Coded Relationship
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Introduction & Key Concepts
Study MaterialCoded Relationship
Coded Relationship is an important topic in Logical Reasoning and Blood Relations. In these questions, relationships between different persons are represented using specific symbols or codes. Candidates are required to decode these symbols and determine the relationship between two or more persons.
The questions may provide a coded relationship-string and ask candidates to identify the relationship represented by it. Although decoding every relationship separately can be time-consuming, a few systematic techniques can make these questions much easier and faster to solve.
The most useful techniques include checking the sex of the person, checking the generation gap, and drawing a family tree when required.
Key Observation:
Do not decode every relationship completely unless necessary. First eliminate obviously wrong options by checking the person's sex and the required generation gap. This can significantly reduce the time required to solve the question.
What is Coded Relationship?
In a Coded Relationship question, different symbols are assigned specific meanings representing relationships such as father, mother, brother, sister, husband, wife, son, or daughter.
Candidates must interpret the given code and determine the relationship asked in the question.
For example, if:
A + B means A is the father of B.
A - B means A is the sister of B.
then the symbols + and - represent specific relationships between the two persons.
Types of Coding Used in Coded Relationship
The standard coding system used in this chapter is divided into two major types:
Type I: Forward Type
In forward-type coding, the first person has the given relationship with the second person.
Type II: Backward Type
In backward-type coding, the second person has the given relationship with the first person.
A Sample Problem
Directions (Q. 1-2): Read the following information to answer the questions.
A + B means A is the father of B
A - B means A is the sister of B
A x B means A is the husband of B
A ÷ B means A is the wife of B
Q. 1. Which of the following means 'T is the nephew of Q'?
(a) Q x R - S + T
(b) Q + R ÷ S + T
(c) Q - R ÷ S + T
(d) Q ÷ R + S - T
(e) None of these
Q. 2. Which of the following means 'S has a blood-relationship with T'?
(a) S ÷ R + T x Q
(b) S ÷ Q + R x T
(c) S - R x T - Q
(d) S x Q - R - T
(e) None of these
Our Standard Coding System
To explain the techniques used throughout this chapter, we use a standard set of codes. In actual examination questions, however, the coding pattern may be different. Always follow the meanings given in the question.
Type I: Forward Type
| Code | Meaning |
|---|---|
| A + B | A is the father of B |
| A - B | A is the mother of B |
| A x B | A is the brother of B |
| A ÷ B | A is the sister of B |
| A @ B | A is the husband of B |
| A Δ B | A is the wife of B |
| A α B | A is the son of B |
| A β B | A is the daughter of B |
Type II: Backward Type
| Code | Meaning |
|---|---|
| A ^ B | B is the father of A |
| A ~ B | B is the mother of A |
| A # B | B is the brother of A |
| A $ B | B is the sister of A |
| A γ B | B is the husband of A |
| A δ B | B is the wife of A |
| A > B | B is the son of A |
| A < B | B is the daughter of A |
Forward Type vs Backward Type Coding
Forward Type
In forward-type coding, the first person has the given relationship with the second person.
For example, in A + B, the relationship is father. Since A appears first, A is the father of B. Therefore, it is a forward-type code.
Backward Type
In backward-type coding, the second person has the given relationship with the first person.
For example, in A ^ B, B is the father of A. Since the second person has the stated relationship with the first person, it is a backward-type code.
Similarly, compare A - B and A ~ B. In the first case, A is the mother of B, whereas in the second case, B is the mother of A.
Quick Techniques for Eliminating Wrong Answers
Instead of solving every option completely, we can use some quick elimination techniques.
Rule #1: Check Sex
Rule:
If the person asked about must be male or female, check the symbol immediately connected to that person. If that symbol indicates the wrong sex, eliminate the option immediately.
Example 1
Which of the following means that "A is the grandmother of B"?
1) A + B x C - D ÷ F
2) A x C - D + B x F
3) A - B - C + D + E
4) A - C x B + D ÷ F
5) None of these
Since A is the grandmother of B, A must be a female.
In choice (1), A + B means A is the father of B. Therefore, A is male and the option can be eliminated.
In choice (2), A x C means A is the brother of C. Therefore, A is also male and this option can be eliminated.
Shortcut: If the first relationship already proves that the person has the wrong sex, there is no need to decode the remaining expression.
Example 2
Which of the following means that "X is the grandson of Y"?
1) X ÷ A + B - C x Y
2) X ÷ A α B α C ÷ Y
3) X α A ÷ B ÷ C α Y
4) X β A β B x C x Y
5) None of these
Since X is the grandson of Y, X must be a male.
In choices (1), (2), and (4), the first relationship makes X female:
- X ÷ A means X is the sister of A.
- X ÷ A in choice (2) also makes X female.
- X β A means X is the daughter of A.
Therefore, choices 1, 2, and 4 can be eliminated immediately.
Example 3
Which of the following means that "B is the grandfather of E"?
