In a certain code language, ‘It’s your life’ is written as ‘Ao Bo Co’ and ‘It’s your food’ is written as ‘Ba Co Bo’. How will ‘food’ be written in that language?

Correct — A. Rule: cross out what the two sentences share; the leftovers must pair with each other.

The sentences share It's and your; the code groups share Co and Bo.

Which shared code goes with which shared word cannot be settled — and does not need to be.

Strike them out and one word and one code are left on each side: 'life' with Ao, and 'food' with Ba.

Why the others are wrong

• (b)
  Bo — Bo appears in both code groups, so it must code one of the two words common to both sentences — 'It's' or 'your'. 'food' appears in only the second sentence.
• (c)
  Ao — Ao appears only in the first code group, so it codes the word unique to the first sentence, which is 'life'.
• (d)
  Co — Co, like Bo, is common to both groups, so it codes a word common to both sentences. 'food' is not one of them.

This is the intersection method run from the other end.

Two shared words give two shared codes. You cannot say which goes with which, and you do not need to.

Strike the shared pair out of both sides and exactly one word and one code are left in each sentence, so that pairing is forced.

The method works whenever the count of shared words equals the count of shared codes; that equality is what makes the leftovers unique.

Key facts

• Shared words correspond to shared codes as a set, even when the individual pairings stay unknown.
• A word appearing in only one sentence must map to a code appearing in only that sentence's group.
• Here 'It's' and 'your' are Co and Bo in an undetermined order.
• Here 'life' is Ao and 'food' is Ba.

Common traps

• Matching by position: 'It's' is the first word and Ao the first code, but they are not a pair
• Choosing a code common to both groups for a word that appears in only one
• Trying to decode 'It's' and 'your' separately, which this data cannot do

No directly related past PYQ was found.