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 — D. Rule: middle number = (2 × first) + third.

(a) 2 × 58 = 116, and 116 + 23 = 139
(b) 2 × 23 = 46, and 46 + 38 = 84
(c) 2 × 89 = 178, and 178 + 34 = 212
(d) 2 × 12 = 24, and 24 + 99 = 123, but the trio prints 122

Three trios land exactly on their middle number. The fourth misses by 1, so option (d) is the one that does not belong.

Why the others are wrong

• (a)
  58 – 139 – 23 — Doubling the first and adding the third lands exactly: 2 × 58 + 23 = 139, the middle number as printed. This trio belongs to the group.
• (b)
  23 – 84 – 38 — 2 × 23 + 38 = 84, which is the middle number given. The rule holds, so this is one of the three that match.
• (c)
  89 – 212 – 34 — 2 × 89 + 34 = 212, the middle number exactly. It follows the same rule as (a) and (b) and so belongs with them.

An odd-one-out on number trios asks for one arithmetic link that ties all three numbers of an option together, tested across the four options.

Start from the largest number in each trio: it is the natural first guess for the result, with the other two as the inputs. In every option here the middle number is the biggest, which is the hint that it is what gets built.

The bracketed NOTE is not decoration. SSC is telling you the operations act on 58 and 139 as whole numbers — you may not split 58 into 5 and 8. That rules out an entire family of digit-based rules before you start.

Key facts

• In each option the middle number is the largest of the three.
• For (a), (b) and (c) the middle number equals twice the first plus the third.
• Option (d) gives 2 × 12 + 99 = 123 against a printed 122, a difference of 1.
• The NOTE bars digit-splitting, so 12 must be used as 12 and never as 1 and 2.

Common traps

• Testing first against middle and never bringing the third number in.
• Splitting digits once the whole-number rule looks hard to find.
• Rejecting the rule because one option fails it — the option that fails is the answer.

No directly related past PYQ was found.