1) A > B > C # D > E
2) A < B < C # D > E
3) A $ B $ C # D $ E
4) A $ B $ C > D # E
5) None of these
Since B is the grandfather of E, B must be a male.
In choice (2), A < B means B is the daughter of A, making B female.
In choice (3), A $ B means B is the sister of A, making B female.
The same issue occurs in choice (4). Therefore, choices 2, 3, and 4 can be eliminated.
Mind It!
In forward-type coding, check the symbol immediately after the person in question.
In backward-type coding, check the symbol immediately before the person in question.
Quick Sex-Checking Rule
Forward Type: Reject an option if the symbol immediately after the person in question indicates the wrong sex.
Backward Type: Reject an option if the symbol immediately before the person in question indicates the wrong sex.
Rule #2: Check Generation Gap
Another quick technique is to check the generation gap between the two persons.
For example, if the question asks whether A is the grandfather of B, there must be a generation gap of 2 between A and B.
Similarly, if X is the grandniece of Y, the generation gap between X and Y must be -2.
Key Observation:
Before drawing a complete family tree, check whether the generation gap is even possible. This can quickly eliminate several incorrect choices.
Understanding Generation Gap
Consider the following statements:
1) A + B + C
2) A x B x C
3) A x B + C
4) A - B Δ C α D
Case 1: A + B + C
A is the father of B and B is the father of C. Therefore, A is the grandfather of C.
The generation gap is:
+1 + +1 = +2
Therefore, A is two generations above C.
Case 2: A x B x C
A is the brother of B and B is the brother of C. All three persons are of the same generation.
0 + 0 = 0
Therefore, there is no generation gap between A and C.
Case 3: A x B + C
A is the brother of B, while B is the father of C. Therefore, A is the uncle of C.
0 + 1 = 1
Therefore, A is one generation above C.
Case 4: A - B Δ C α D
A is the mother of B, B is the wife of C, and C is the son of D.
The generation gap is calculated as:
+1 + 0 + (-1) = 0
Therefore, A and D are of the same generation.
Generation Gap Values
| Relationship | Generation Gap |
|---|---|
| Father / Mother | +1 |
| Brother / Sister / Husband / Wife | 0 |
| Son / Daughter | -1 |
Important Note:
A son or daughter belongs to the generation below the father's or mother's generation, so the generation gap is taken as -1.
For each answer choice, calculate the generation gap between the two persons under consideration. If the resulting gap is not compatible with the relationship asked in the question, reject that choice.
How to Calculate the Generation Gap
The following step-by-step method can be used to calculate the generation gap.
Step-by-Step Method
- Take one of the persons under consideration.
- Move through the coded relationships in the appropriate direction.
- For every father or mother relation, use +1.
- For every brother, sister, husband, or wife relation, use 0.
- For every son or daughter relation, use -1.
- Add all the values to obtain the generation gap.
Mind It!
For forward-type coding, move from left to right.
For backward-type coding, start from the right side and move towards the left.
Example 4: Calculating Generation Gap
Consider the following:
A - B x C β D α E Δ F x G
Find the generation gap between:
- A and C
- C and E
- E and B
- G and A
(i) A and C
Since A is on the left, start from A and move towards C.
The - symbol means mother, so use +1. The x symbol means brother, so use 0.
Gap = +1 + 0 = +1
Conclusion: A is of C's father's generation.
(ii) C and E
C is to the left of E, so move from C towards E.
There are two son/daughter relations, represented by β and α. Each contributes -1.
Gap = (-1) + (-1) = -2
Conclusion: C is of E's grandson's generation.
(iii) E and B
E is to the right of B. Therefore, start from B and move towards E.
The relations are:
- x means brother = 0
- β means daughter = -1
- α means son = -1
Gap = 0 + (-1) + (-1) = -2
Conclusion: B is of E's grandson's generation.
Note: If the gap between B and E is -2, the gap between E and B is +2. Therefore, E is of B's grandfather's generation.
(iv) G and A
Start from A because A is on the left of G.
The values are:
- - means mother = +1
- x means brother = 0
- β means daughter = -1
- α means son = -1
- Δ means wife = 0
- x means brother = 0
Gap = +1 + 0 + (-1) + (-1) + 0 + 0 = -1
Conclusion: A is of G's son's generation.
Note: If the gap between A and G is -1, the gap between G and A is +1. Therefore, G is of A's father's generation.
Example 5: Generation Gap in Backward Coding
Consider the following:
S # R δ Q > P < O # N ^ M
Find the generation gap between:
- S and Q
- R and O
- O and Q
- M and S
Important:
This is a backward-coding case. Therefore, take the person on the right and move towards the left.
(i) S and Q
Take Q and move towards the left.
δ means wife = 0 and # means brother = 0.
Gap = 0 + 0 = 0
Conclusion: S and Q are of the same generation.
(ii) R and O
Take O and proceed towards the left.
