SSC CGL 2024 Tier-I · 12 September 2024, Shift 3 · General Intelligence and Reasoning · Question 16 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Three of the following number-pairs are alike in some manner and hence form a group. Which number-pair 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.)

(a)14 – 121
(b)21 – 361
(c)18 – 256
(d)11 – 81

Answer

Why

Correct — A. Test every pair against second = (first − 2)².

21 → (21 − 2)² = 19² = 361 ✓
18 → (18 − 2)² = 16² = 256 ✓
11 → (11 − 2)² = 9² = 81 ✓
14 → (14 − 2)² = 12² = 144, but the pair prints 121, which is 11².

Three pairs obey the rule and 14 – 121 does not, so option (a) is the pair outside the group.

Why the others are wrong

(b)
21 – 361 — 21 – 361 belongs to the group: 19² = 361, and 19 is 21 − 2. Obeying the shared rule is precisely what stops it being the odd pair.
(c)
18 – 256 — 18 – 256 belongs: 16² = 256, and 16 is 18 − 2. It fits, so it cannot be the pair that breaks the pattern.
(d)
11 – 81 — 11 – 81 belongs: 9² = 81, and 9 is 11 − 2. Its small numbers make it look unlike the others, but arithmetically it follows the same rule.

Concept

An odd-one-out on number pairs asks for one rule that three pairs share. Read the rule off the pairs that agree, then test the fourth against it — never try to find what is interesting about a single pair on its own.

The rule here is a shift then a square: subtract 2, then square. Both halves matter, because every second number in this question is already a perfect square.

SSC's NOTE forbids splitting a number into digits, so 121 may not be read as 1, 2 and 1. The operation has to act on the whole number.

121 is a perfect square, so a candidate who checks nothing but squareness finds all four pairs acceptable and has to guess. The discriminating step is the − 2 before the squaring.

Key facts

The group rule is second = (first − 2)², giving 21 → 361, 18 → 256 and 11 → 81.
14 – 121 fails because (14 − 2)² = 144, while 121 is 11².
All four second numbers are perfect squares, so squareness alone separates nothing.

Study next

Odd-one-out on number pairs built from squares and cubes of a shifted numberPerfect squares from 1 to 30 recognised on sightLetter-cluster odd-one-out decided by the gaps between letters

Common traps

Noticing that 121 is a perfect square and stopping there.
Working on the digits of 121 or 361 after the NOTE has forbidden it.

Odd-one-out returns at 12 Sep 2024, 16:00, Reasoning Q.11 on letter clusters, where the shared gap is +5 then +3. SSC's whole-number NOTE is printed again at Reasoning Q.19, Q.21 and Q.22 of that sitting.

Related PYQs

No directly related past PYQ was found.