.
"A ratio is said to be ratio of greater or less quantity or of quantity according as antecedent is greater than, less than or equal to consequent". In other words,
- the ratio a:b where a>b is called a ratio of greater inequality (example 3:2)
- the ratio a:b where a<b is called a ratio of less inequality (example 3:2)
- the ratio a:b where a=b is called a ratio of equality (example 1:1)
From this we can find that a ratio of greater inequality is diminished and a ratio of less inequality is increased by adding the same quantity to both terms, i.e., in the ratio a:b, when we add the same quantity x (positive) to both the terms of the ratio, we have the following results
   If a<b then (a+x):(b+x) > a:b
   If a>b then (a+x):(b+x) < a:b
   If a=b then (a+x):(b+x) = a:b
this idea can be helpful in questions on data interpretation when we need to compare fractions to find the larger of two given fractions.
If two quantities are in the ratio a:b , then the first quantity will be a/(a+b) times the total of two quantities and the second quantity will be equal to b/(a+b) times the total of two quantities.

To understand the concept of Ratio, we have to come across the more examples.
Example 1:The sum of two numbers is 84. if the two numbers are in the ratio 4:3, find the two numbers ?
solution: As the two numbers are in the ratio 4:3, let their actual values be 4x and 3x. As the sum of two numbers is 84, we have 4x + 3x = 84,which is equal to 7x = 84. so, x = 12.
Hence, 4x = 48 and 3x = 36.
Alternatively, the two numbers are (4/7)*84 = 48 and (3/7)*84 = 36 i.e., 48 and 36 respectively since the ratio of two numbers is 4:3..

Example 2: If 4a = 3b, find (7a+9b) : (4a:5b) .
Solution: it is given that 4a = 3b, hence, (a/b) = (3/4)
 => a =3k and b=4k, where k is the common factor of a and b. Required expression (7a+9b):(4a +5b)
= [(7*3k)+(9*4k)]:[(4*3k)+(5*4k)] = (21k + 36k) : (12k+20k) = 57k:32k = 57 : 32.

Example 3: The number of red balls and green balls in a bag are in the ratio of 16:7. if there are 45 more red balls than the green balls, find the number of green balls in the bag.
Solution: Since, the ratio of number of red and green balls is 16:7, let the number of red balls and green balls in the bag be 16x and 7x. so, the difference of red and green balls is 9x. 16x-7x = 9x = 45.
That means x =5. Hence, the number of green balls = 7x i.e., 35
Alternatively, 7x = (7/9)*(9x) = (7/9)*(45) = 35. Hence, there are 45 green balls in the bag.

Example 4: What least number must be added to each of a pair of numbers which are in the ratio
7 : 16 . so, that the ratio between the terms becomes 13 : 22 .
Solution : Let the number to be added to each number be a. Let the actual values of the numbers be 7x and 16x, since their ratio is 7 : 16. Given that, (7x+a)/(16x+a) = (13/22)
=> 154x + 22a = 208x + 13a => 9a = 54x.
=> a = 6x. when x =1, a is the least number required and is equal to 6.

Example 5: A number is divided into four parts such that 4 times the first part, 3 times the second part, 6 times the third part and 8 times the fourth part are all equal. in what ratio is number is divided .
Solution: lets the four parts into which the number is divided be a,b,c and d. 4a = 3b =6c = 8d.
Let the value of each of these equal to e. a = e/4, b = e/3, c = e/6, and d = e/8.
Hence, a:b:c:d = e/4 : e/3 : e/6 : e/8 = 6/24 : 8/24 : 4/24 : 3/24.The ratio of the parts into which the number is divided is 6 : 8 : 4 : 3.

Example 6: If x:y = 4:3, y:z = 2:3, find x : y : z ?
Solution: As y is common to both ratios , make y in both ratios equal. this is done by making y have the value equal to the LCM of two parts corresponding to y in the ratios i.e., LCM(3,2) is 6. if y = 6,
x = (4/3) * 6 = 8, z= (3/2)*6 = 9. Hence x : y : z = 8 : 6 : 9.

Example 7: In a mixture of milk and water, ratio of milk to water is 5:1 . if 5 liters of water is added to the mixture, the ratio becomes 5:2. Determine the quantity of milk in mixture initially?
Solution: The ratio of milk and water is 5 : 1. let water and milk are 5k and k. when the k is common factor. (5k +5) / (k + 5) = 5/2. 10k +10  = 5k + 25, k = 3. So the answer is 15 liters of milk is there in the initial mixture of milk and water.

