Number Series, Coding-Decoding and the Odd Man Out

This chapter covers the Logical Reasoning unit of the WBCHSE Class 12 Business Mathematics and Basic Statistics syllabus; the same number-series, coding-decoding, direction-sense, seating-arrangement and blood-relation puzzle types taught here are also the standard reasoning-ability questions asked in most national banking, government and management-entrance aptitude tests, so the skill built in this chapter carries well beyond the West Bengal syllabus alone.

Logical reasoning questions test the ability to spot a pattern or a rule that connects a set of numbers, letters or words — no calculation beyond simple arithmetic is needed, but careful, systematic checking is essential. This chapter covers four common reasoning-puzzle types: number series, coding-decoding and the odd man out (grouped together here, since all three are short, single-rule puzzles), direction tests, seating arrangements, and blood relations.

Number series. A number series is a sequence of numbers that follows a single hidden rule; the task is to work out that rule and use it to find a missing or a next term. The most common rules are: a constant difference between consecutive terms (an arithmetic pattern, e.g. adding 4 each time), a constant ratio between consecutive terms (a geometric pattern, e.g. doubling each time), a CHANGING difference that itself follows a pattern (e.g. the differences are 3, 5, 7, 9 — increasing by 2 each time), or a rule combining two operations. The reliable method is to write out the difference (or ratio) between every pair of consecutive terms FIRST, before guessing at the overall pattern — the pattern is usually much easier to see in the row of differences than in the original series.

Coding-decoding. In a coding-decoding question, a word is first shown transformed into a "code" by some fixed rule, and the same rule must then be applied to a different word. The most common coding rules are: shifting every letter forward (or backward) by a fixed number of places in the alphabet, replacing every letter by the number of its position in the alphabet (A = 1, B = 2, and so on up to Z = 26), or reversing the order of the letters. The method is always the same: compare the given word with its given code, letter by letter, to work out EXACTLY what rule was applied — then apply that identical rule, letter by letter, to the new word.

Odd man out. Here, a group of numbers, letters or words is given, and all but one of them share a common property; the task is to spot the one item that breaks the pattern. The shared property can be almost anything — all prime numbers, all perfect squares, all multiples of a number, all belonging to the same category — so the first step is always to identify what the MAJORITY of the items have in common, and only then check which single item fails to share it.