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Question

‘A + B’ means ‘A is the daughter of B’.

‘A - B’ means ‘A is the brother of B’.

‘A × B’ means ‘A is the mother of B’.

‘A ÷ B’ means ‘A is the son of B’.

If U + C × Q – P ÷ R ÷ S – T, then how is S related to U?

This question was previously asked in
SSC CGL 2018 (Tier 2) Statistics Previous Year Paper (22-feb-2018)
The correct answer is

Paternal grandfather

Understanding Blood Relations and Symbols

This question involves decoding relationships expressed using symbols like '+', '-', '×', and '÷'. Each symbol represents a specific relationship between two individuals, say A and B.

  • A + B means A is the daughter of B. This tells us the gender of A (female) and that B is a parent of A.
  • A - B means A is the brother of B. This tells us the gender of A (male) and that A and B are siblings.
  • A × B means A is the mother of B. This tells us the gender of A (female) and that A is a parent of B.
  • A ÷ B means A is the son of B. This tells us the gender of A (male) and that B is a parent of A.

To solve the problem, we need to build a family tree or a chain of relationships based on the given expression: U + C × Q – P ÷ R ÷ S – T.

Analyzing the Blood Relation Expression

Let's break down the expression step by step from left to right:

  1. U + C: According to the rule 'A + B' means 'A is the daughter of B', U + C means U is the daughter of C. This makes C a parent of U. U is female.
  2. C × Q: According to the rule 'A × B' means 'A is the mother of B', C × Q means C is the mother of Q. This makes C a parent of Q. C is female. Since C is the mother of both U and Q, U and Q must be siblings.
  3. Q – P: According to the rule 'A - B' means 'A is the brother of B', Q – P means Q is the brother of P. This means Q and P are siblings. Q is male. Now we know U, Q, and P are siblings. C is their mother.
  4. P ÷ R: According to the rule 'A ÷ B' means 'A is the son of B', P ÷ R means P is the son of R. This makes R a parent of P. P is male. We already know C is the mother of P (as she is the mother of his siblings U and Q). Therefore, R must be the father of P. This also means C and R are married (parents of P, Q, U).
  5. R ÷ S: According to the rule 'A ÷ B' means 'A is the son of B', R ÷ S means R is the son of S. This makes S a parent of R. R is male.
  6. S – T: According to the rule 'A - B' means 'A is the brother of B', S – T means S is the brother of T. This means S is male and T is his sibling. This information about T is not directly relevant to the relationship between S and U.

Deducing the Relationship between S and U

Let's connect the relevant parts of the chain:

  • From step 1, U is the daughter of C.
  • From steps 2 & 3, U, Q, and P are siblings, and C is their mother.
  • From step 4, P is the son of R, and since C is the mother, R must be the father of U, Q, and P. So, R is the father of U.
  • From step 5, R is the son of S. This means S is a parent of R. Since R is male (son of S), S is either R's father or mother.
  • From step 6, S is the brother of T. This confirms that S is male.

So, S is the male parent of R. R is the father of U. This means S is the father of U's father (R). The father of one's father is the paternal grandfather.

Therefore, S is the paternal grandfather of U.

Final Relationship Analysis

Let's summarize the direct links relevant to S and U:

S ← Parent ← R ← Father ← U

Since S is male (brother of T) and R is the son of S, S is the father of R. Since R is the father of U, S is the father of U's father. This relationship is called paternal grandfather.

Relationship Step Deduction Gender/Relation
U + C U is daughter of C U (Female), C (Parent)
C × Q C is mother of Q C (Female), Q (Child)
Q – P Q is brother of P Q (Male), P (Sibling)
P ÷ R P is son of R P (Male), R (Parent)
R ÷ S R is son of S R (Male), S (Parent)
S – T S is brother of T S (Male), T (Sibling)

Combining these, we establish that C is the mother of U, Q, and P, and R is the father of U, Q, and P. R is the son of S, and S is male. Thus, S is the paternal grandfather of U.

Revision Table: Key Relationship Symbols

Symbol Meaning Gender Indicated
+ Daughter of First person is female
- Brother of First person is male
× Mother of First person is female
÷ Son of First person is male

Additional Information: Solving Blood Relation Puzzles

Solving blood relation puzzles effectively often involves visualizing the family tree or using diagrams. Here are some tips:

  • Break down the expression: Analyze each part of the given coded expression individually.
  • Determine genders: Note the gender of each person if indicated by the symbol.
  • Build the chain: Connect the relationships step-by-step. Work from left to right or find common individuals connecting different parts of the expression.
  • Draw a diagram: A simple family tree diagram can make complex relationships easier to see. Use symbols like squares for males, circles for females, and lines to connect relationships (vertical for parent-child, horizontal for siblings/spouses).
  • Identify generations: Keep track of which generation each person belongs to. This helps in quickly identifying relationships like grandparent, parent, child, grandchild.
  • Focus on the required relationship: Once the full or relevant part of the family tree is established, identify the direct path between the two individuals asked about in the question.

Practicing with different types of relationship codes and expressions will help improve speed and accuracy in solving these problems.

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Important Questions from Family Tree Problems

  1. Six members of a family namely A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B. A and C are married couple. E is the brother of C, D is the daughter of A. F is the brother of B. How many male members are there in the family?
  2. Sunil is the son of Kesav. Simran, who is Kesav's sister, has a son Maruti and daughter Sita. Prem is the maternal uncle of Maruti. How is Sunil related to Maruti?
  3. A and B are brothers. C and D are sisters. A's son is D's brother. How is B related to C?

  4. A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?

  5. P, Q, R, S, T and U are six members of a family. Ris the spouse of Q. U is the mother of Tand Sis the daughter of U. P's daughter is Tand R's son is P. There are two couples in the family. Which one of the following is correct?
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