In a certain code language, A + B means ‘A is the son of B’, A − B means ‘A is the wife of B’, A × B means ‘A is the brother of B’ and A ÷ B means ‘A is the mother of B’. Based on the above, if ‘P + Q ÷ R − T × M’, which of the following is true?

Correct — C. Rule: translate the string one operator at a time, left to right, before concluding anything.

P + Q means P is the son of Q.
Q ÷ R means Q is the mother of R.
R − T means R is the wife of T.
T × M means T is the brother of M.

So Q is mother to both P and R — to P by the first link, to R by the second. P is called a son, so P is male.

Two children of one mother, one of them male: P is the brother of R, option (c).

Why the others are wrong

• (a)
  T is the brother of P. — T is R's husband, since R is the wife of T. That makes T a brother-in-law to P, not a brother.
• (b)
  M is the sister of T. — T is the brother of M, which fixes T's gender and not M's. M may be male, so 'sister' is never established.
• (d)
  Q is the mother of M. — Q is mother to P and R only. M is reached through T, who married into the family, so no parent link runs from Q to M.

Symbol-coded relations are solved by translating the whole string first and reading the family off the translation.

Two habits save the mark. First, note the gender each symbol fixes: son, wife, brother and mother each fix one person, and options often turn on a gender that was never fixed at all.

Second, keep the direction straight. A ÷ B means A is the mother of B, never B the mother of A. Here the whole chain is not even needed — P and R both hang off Q, and that settles it.

Key facts

• In this question A ÷ B means A is the mother of B, and A − B means A is the wife of B.
• 'P is the son of Q' fixes P as male, while 'T is the brother of M' fixes T as male and leaves M open.
• P and R share the mother Q, which makes them siblings.

Common traps

• Assuming M is female because T is called a brother
• Reversing a link and reading A ÷ B as B being the mother of A
• Carrying a symbol legend over from another question instead of reading the printed one

No directly related past PYQ was found.