LOGARITHMS

the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 10³.The logarithm to base 10 (b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the irrational (transcendental) number e (≈ 2.718) as its base; its use is widespread in pure mathematics, especially calculus. The binary logarithm uses base 2 (b = 2) and is prominent in computer science.

Some properties of logarithms are given below:
 If a^m = x, then m = loga(x).
 Properties :
 a. log_b(b) = 1
 b.log_b(1) = 0
 c.log_b(mn) = log_b(m) + log_b(n)
 d. log_b(^m/_n) = log_b(m) – log_b(n)
 e. log_b(m) = 1/log_m(b)
 f.  log_b(mⁿ) = n · log_b(m)
 g.log_b(m)= log_a(m)/log_a(m)
 Logarithms for base 1 does not exist.Remember that, when base is not mentioned,it is taken as 10.

 In less formal terms, the log rules might be expressed as:

1) Multiplication inside the log can be turned into addition outside the log, and vice versa.
2) Division inside the log can be turned into subtraction outside the log, and vice versa.
3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

Warning: Just as when you're dealing with exponents, the above rules work only if the bases are the same. For instance, the expression "log_d(m) + log_b(n)" cannot be simplified, because the bases (the "d" and the "b") are not the same, just as x² × y³ cannot be simplified (because the bases x and y are not the same).

Expanding logarithms

Log rules can be used to simplify expressions, to "expand" expressions, or to solve for values. 

Expand log₄( ¹⁶/_x ). I have division inside the log, which can be split apart as subtraction outside the log, so

    log₄( ¹⁶/_x ) = log₄(16) – log₄(x)

The first term on the right-hand side of the above equation can be simplified to an exact value, by applying the basic definition of what a logarithm is: 

        log₄(16) = 2

Then the original expression expands fully as: 

      log₄( ¹⁶/_x ) = 2 – log₄(x)

Always remember to take the time to check to see if any of the terms in your expansion (such as the log₄(16) above) can be simplified.

Expand the following:  
The 5 is divided into the 8x⁴, so split the numerator and denominator by using subtraction:
        
Don't take the exponent out front yet; it is only on the x, not the 8, and you can only take the exponent out front if it is "on" everything inside the log. The 8 is multiplied onto the x⁴, so split the factors by using addition:      
       log₂(8x⁴) – log₂(5) = log₂(8) + log₂(x⁴) – log₂(5)
The x has an exponent (which is now "on" everything inside its log), so move the exponent out front as a multiplier: 
        log₂(8) + log₂(x⁴) – log₂(5)  =   log₂(8) + 4log₂(x) – log₂(5)
Since 8 is a power of 2, I can simplify the first log to an exact value:
       log₂(8) + 4log₂(x) – log₂(5) = 3 + 4log₂(x) – log₂(5)
Each log contains only one thing, so this is fully simplified. The answer is: 3 + 4log₂(x) – log₂(5)

some simple problems
A. Solve log₂(8) = x.
I can solve this by converting the logarithmic statement into its equivalent exponential form, using The Relationship: 

         log₂(8) = x  

         2 ^x = 8

  But 8 = 2³, so:2 ^x = 2³  x = 3

Note that this could also have been solved by working directly from the definition of a logarithm: What power, when put on "2", would give you an 8? The power 3, of course!

If you wanted to give yourself a lot of work, you could also do this one in your calculator, using the change-of-base formula:

             log₂(8) = ln(8) / ln(2)

