In a certain code language, A + B means ‘A is the brother of B’. A − B means ‘A is the father of B’. A × B means ‘A is the mother of B’. A ÷ B means ‘A is the wife of B’. Based on the above, how is P related to T if ‘P × Q + R ÷ S − T’?

Correct — A. Walk the string left to right, one symbol at a time, building a small family tree.

Rule: × is 'is the mother of', + is 'is the brother of', ÷ is 'is the wife of', − is 'is the father of'.

P × Q: P is Q's mother.
Q + R: Q is R's brother, so P is R's mother as well.
R ÷ S: R is S's wife, so R is female.
S − T: S is T's father, and R being S's wife makes R T's mother.

So P is R's mother and R is T's mother. P is T's mother's mother — option (a).

Why the others are wrong

• (b)
  Mother — P is the mother of R, and R is T's mother, so P stands one generation further back. Calling P the mother of T collapses two generations into one.
• (c)
  Sister — P and T are in different generations. P is R's mother and R is a parent of T, so there is no sibling link anywhere in the chain.
• (d)
  Wife — The only wife in the chain is R, from R ÷ S. P is never joined to anybody by the division sign.

Symbol-coded relation questions are solved by reading the string left to right and drawing the family tree as you go, rather than by trying to hold it all in your head.

Each symbol carries two pieces of information: the relation itself, and usually the gender of the person on its left. Here × makes P female, + makes Q male and ÷ makes R female.

Gender matters because the options separate a mother from a mother's mother, and because a sibling link lets a relation pass sideways to a new person.

Key facts

• P × Q makes P the mother of Q, and Q + R makes Q the brother of R, so P is R's mother too.
• R ÷ S makes R the wife of S, and S − T makes S the father of T, so R is T's mother.
• Two mother-links one after the other give a maternal grandmother.
• A sibling symbol passes a parent's relation across to the sibling.

Common traps

• Reading the symbol string from right to left instead of left to right
• Missing that Q being R's brother makes P the mother of R as well
• Stopping at P as R's mother and answering 'mother' without carrying the chain on to T

No directly related past PYQ was found.