Classification (Odd One Out)

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Four items are given and three share a property. Your task is to name that property — and the discipline is to find what unites the three, not to hunt for what looks unusual about one. Starting from the odd item is how people talk themselves into the wrong answer.

Checklist for Numbers

Test	Look for
Prime	three primes and one composite
Perfect square or cube	and then check parity of the root
Divisibility	all multiples of some number except one
Digit sum or digit pattern	same digit sum, reversed digits, repeated digits
Odd / even	the simplest test — always try it first

Checklist for Letters

Convert to positions immediately — then look for a constant gap between letters.

Check whether the groups are all vowels or all consonants.

For mixed letter-number groups, test whether the number relates to the letters' positions.

Two valid answers can appear. Occasionally an item is odd on more than one test. When that happens, prefer the property that the other three share most precisely — a constant gap of 4 beats a loose grouping like "these are common letters".

Worked Examples from Real Papers

TS Police SI 2022 — Q89

Choose the odd pair: (1) Short : long (2) Light : Heavy (3) Crime : Blame (4) Poor : Rich

Short/long, light/heavy and poor/rich are all antonym pairs.
Crime and blame are associated ideas but not opposites.
Answer: Crime : Blame.
Method: with word pairs, always name the relationship within each pair. The odd one usually has a different internal relationship, not a different subject matter.

TS Police Constable 2022 — Q189

Choose the odd one: (1) Fly (2) Walk (3) Run (4) Static

Fly, walk and run are all forms of movement.
Static means stationary — the absence of movement.
Answer: Static.
Note: it is also the only adjective among three verbs, which points the same way. When two tests agree, you can answer with confidence.

TS Police SI 2022 — Q90

Among 131, 151, 161, 181, 191, one is different. Which?

All five are odd, all end in 1, and all are three digits — so test primality.
131, 151, 181 and 191 are prime. But 161 = 7 × 23.
Answer: 161.
Method: when a set is suspiciously uniform in appearance, primality is almost always the intended property. To test 161 quickly, work through 7, 11 and 13 — you only need divisors up to √161 ≈ 12.7.

TS Police Constable 2022 — Q147

Choose the odd one: (1) 49 (2) 81 (3) 25 (4) 64

All four are perfect squares, so that is not the distinguishing property — go one level deeper to the roots.
49 = 7², 81 = 9², 25 = 5² are squares of odd numbers; 64 = 8² is the square of an even number.
Answer: 64.
This is the key habit: when the obvious property is shared by all four, the answer lies in a property of the property. Squares → check the roots. Multiples → check the multipliers.

TS Police Constable 2022 — Q84

Choose the odd one: (1) DHLP (2) EIMQ (3) LPTX (4) AEIO

Convert each group to positions and check the gaps:
DHLP → 4, 8, 12, 16 — gaps of 4.
EIMQ → 5, 9, 13, 17 — gaps of 4.
LPTX → 12, 16, 20, 24 — gaps of 4.
AEIO → 1, 5, 9, 15 — gaps of 4, 4, then 6.
Answer: AEIO.
Note: AEIO is also the only group made entirely of vowels, so both tests agree. The near-miss is deliberate — AEIM would have fitted the pattern, and the setter changed only the final letter.

TS Police SI 2022 — Q91

Choose the odd one: (1) V21T (2) N15L (3) I8G (4) E4C

Each group is letter, number, letter — so test the number against the letters' positions.
V(22), 21, T(20) → the pattern is n, n−1, n−2.
I(9), 8, G(7) → fits.
E(5), 4, C(3) → fits.
N(14), 15, L(12) → the number should be 13, but it is 15.
Answer: N15L.
Note: the two letters in N15L are still correctly two apart, so the group looks right at a glance. Only the middle number breaks it.

Test the simplest property first. Odd/even, vowel/consonant and constant gaps account for most of these questions. Reach for primality or digit sums only once the easy tests have failed — working the other way round costs time you need elsewhere in the paper.

Also see: Analogy · Series · Coding & Decoding