Average of Six Numbers — Find the Missing Value

Let's start with the single most important insight in every OC MR averages question: an average is just a sum in disguise. The moment you realise you can always recover the total by multiplying the average by the count, a whole family of questions becomes straightforward.

Mean and averages questions appear in almost every OC MR paper — usually one or two per test, spread across easy and difficult. The easy variants involve a single group; the harder ones split the group in two and ask you to work back and forth between both halves.

The examiner is checking whether you know that mean × count = total. Students who try to reason about averages directly — without converting to totals first — consistently pick the wrong answer on split-group questions.

You are told the average of a full group (e.g. 6 numbers averaging 18) and the average of one part of it (e.g. the first 3 average 14). You must find the average of the remaining part. The numbers are deliberately chosen so that trial-and-error is slow — the total-sum method is the only clean path.