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Mixed Relation + Coded Puzzle

Introduction

Mixed Relation + Coded Puzzle questions combine family or blood relations with symbolic or coded expressions. These problems use special symbols like +, -, ×, ÷ or other operators to represent relationships such as “father of”, “mother of”, “brother of”, or “wife of”.

The challenge is twofold - decode the symbolic relationships correctly and then interpret the entire chain to identify the final relationship between two people.

Pattern: Mixed Relation + Coded Puzzle

Pattern

The key idea: Replace each coded symbol with its meaning and read the chain from left to right or right to left as per instruction.

  • Each symbol (+, -, ×, ÷, etc.) represents a specific family relation.
  • Sometimes, the chain must be read in reverse (e.g., A + B means “B is the brother of A”).
  • More than one symbol may appear - so decoding order becomes critical.
  • Gender clues are hidden inside the meanings (e.g., “brother” = male, “daughter” = female).

Step-by-Step Example

Question

If A + B means “A is the father of B” and A × B means “A is the sister of B”, then what does P × Q + R mean?
(A) P is the sister of R (B) P is the aunt of R (C) P is the mother of R (D) P is the grandmother of R

Solution

  1. Step 1: Decode symbol meanings.

    × → sister of, + → father of.

  2. Step 2: Read from left to right.

    P × Q → P is the sister of Q.
    Q + R → Q is the father of R.

  3. Step 3: Combine both relations.

    P is sister of Q, and Q is father of R → P is R’s aunt.

  4. Final Answer:

    Aunt → Option B.

  5. Quick Check:

    Sister of father = aunt ✅

Quick Variations

1. Reverse-coded chains (read right to left) are common - always note instruction direction.

2. A single symbol may carry multi-role (e.g., “×” = husband of; “÷” = daughter of).

3. Some puzzles include more than 3-4 persons - use arrows or generation markers to avoid confusion.

4. Neutral or unknown genders should trigger a “Cannot be determined” choice.

Trick to Always Use

  • Step 1 → Write down each symbol with its meaning before solving.
  • Step 2 → Decode each mini-link (e.g., A + B → A father of B).
  • Step 3 → Connect all people in the correct generational order.
  • Step 4 → Verify gender and generation count before finalizing the relationship.

Summary

Summary

  • Translate coded symbols into readable family relations first.
  • Always note whether the chain reads left-to-right or right-to-left.
  • Draw quick connection diagrams for clarity when more than 3 persons appear.
  • Use generation count and gender clues to eliminate similar options.

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 the father of C’s aunt → A is C’s grandfather.

Practice

(1/5)
1. If A + B means “A is the mother of B” and A × B means “A is the brother of B”, then what does P + Q × R mean?<br><br>(A) P is the mother of R (B) P is the aunt of R (C) P is the sister of R (D) Cannot be determined
easy
A. P is the mother of R
B. P is the aunt of R
C. P is the sister of R
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    ‘+’ → mother of, ‘×’ → brother of.

  2. Step 2: Decode chain.

    P + Q → P is the mother of Q. Q × R → Q is the brother of R.

  3. Step 3: Combine logically.

    P is mother of Q, and Q is brother of R → Q and R are siblings and both children of P → P is the mother of R.

  4. Final Answer:

    P is the mother of R → Option A.

  5. Quick Check:

    Mother of one sibling = mother of the other sibling ✅
Hint: If one person is mother of a sibling, she’s mother of both siblings.
Common Mistakes: Assuming aunt by misreading the sibling chain direction.
2. If A - B means “A is the wife of B” and A ÷ B means “B is the daughter of A”, then what does P - Q ÷ R mean?<br><br>(A) P is the wife of R (B) P is the mother of R (C) P is the mother-in-law of R (D) Cannot be determined
easy
A. P is the wife of R
B. P is the mother of R
C. P is the mother-in-law of R
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    ‘-’ → wife of, ‘÷’ → 'B is daughter of A' (so A ÷ B means B is A’s daughter).

  2. Step 2: Decode step by step.

    P - Q → P is the wife of Q. Q ÷ R → R is the daughter of Q (so Q is parent of R).

  3. Step 3: Combine.

    P is wife of Q (the parent of R) → P is R’s mother (spouse of the parent = the other parent).

  4. Final Answer:

    P is the mother of R → Option B.

  5. Quick Check:

    Wife of a parent = other parent (mother) ✅
Hint: If Q is parent of R and P is spouse of Q → P = parent of R.
Common Mistakes: Misreading the direction of '÷' and overcomplicating spouse logic.
3. If A ÷ B means “A is the father of B” and A + B means “A is the brother of B”, then what does P ÷ Q + R mean?<br><br>(A) P is the uncle of R (B) P is the uncle of R (alternate) (C) P is the father of R (D) Cannot be determined
easy
A. P is the uncle of R
B. P is the brother of R
C. P is the father of R
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    ‘÷’ → father of, ‘+’ → brother of.

  2. Step 2: Decode chain.

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

  3. Step 3: Combine.

    Q and R are siblings and P is parent of Q → P is also parent of R → P is R’s father.

  4. Final Answer:

    P is the father of R → Option C.

  5. Quick Check:

    Parent of a sibling = parent of both siblings ✅
Hint: If Q is sibling of R and P is parent of Q → P is parent of R.
Common Mistakes: Choosing 'uncle' by mistake (mixing generation levels).
4. If A × B means “A is the sister of B” and A ÷ B means “A is the father of B”, then what does P × Q ÷ R mean?<br><br>(A) P is the aunt of R (B) P is the sister of R (C) P is the mother of R (D) Cannot be determined
medium
A. P is the aunt of R
B. P is the sister of R
C. P is the mother of R
D. Cannot be determined

Solution

  1. Step 1: Decode symbols.

    ‘×’ → sister of, ‘÷’ → father of.

  2. Step 2: Decode chain left→right.

    P × Q → P is sister of Q. Q ÷ R → Q is father of R.

  3. Step 3: Combine.

    P is sister of R’s father → P is R’s aunt.

  4. Final Answer:

    Aunt → Option A.

  5. Quick Check:

    Sister of father = aunt ✅
Hint: Sister of parent = aunt.
Common Mistakes: Confusing sister-of-parent with sister-of-child.
5. If A + B means “A is the parent of B”, then what does P + Q + R mean?<br><br>(A) P is the grandfather of R (B) P is the grandmother of R (C) P is the parent of R (D) Cannot be determined
medium
A. P is the grandfather of R
B. P is the grandmother of R
C. P is the parent of R
D. Cannot be determined

Solution

  1. Step 1: Decode the chain.

    P + Q → P is parent of Q. Q + R → Q is parent of R. So P is grandparent of R.

  2. Step 2: Check gender information.

    The relation 'parent' is gender-neutral - P could be grandfather or grandmother.

  3. Final Answer:

    Cannot be determined → Option D, because gender (grandfather vs grandmother) is unspecified.

  4. Quick Check:

    When coded relation is gender-neutral but options are gendered, choose DNT ✅
Hint: If the code gives 'parent' and options are gendered, pick DNT.
Common Mistakes: Assuming male/female when code uses gender-neutral 'parent'.

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