Three of the following four options are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Correct — B. Rule: in a trio that belongs to the group, the gap from the first number to the second equals the gap from the second to the third — one constant step, applied twice.

90 → 99 → 108 steps by +9 and then +9.
82 → 46 → 10 steps by −36 and then −36.
67 → 45 → 23 steps by −22 and then −22.

Option (b) is 90 → 51 → 13. The first drop is 39, the second is 38.

The step changes, so (b) is the trio that does not belong. Note that direction and size are irrelevant to the rule — only that the gap repeats.

Why the others are wrong

• (a)
  90 – 99 – 108 — 90, 99, 108 rises by +9 and then by +9. The gap repeats, so (a) belongs to the group and cannot be the odd one out.
• (c)
  82 – 46 – 10 — 82, 46, 10 falls by −36 twice. A falling trio is as valid as a rising one under this rule, so (c) belongs.
• (d)
  67 – 45 – 23 — 67, 45, 23 falls by −22 twice. (d) has the same shape as (a) and (c) — one constant step applied twice — and therefore belongs.

An odd-one-out over number trios asks for the shared relation, not for a shared property of the numbers themselves. Compute the same quantity for all four and the outlier declares itself.

Differences are what to compute first, because they are cheap and they settle most of these items.

Here three trios step by a constant amount and one does not. Since the rule is that the two gaps are equal, whether the trio rises or falls, and by how much, makes no difference at all.

Key facts

• A trio belongs to the group when its two consecutive differences are equal.
• 90, 99, 108 has differences of +9 and +9.
• 82, 46, 10 has differences of −36 and −36, and 67, 45, 23 has −22 and −22.
• 90, 51, 13 has differences of −39 and −38, which is why it stands apart.

Common traps

• Looking for a property of the numbers, such as all being even, instead of a relation between them
• Subtracting carelessly and reading 39 and 38 as the same gap
• Assuming the odd one must be the trio that rises when the other three fall

No directly related past PYQ was found.