Plug this into your calculator, and you'll get "3" as your answer. While this change-of-base technique is not particularly useful in this case, you can see that it does work. (Try it on your calculator, if you haven't already, so you're sure you know which keys to punch, and in which order.) You will need this technique in later problems.B. Solve log₂(x) + log₂(x – 2) = 3
I can't do anything yet, because I don't yet have "log equals a number". So I'll need to use log rules to combine the two terms on the left-hand side of the equation: 
                   log₂(x) + log₂(x – 2) = 3  
                   log₂((x)(x – 2)) = 3  
                   log₂(x² – 2x) = 3.Then I'll use The Relationship to convert the log form to the corresponding exponential form, and then I'll solve the result: 
                log₂(x² – 2x) = 3   
               2³ = x² – 2x   
               8 = x² – 2x  
              0 = x² – 2x – 8   
              0 = (x – 4)(x + 2)   
               x = 4, –2.But if x = –2, then "log₂(x)", from the original logarithmic equation, will have a negative number for its argument (as will the term "log₂(x – 2)"). Since logs cannot have zero or negative arguments, then the solution to the original equation cannot be x = –2.so,the solution is 4.
Keep in mind that you can check your answers to any "solving" exercise by plugging those answers back into the original equation and checking that the solution "works":
          log₂(x) + log₂(x – 2) = 3  
         log₂(4) + log₂(4 – 2) = 3  
          log₂(4) + log₂(2) = 3
Since the power that turns "2" into "4" is 2 and the power that turns "2" into "2" is "1", then we have:
           log₂(4) + log₂(2) = 3  
          log₂(2²) + log₂(2¹) = 3   
             2 + 1 = 3 ,The solution checks. Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved 
C. Solve log₂(log₂(x))   = 1.
This may look overly-complicated, but it's just another log equation. To solve this, I'll need to apply The Relationship twice: 
      log₂(log₂(x)) = 1
       2¹ = log₂(x)  
       2 = log₂(x) x = 2²   
       x = 4,Then the solution is x = 4.
D. Solve log₂(x²)  = (log₂(x))². First, I'll write out the square on the right-hand side: 
log₂(x²) = (log₂(x))²
log₂(x²) = (log₂(x)) (log₂(x))
Then I'll apply the log rule to move the "squared", from inside the log on the left-hand side of the equation, out in front of that log as a multiplier. Then I'll move that term to the right-hand side:
2log₂(x) = [log₂(x)] [log₂(x)]
0 = [log₂(x)] [log₂(x)]  –  2log₂(x)
This may look bad, but it's nothing more than a factoring exercise at this point. So I'll factor, and then I'll solve the factors by using The Relationship:
0 = [log₂(x)] [log₂(x) – 2]
log₂(x) = 0  or  log₂(x) – 2 = 0
2⁰ = x   or  log₂(x) = 2
1 = x  or  2² = x
1 = x  or  4 = x
The solution is x = 1, 4.

Seating arrangement

The process of making a group of people in a prefixed manner is called seating arrangement.
Sitting arrangement problems are common in every competitive examination.these are very simple and scoring area for everyone.if we made one single mistake,causes big lose in score of exam.for this type of problems,no shortcuts available.we have to read carefully and understand clearly every line given in question.
Here,Some general guidelines to solve seating arrangement problems.
1. Have a glance at the problem.by this step you can notify the type of arrangement and size of the group.
2. Next you have  to determine the useful information and classify into definite information, comparative information and negative information.
3. In Definite information you will get exact position of person.
Eg: raju is sitting at extreme left corner
4. In Comparative information you will get the position of person with comparing to another person.
Eg: A is sitting second to the right of B
5. A Negative information does not give any definite information but it gives an idea to eliminate the possibility.
Eg: A is not an immediate neighbor of B

Basically,seating arrangement problems are two types:
Type-I : Linear arrangement
In this type of arrangement, we have to arrange them in a row or line. In linear arrangement generally there are two ways of arrangements.
1. Single row arrangement
2. Two row arrangement
Type-II : Circular arrangement
In this type of arrangement, we have to arrange them in a circular shape.
Some tips to get notify easily,
Tip-1:
Clockwise direction-left of person/object and Anti-Clockwise direction-right of person/object.
( if facing towards center )

Blood Relation

A person who is related to another by birth rather than by marriage.Blood relations of a group of persons are given in jumbled form. In these tests, the success of a candidate depends upon knowledge of the Blood Relations, some of which are summarized below. The questions which are asked in this section depend upon Relation.

Questions on Blood Relationship are related to our day to day life. We are bound by our kit hand kin through a chain of relationships. The examiner defines the simple relationships by using rather complicated set of definitions and expects from us to comprehend these definitions rather quickly.
In order to solve these problems, analyse the given statements carefully and systematically.
For examples :
(i) My father's only child means I (Myself).
(ii) Ritu's husband's father-in-law's only daughter means - Ritu (Herself).

