SSC CGL 2024 Tier-I · 13 September 2024, Shift 3 · General Intelligence and Reasoning · Question 14 of 98

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.

Which of the following numbers will replace the question mark (?) in the given series? 22, 23, 27, 54, 70, 195, ?

(a)231
(b)200
(c)230
(d)196

Answer

Why

Correct — A. Take the gaps between consecutive terms, and read those gaps as a series of their own.

Rule: +1³, +2², +3³, +4², +5³, +6² — cubes and squares alternate while the base counts up.

22 + 1 = 23
23 + 4 = 27
27 + 27 = 54
54 + 16 = 70

70 + 125 = 195
195 + 36 = 231 → option (a)

Why the others are wrong

(b)
200 — 200 needs a gap of 5 from 195. Five is neither 6² nor any cube, so it does not continue the alternating chain.
(c)
230 — 230 uses a gap of 35, one short of 6² = 36. Redo the last addition: 195 + 36 = 231.
(d)
196 — 196 adds only 1. That is 1³, the gap already spent between 22 and 23, not the sixth term of the chain.

Concept

Alternating-difference series hide two sequences inside one. Compute the gaps first, then look at the gaps on their own.

Here the gaps are 1, 4, 27, 16, 125 — read them as 1³, 2², 3³, 4², 5³. Odd positions take cubes, even positions take squares, and the base climbs 1, 2, 3, 4, 5 without a skip.

The sixth gap is therefore 6², not 6³. Getting that parity right is the whole question.

The jump from 27 to 54 is what makes the series look irregular. A single cube, 3³ = 27, doubles the term, which is why a run of small gaps suddenly breaks open.

Key facts

The gaps run 1, 4, 27, 16, 125, 36 — cubes at the odd positions and squares at the even ones.
The base of each gap rises 1, 2, 3, 4, 5, 6 with no repeat and no skip.
195 + 36 = 231, so the seventh term is 231.

Study next

Alternating-difference series where two rules interleaveRecognising cubes to 10³ and squares to 20² on sightSecond-difference series, where the gaps between the gaps carry the pattern

Common traps

Taking 6³ = 216 for the sixth gap because the fifth gap was a cube.
Adding 35 instead of 36 and landing on 230.
Treating the run as one arithmetic rule because the first two gaps are small.

These are built from a gap sequence rather than from the terms, so the first move is always to subtract. A series whose gaps are pure squares is set at 10 Sep 2024, 09:00, Reasoning Q.24 — 23, 27, 43, 79, 143 — where the gaps run 2², 4², 6², 8², 10².

Related PYQs

No directly related past PYQ was found.