Directions: Study the following information carefully and answer the question…

2022

Directions: Study the following information carefully and answer the question that follows. 'P@Q' means 'P is the son of Q'; 'P^Q' means 'P is the father of Q'; 'P÷Q' means 'P is the brother of Q'; 'P+Q' means 'P is the daughter of Q'; 'P-Q' means 'P is the mother of Q'; 'P=Q' means 'P is the sister of Q'; 'P%Q' means 'P is the husband of Q'. Which of the following expressions holds true that 'E is the maternal grandmother of A'?

  1. A.

    A-B÷C^D=E

  2. B.

    A-B÷C^D^E

  3. C.

    A-B+C^D÷E

  4. D.

    A=B+C÷D+E

  5. E.

    A+D=C@B%E

Attempted by 3 students.

Show answer & explanation

Correct answer: E

Concept

Concept: In symbolic coding of blood relations, each symbol fixes one direct relationship between the two people it sits between, and the chain is read strictly left to right, one operator at a time. A person's gender is settled by whichever clause names a gender-specific role (mother/father/son/daughter/brother/sister/husband). 'Maternal grandmother of X' is the mother of X's MOTHER, so the target person must be female and must reach X through X's mother's side.

Key: @ = son of, ^ = father of, ÷ = brother of, + = daughter of, − = mother of, = = sister of, % = husband of. To verify a relation, decode every link, fix each person's gender, then check whether the required ancestor sits two generations above on the correct (maternal) side.

Step-by-step decoding

  1. Decode A+D: A is the daughter of D, so D is a parent of A and A is female.

  2. Decode D=C: D is the sister of C, which fixes D as female. A female parent of A means D is A's mother.

  3. Decode C@B: C is the son of B, so B is a parent of C (and therefore also of C's sibling D).

  4. Decode B%E: B is the husband of E, so E is female and is the wife of B. As B and E are the couple who are parents of D, E is the mother of D.

  5. Combine: E is the mother of D, and D is the mother of A. So E is the mother of A's mother — that is, the maternal grandmother of A.

Cross-check

Cross-check the side: D is established as female (sister of C), so D is A's mother, not father; therefore E reaches A through A's mother's line, making her maternal — not paternal — grandmother. The chain links every person exactly once with no contradiction, so this expression alone satisfies the requirement.

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