In a certain code language, 'A & B' means ‘ A is the brother of B’, 'A x B' means ‘A is the father of B’, 'A ? B' means ‘A is the mother of B’ and 'A ! B' means ‘A is the wife of B’. Which of the following means that W is the mother's mother of P?

Correct — D. Write the dictionary out first: & is brother, x is father, ? is mother, ! is wife, and in every statement the first letter is the one being described.

Option (d) reads W ! R x Y ? O & P.

W ! R makes W the wife of R
R x Y makes R the father of Y, so W is Y's mother
Y ? O makes Y the mother of O
O & P makes O the brother of P, so Y is P's mother as well

W is Y's mother and Y is P's mother, which is exactly P's mother's mother → option (d).

Why the others are wrong

• (a)
  W & R ! Y x O ? P — W & R makes W the brother of R, which fixes W as male. A mother's mother must be female, so this chain dies at its first symbol.
• (b)
  W ? R x Y ! O & P — Here W ? R x Y makes W the mother of R and R the father of Y, so W is Y's paternal grandmother. Y is only P's brother's wife, so W is nothing to P by blood.
• (c)
  W ? R ! Y & O x P — W ? R ! Y makes W the mother of R and R the wife of Y. Since Y is P's father's brother, W ends up as the mother of P's aunt by marriage, not P's grandmother.

Symbol-coded relation items give you a dictionary and a chain. Some ask you to read a chain, and some, like this one, ask which chain produces a stated relation.

Two habits solve them. First, copy the dictionary into the margin before touching the options — & brother, x father, ? mother, ! wife — because a symbol means only what this stem says: ! is wife here but father at 19 Sep 2024, 12:30, Reasoning Q.24.

Second, work by gender first. The target here is a mother's mother, so W must be female, and any option that opens by making W a brother or a father is dead before you trace it.

Key facts

• In this dictionary A & B means A is the brother of B, and A ! B means A is the wife of B.
• Mother's mother is the maternal grandmother, so the person asked about must be female.
• W is the wife of R and R is the father of Y, which together make W the mother of Y.
• Reading direction is fixed: the first letter is the one described and the second is the reference point.

Common traps

• Tracing a chain from the wrong end. In A x B it is A who is the father, not B.
• Forgetting that the answer must be female and testing options that open with a brother or father symbol.
• Stopping once a grandmother appears. In option (b), W is Y's father's mother, but Y is only P's brother's wife, so W is not P's grandmother at all.

No directly related past PYQ was found.