The relations are:
- < means daughter = -1
- > means son = -1
- δ means wife = 0
Gap = (-1) + (-1) + 0 = -2
Conclusion: O is of R's grandson's generation.
Note: If the gap between O and R is -2, the gap between R and O is +2. Therefore, R is of O's grandfather's generation.
(iii) O and Q
Take O and proceed towards the left.
For < use -1 and for > use -1.
Gap = (-1) + (-1) = -2
Conclusion: O is of Q's grandson's generation.
(iv) M and S
Take M and proceed towards the left.
The values are:
- ^ means father = +1
- # means brother = 0
- < means daughter = -1
- > means son = -1
- δ means wife = 0
- # means brother = 0
Gap = +1 + 0 + (-1) + (-1) + 0 + 0 = -1
Conclusion: M is of S's son's generation.
Quick Examination Tip
In examinations, questions generally contain fewer relationships in a single expression. Therefore, calculating the generation gap can often be done very quickly.
Just consider the symbols between the two persons:
- Ignore brother, sister, husband, and wife relations because they contribute 0.
- Put +1 for father and mother.
- Put -1 for son and daughter.
- Add the values.
- For forward coding, normally move from left to right.
Drawing a Family Tree
The quick elimination techniques may not always be sufficient. Sometimes two or more choices may still remain after checking sex and generation gap.
In such cases, the best way to determine the exact relationship is to draw a family tree.
A family tree provides a visual representation of the relationships between different persons and makes complicated relationship questions easier to understand.
Rules for Drawing a Family Tree
- Use vertical or diagonal lines to represent parent-child relationships.
- Use a double horizontal line to represent marriage relationships.
- Use a dashed line to represent brother or sister relationships.
- Put a + sign before a person who is male.
- Put a - sign before a person who is female.
- Use a ? mark or another symbol when the information is unknown.
Note:
Brother or sister relationships can also be identified when two persons have the same root, meaning they have the same parents.
Example of a Family Tree
The following diagram represents a family structure:
From the diagram, we can identify the following relationships:
- F and A are a couple. F is the husband and A is the wife.
- F has a sister K.
- The couple F and A has three children: M, C, and another son whose name is unknown.
- C is also a son, while the sex of M is unknown.
- M and the other unknown son are unmarried.
- C is married to D.
- The couple C and D has a daughter S and a son whose name is unknown.
Suggested Method for Solving Coded Relationship Questions
The most effective approach is to combine the quick elimination techniques with the family-tree method.
Step I: Eliminate Wrong Choices
First eliminate obviously incorrect choices using:
- Check the sex of the person under consideration.
- Check the required generation gap.
Step II: Draw the Family Tree
For the choices that remain, draw a quick family tree and determine the exact relationship.
Identify the Person Asked About
↓
Check Sex
↓
Check Generation Gap
↓
Eliminate Wrong Choices
↓
Draw Family Tree if Required
↓
Identify the Exact Relationship
↓
Select the Correct Answer
Quick Revision Table
| Technique | What to Check | Purpose |
|---|---|---|
| Check Sex | Male or female requirement | Eliminate impossible options quickly |
| Check Generation Gap | Number of generations between persons | Reject relationships with impossible gaps |
| Forward Coding | Move left to right | Interpret the relationship normally |
| Backward Coding | Move right to left | Interpret reversed relationships |
| Family Tree | Complete relationship structure | Determine the exact relationship |
Important Rules to Remember
- Always read the meaning of each code carefully.
- Do not assume that the same symbol has the same meaning in every question.
- Identify whether the coding is forward or backward.
- For forward coding, normally move from left to right.
- For backward coding, start from the right and move towards the left.
- Check the sex of the person before solving the complete expression.
- Check the generation gap before drawing a complete family tree.
- Ignore same-generation relationships when calculating generation gap because they contribute 0.
- Use +1 for father or mother relationships.
- Use -1 for son or daughter relationships.
- Draw a family tree when quick elimination techniques are not sufficient.
- Never spend time completely decoding an option that can already be eliminated.
Quick Learning Framework
Read the Given Codes
↓
Identify Forward or Backward Type
↓
Identify the Person Asked About
↓
Check Sex
↓
Check Generation Gap
↓
Eliminate Wrong Choices
↓
Draw Family Tree
↓
Find Exact Relationship
↓
Select the Correct Answer
Final Takeaway
Coded Relationship questions become much easier when solved systematically rather than by decoding every relationship from the beginning.
The two fastest elimination techniques are checking the sex and checking the generation gap. These techniques can eliminate several incorrect options without requiring a complete family-tree analysis.
When multiple options still remain, drawing a family tree provides a clear visual representation of the relationships and helps identify the correct answer accurately.
With regular practice, candidates can quickly recognize coding patterns, eliminate impossible choices, calculate generation gaps, and solve even complex Coded Relationship questions with greater speed and accuracy.