Pay particular attention to the information given in the question itself without your personal biases and preconceived notions and assumptions coming to the fore. Questions on Blood Relationship can be solved by any of the following methods:
(i) Deduction Method and
(ii) Pictorial Method
While attempting questions on Blood Relationship, first read all the pieces of information as quickly as possible and then point out the two persons between whom relationship is to be established. Finally, try to co-relate the given relationships. While concluding relationship between two persons be careful about the sexes of the persons involved. Majority of the students tend to define or derive relationship without caring for sex of the persons. Is it possible to define relationship between two persons without knowing their sex?
 Consider the following illustration: A is the child of P and Q.
From this statement can we conclude that P is the father of A. No, it is not possible. Without knowing the sex of either P or Q, it is not possible to conclude that P is the father of A. What we can conclude from the above statement is that'P and Q are parents of A. Thus, we see that the knowledge about the sex of persons is necessary to conclude relationship between the two persons.
Some Important Tips:
(i) First of all choose the two persons, between whom relationship is to be established.
(ii) Next, pin-point the intermediate relationship i.e., such relationship through which long drawn   relationship can be established between the required persons.
(iii) Finally, conclude the relationship directly between the two persons as per the requirement of the question.
(iv) From a particular name we cannot ascertain the sex (gender) of that person. The name does not always show the gender beyond reasonable doubt.
For example, we often hear the same name for male and female in the Punjabi community.The names, Harvinder, Sukhwinder, Gurinder etc. are used for both the sexes in the Punjabi community.
There are certain other names which are used for both the sexes all over the country. For example, Suman, Kamal etc.

The list given below is quite helpful in recognising some indirect relationships and to remember easily the relations may be divided into two sides as given below:
I. Relations of Paternal side:
1.Father's father→ Grandfather
2.Father's mother→ Grandmother
3.Father's brother→ Uncle
4.Father's sister→ Aunt
5.Children of uncle→ Cousin
6.Wife of uncle→ Aunt
7.Children of aunt→ Cousin
8.Husband of aunt→ Uncle
II. Relations of Maternal side:
1.Mother's father→ Maternal grandfather
2.Mother's mother→ Maternal grandmother
3.Mother's brother Maternal uncle
4.Mother's sister→ Aunt
5.Children of maternal uncle→ Cousin
6.Wife of maternal uncle→ Maternal aunt
Relations:
1.Grandfather’s son»Father or Uncle
2.Grandmother’s son»Father or Uncle
3.Grandfather’s only son»Father
4.Grandmother’s only son»Father
5.Mother’s or father’s mother»Grandmother
6.Son’s wife»Daughter-in-Law
7.Daughter’s husband»Son-in-Law
8.Husband’s or wife’s sister»Sister-in-Law
9.Brother’s son»Nephew
10.Brother’s daughter»Niece
11.Uncle or aunt’s son or daughter»Cousin
12.Sister’s husband»Brother-in-Law
13.Brother’s wife»Sister-in-Law
14.Grandson’sor grand daughter’s daughter»Great grand daughter


The questions on Blood Relationship are asked in various formats but substantially there is no difference between them. However, consider the pattern of the question we are obliged to discuss them separately.
                                                                       TYPE-I
Ex.l. Pointing to a man, a woman said, "His mother is the only daughter of my mother". How is the woman related to man?
(1) Mother            (2) Grandmother             (3) Sister           (4) Daughter            (5) None of these
Ex.2. Pointing to a man, a woman said, "His mother is the daughter of my mother's only daughter, How is the man related to that woman?
(l)Son                (2) Father                (3) Brother                 (4) Grandson              (5) None of these
                                           ANSWERS WITH EXPLANATION
1. (1) The two persons between whom relationship is to established.MAN <----------->WOMEN
Therefore, the woman in question is the mother of man in the photograph.Only daughter of woman's mother means woman (herself). Only daughter of woman's mother is the mother of the man in the photograph.
                                                    PICTORIAL METHOD
                                                        women's mother
                                                                   ^
                                                                    |
                                                                    |     daughter
                                                                    |
                                                                women
                                                                   ^
                                                                    |
                                                                    |      son
                                                                    |
                                                                  man
                                                                            
2. (4) The two persons between whom relationship has to be established.MAN <----------->WOMEN
My (Woman's) mother's only daughter means the woman herself. Woman's daughter is the mother of
man in question. Therefore, the woman (speaker) is the grandmother of the man. Thus, man is the grandson of the woman (speaker).
                                                   PICTORIAL METHOD
                                                        women's mother
                                                                    |
                                                                    |    only daughter
                                                                    |
                                                                women
                                                                    |
                                                                    |      daughter
                                                                    |
                                                           man's mother
                                                                        
                                                               TYPE-II
Ex.1. If A is B's brother, B is C's sister and C is D's father, D is A's...
(1) Brother        (2) Sister      (3) Nephew    (4) Cannot be determined         (5) None of these
Ex.2. P is brother of Q. R is the sister of Q. How P is related to R?
(1) Brother       (2) Sister        (3) Uncle         (4) Data inadequate              (5) None of these
                                        ANSWERS WITH EXPLANATION
1. (4) A is the brother of B. (A is male). B is sister of C. (B is female). C is father of D. (C is male)
The sex of D is not known. A and C are brothers of B. A is the uncle of D. Since, sex of D is not clear, we cannot determine what is D to A.
2. (1) P is brother of Q. (P is male). R is sister of Q. (R is female). Therefore, P is the brother of R.

