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Coded Relationship Statements

Introduction

Coded relationship statements replace words like "father", "sister" or "husband" with symbols or operators. These problems test your ability to decode the symbols first and then connect the decoded relations to find the final link.

This pattern is important because many competitive exams use symbolic notation to compress family information - decoding accurately is the first and most crucial step.

Pattern: Coded Relationship Statements

Pattern

Key concept: First translate each symbol into its relationship meaning, then follow the decoded chain step-by-step to infer the asked relation.

Typical workflow: Decode → Map → Connect → Answer.

Step-by-Step Example

Question

Let 'A + B' mean A is the father of B.
Let 'B - C' mean B is the sister of C.
What does 'P + Q - R' mean?
(A) P is the uncle of R (B) P is the father of R (C) P is the brother of R (D) Cannot be determined

Solution

  1. Step 1: Decode each symbol.

    'P + Q' → P is the father of Q.
    'Q - R' → Q is the sister of R.

  2. Step 2: Map decoded relations into a mini-tree.

    P (father) → Q (sister) → R. So Q is sibling of R and female; P is parent of Q.

  3. Step 3: Connect the chain to find P → R relation.

    P is the father of Q, who is the sister of R. Therefore P is the father of R as well (same parent of siblings) → P is father of R.

  4. Final Answer:

    P is the father of R → Option B.

  5. Quick Check:

    If Q and R are siblings, they share the same parent. Since P is parent of Q, P is also parent of R → father fits ✅

Quick Variations

1. Symbols may represent spouse relations (e.g., 'A * B' → A is husband of B).

2. Some codes reverse direction (e.g., 'A + B' may mean B is father of A) - always read definition carefully.

3. Multiple symbols chained: decode left-to-right unless specified otherwise.

4. Codes can combine gender + generation info (e.g., '+' for father, '#' for mother, '-' for sister, '~' for brother).

Trick to Always Use

  • Step 1 → Underline each code definition before solving.
  • Step 2 → Translate into short phrases (e.g., "P is father of Q").
  • Step 3 → Draw a 2-3 node mini-tree for the decoded segment and extend only as needed.

Summary

Summary

  • Always decode symbols first - solving without decoding causes mistakes.
  • Translate symbols into one-line relations (e.g., "A is mother of B") before connecting chains.
  • When siblings appear, remember parents are shared - use that to infer parent-child links.
  • Confirm directionality: some codes may be defined right-to-left; re-check definitions before finalizing.

Example to remember:
If 'A + B' → A is father of B and 'B - C' → B is sister of C, then 'A + B - C' → A is father of C (because siblings share parents).

Practice

(1/5)
1. If 'P # Q' means P is the mother of Q and 'Q @ R' means Q is the brother of R, then what is the relation of P to R?
easy
A. Mother
B. Aunt
C. Grandmother
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    'P # Q' → P is mother of Q; 'Q @ R' → Q is brother of R.

  2. Step 2: Connect chain.

    P is mother of Q and Q is brother of R → Q and R are siblings with the same mother.

  3. Step 3: Infer relation.

    P is mother of both Q and R.

  4. Final Answer:

    Mother → Option A.

  5. Quick Check:

    Mother of one sibling is mother of the other ✅
Hint: Sibling relationships share the same parent.
Common Mistakes: Choosing grandmother instead of mother.
2. If 'P × Q' means P is the brother of Q and 'Q ÷ R' means Q is the mother of R, then what is the relation of P to R?
easy
A. Uncle
B. Father
C. Brother
D. Cannot be determined

Solution

  1. Step 1: Decode codes.

    'P × Q' → P is brother of Q; 'Q ÷ R' → Q is mother of R.

  2. Step 2: Build connection.

    P is brother of Q → Q is mother of R → P is maternal uncle of R.

  3. Step 3: Confirm gender.

    P is male, so 'uncle' is correct.

  4. Final Answer:

    Uncle → Option A.

  5. Quick Check:

    Brother of mother = maternal uncle ✅
Hint: Brother of a mother = maternal uncle.
Common Mistakes: Selecting father instead of uncle.
3. If 'M + N' means M is the husband of N and 'N - O' means N is the sister of O, then how is O related to M?
easy
A. Brother-in-law
B. Sister-in-law
C. Brother
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    'M + N' → M is husband of N; 'N - O' → N is sister of O.

  2. Step 2: Build relation chain.

    M is spouse of N; N is sibling of O → O is the sibling of M’s spouse.

  3. Step 3: Apply gender-ambiguity rule.

    O could be male (brother-in-law) or female (sister-in-law). Since both gendered in-law options exist and O’s gender is not given, answer must be 'Cannot be determined'.

  4. Final Answer:

    Cannot be determined → Option D.

  5. Quick Check:

    Without O’s gender, you cannot pick between brother-in-law and sister-in-law ✅
Hint: If spouse’s sibling gender unknown and both gendered options exist, choose 'Cannot be determined'.
Common Mistakes: Assuming spouse’s sibling is male or female without evidence.
4. If 'A - B' means A is the sister of B and 'B × C' means B is the husband of C, then what is the relation of A to C?
medium
A. Daughter
B. Sister-in-law
C. Mother
D. Cannot be determined

Solution

  1. Step 1: Decode codes.

    'A - B' → A is sister of B; 'B × C' → B is husband of C.

  2. Step 2: Connect chain.

    A is sister of B and B is husband of C → C is wife of B.

  3. Step 3: Determine A to C relation.

    A is sister of C’s husband → sister-in-law.

  4. Final Answer:

    Sister-in-law → Option B.

  5. Quick Check:

    Spouse’s sibling = sister-in-law ✅
Hint: Sister of husband = sister-in-law.
Common Mistakes: Mistaking parent-child relation.
5. If 'P + Q' means P is the father of Q and 'Q ÷ R' means Q is the brother of R, then how is P related to R?
medium
A. Uncle
B. Grandfather
C. Father
D. Cannot be determined

Solution

  1. Step 1: Decode statements.

    'P + Q' → P is father of Q; 'Q ÷ R' → Q is brother of R.

  2. Step 2: Connect family chain.

    P is father of Q; Q and R are siblings → they share the same parent.

  3. Step 3: Infer final relation.

    P is father of R as well.

  4. Final Answer:

    Father → Option C.

  5. Quick Check:

    Father of one sibling = father of the other ✅
Hint: Combine sibling logic to identify shared parent.
Common Mistakes: Choosing uncle instead of father.

Mock Test

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