In a certain code language, ‘A + B’ means ‘A is the mother of B’; ‘A − B’ means ‘A is the brother of B’; ‘A × B’ means ‘A is the wife of B’ and ‘A ÷ B’ means ‘A is the father of B’. Based on the above, how is A related to D if ‘A × B ÷ C + D’?

Correct — D. Rule: × = wife of, ÷ = father of, + = mother of, and the chain is read strictly left to right.

A × B: A is the wife of B.
B ÷ C: B is the father of C.
The father's wife is the mother, so A is the mother of C.

C + D: C is the mother of D.
A is therefore the mother of D's mother — D's mother's mother, which is option (d).

Why the others are wrong

• (a)
  Father’s mother — Father's mother would need C to be D's father. The last link is C + D, and + means mother of, so A reaches D through D's mother.
• (b)
  Mother’s father — Mother's father makes A male. The first link is A × B, and × means A is the wife of B, which fixes A as female.
• (c)
  Father’s father — Father's father needs A and C both male. A is a wife and C is a mother, so neither of those two links is a male one.

These items hand you a four-symbol dictionary — here + mother, − brother, × wife, ÷ father — and one chain to decode.

Two habits make them quick. Draw the chain as a family tree with each arrow pointing from the earlier letter to the later one, and mark a person's sex the moment a symbol fixes it.

Here × fixes A as female and ÷ fixes B as male. That is what lets you compress wife-of-the-father into the single word mother.

Key facts

• A × B means A is the wife of B, so A is female and B is male.
• A ÷ B means A is the father of B, and A + B means A is the mother of B.
• The wife of C's father is C's mother, which is the step that turns this chain into a grandmother relation.

Common traps

• Reading the chain right to left, which inverts every relation in it.
• Forgetting that × fixes A as female, which is what rules out any father's-side answer.
• Answering how D relates to A when the question asks how A relates to D.

No directly related past PYQ was found.