SOME QUESTIONS TO PRACTICE:
1. Pointing towards Women, Madhav said "I am the only son of his father's one of the sons". How
Women is related to Madhav ?
(1) Nephew       (2) Uncle              (3) Either father or uncle        (4) Father          (5) None of these
2. Pointing to a man in the photograph, a woman said, "He is the only son of my mother's father".
How is the woman related to the man in the photograph?
(1) Niece                (2) Sister               (3) Mother             (4) Daughter               (5) None of these
3. Pointing to a gentleman, Deepak said, "His only brother is the father of my daughter's father", How is the gentleman related to Deepak?
(1) Father        (2) Grandfather           (3) Uncle          (4) Brother-in-law           (5) None of these
4. Pointing towards Neeru, Asha said, "I am the only daughter of her mother's son". How is Neeru related to Asha?
(l)Aunt '             (2) Cousin                (3) Niece               (4) Mother              (5) None of these
5. If Neha says, "Amruta's father Raj is the only son of my father-in-law, Mahesh"; then how Bindu, who is sister of Amruta, is related to Mahesh?
(1) Daughter       (2) Wife         (3) Daughter-in-law           (4) Niece            (5) None of these
6. Pointing towards a photograph of a girl, Rajan said, "She has no sisters or daughters but her mother is the only daughter of my mother". How is the girl in the photograph related to Rajan's mother?
(1) Sister-in-Law (2) Granddaughter (3) Daughter-in-Law (4) Cannot be determined (5) None

Directions (7-10) : Study the following information carefully and answer the questions given below :
Five persons are sitting around dinning table. - K, L,M, N and O - K is the mother of M, who is the wife of O. N is the brother of K and L is the husband of K.
Ex.7. How is L related to O?
(1) Father      (2) Mother-in-law  (3) Brother-in-law      (4) Father-in-law       (5) Niece
Ex.8. How is K related to O?
(1) Sister      (2) Mother            (3) Mother-in-law            (4) Brother-in-law     (5) Aunt
Ex.9. How is N related to L?
(l)Son           (2) Cousin           (3) Brother              (4) Brother-in-law           (5) Uncle
Ex.10. How is M related to L ?
(l)Aunt         (2) Niece              (3) Daughter              (4) Daughter-in-law    (5) Mother

11. Pointing towards a person in a photograph, Raman said, "She is the only daughter of the mother of my brother's sister". How is the person in photograph related to Raman?'
(1) Daughter                 (2) Sister              (3) Wife             (4) Cousin           (5) None of these
12. Pointing to a man in a photograph, a woman said, "His brother's father is the only son of my grandfather". How is the woman related to the man in the photograph?
(1) Sister      (2) Mother            (3) Grandmother         (4) Aunt                        (5) Daughter

Divisibility Rules

A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, and they are all different, this article presents rules and examples only for decimal numbers.

Divisibility rule for '2' : First, take any number (for this example it will be 376) and note the last digit in the number, discarding the other digits. Then take that digit (6) while ignoring the rest of the number and determine if it is divisible by 2. If it is divisible by 2, then the original number is divisible by 2.
Example:

1. 376 (The original number)
2. 37 6 (Take the last digit)
3. 6 ÷ 2 = 3 (Check to see if the last digit is divisible by 2)
4. 376 ÷ 2 = 188 (If the last digit is divisible by 2, then the whole number is divisible by 2)

( OR ) We can easily conclude a number divisible by '2' or not. By seeing the last digit of number if it  is even number (0,2,4,6,8). Then, the number is divisible by '2'.

Divisibility rule for '3' or '9 ': First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3
 (or 9). If a number is a multiplication of 3 consecutive numbers then that number is always divisible by 3. This is useful for when the number takes the form of (n × (n − 1) × (n + 1)).
Example:

1. 492 (The original number)
2. 4 + 9 + 2 = 15 (Add each individual digit together)
3. 15 is divisible by 3 at which point we can stop. Alternatively we can continue using the same method if the number is still too large:
4. 1 + 5 = 6 (Add each individual digit together)
5. 6 ÷ 3 = 2 (Check to see if the number received is divisible by 3)
6. 492 ÷ 3 = 164 (If the number obtained by using the rule is divisible by 3, then the whole number is divisible by 3)

Example:

1. 336 (The original number)
2. 6 × 7 × 8 = 336
3. 336 ÷ 3 = 112

Divisibility rule for '4' :The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4^. this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that you know is divisible by 4 (e.g. 24, 04, 08, etc.), then the whole number will be divisible by 4 regardless of what is before the last two digits.
Alternatively, one can simply divide the number by 2, and then check the result to find if it is divisible by 2. If it is, the original number is divisible by 4. In addition, the result of this test is the same as the original number divided by 4.
General rule and example

1. 2092 (The original number)
2. 20 92 (Take the last two digits of the number, discarding any other digits)
3. 92 ÷ 4 = 23 (Check to see if the number is divisible by 4)
4. 2092 ÷ 4 = 523 (If the number that is obtained is divisible by 4, then the original number is divisible by 4)

Example:

1. 1720 (The original number)
2. 1720 ÷ 2 = 860 (Divide the original number by 2)
3. 860 ÷ 2 = 430 (Check to see if the result is divisible by 2)
4. 1720 ÷ 4 = 430 (If the result is divisible by 2, then the original number is divisible by 4)

Divisibility rule for '5' : Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2. For example, the number 40 ends in a zero (0), so take the remaining digits (4) and multiply that by two (4 × 2 = 8). The result is the same as the result of 40 divided by 5(40/5 = 8).
If the last digit in the number is 5, then the result will be the remaining digits multiplied by two (2), plus one (1). For example, the number 125 ends in a 5, so take the remaining digits (12), multiply them by two (12 × 2 = 24), then add one (24 + 1 = 25). The result is the same as the result of 125 divided by 5 (125/5=25).
If the last digit is 0

1. 110 (The original number)
2. 11 0 (Take the last digit of the number, and check if it is 0 or 5)
3. 11 0 (If it is 0, take the remaining digits, discarding the last)
4. 11 × 2 = 22 (Multiply the result by 2)
5. 110 ÷ 5 = 22 (The result is the same as the original number divided by 5)

If the last digit is 5

1. 85 (The original number)
2. 8 5 (Take the last digit of the number, and check if it is 0 or 5)
3. 8 5 (If it is 5, take the remaining digits, discarding the last)
4. 8 × 2 = 16 (Multiply the result by 2)
5. 16 + 1 = 17 (Add 1 to the result)
6. 85 ÷ 5 = 17 (The result is the same as the original number divided by 5)

Divisibility rule for '6' : A number can be divisible by 6. If the number is divisible by '2' and '3'.
Example: 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6.

Divisibility rule for '7' : If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7.
Example:  i.672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
                ii. 905 (Double 5 is 10, 90-10=80, and 80÷7=11 ) No
                                  OR
 Multiply each digit (from right to left) by the digit in the corresponding position in this pattern (from left to right): 1, 3, 2, -1, -3, -2 (repeating for digits beyond the hundred-thousands place). Then sum the results.
Example: 483595 - (4 × (-2)) + (8 × (-3)) + (3 × (-1)) + (5 × 2) + (9 × 3) + (5 × 1) = 7.
Divisibility rule for '8' : The last three digits are divisible by 8.
Example  i. 109816 (816÷8=102) Yes
               ii. 216302 (302÷8=37 ) No

Divisibility rule for '10' : The given number is divisible by '10' or not can easily predict by seeing last digit of the number. If it is '0' then, the number is divisible.

Divisibility rule for '11' : If you sum every second digit and then subtract all other digits and the answer is 0, or divisible by 11
Ex: i. 1364 ((3+4) -(1+6) = 0) Yes
     ii. 3729 ((7+9) -(3+2) = 11) Yes
     iii.25176 ((5+7) -(2+1+6) = 3) No

Divisibility rule for '13' : Multiply each digit (from right to left) by the digit in the corresponding position in this pattern (from left to right): -3, -4, -1, 3, 4, 1 (repeating for digits beyond the hundred-thousands place). Then sum the results.
Example : 30,747,912: (2 × (-3)) + (1 × (-4)) + (9 × (-1)) + (7 × 3) + (4 × 4) + (7 × 1) + (0 × (-3)) + (3 × (-4)) = 13.