SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · General Intelligence and Reasoning · Question 19 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 10 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.

Select the number from among the given options that can replace the question mark (?) in the following series. 672, 677, 686, 699, 716, ?

(a)749
(b)737
(c)747
(d)757

Answer

Why

Correct — B. Write the first differences before looking for anything cleverer.

672 → 677 is +5
677 → 686 is +9
686 → 699 is +13
699 → 716 is +17

Rule: the differences run 5, 9, 13, 17 — each one 4 more than the last.

So the next difference is 17 + 4 = 21.

716 + 21 = 737 → option (b).

Why the others are wrong

(a)
749 — 749 is 716 + 33. The differences climb by a fixed 4, so 17 is followed by 21, not by 33. A jump of 33 would destroy the constant second difference.
(c)
747 — 747 is 716 + 31. Every difference in this series is one more than a multiple of 4, and 31 is not — it cannot belong to the row 5, 9, 13, 17, 21.
(d)
757 — 757 is 716 + 41, a step nearly double the 21 the pattern calls for. The series is being advanced one term, not two.

Concept

When a numeric series shows no obvious ratio, the first move is always the row of differences.

Here the differences 5, 9, 13 and 17 are themselves an arithmetic progression with common difference 4, so the second differences are constant.

That makes the series quadratic, and the next term comes from extending the difference row by one and adding, not from hunting a formula for the original row.

The arithmetic is easy once the row is on paper. The commonest slip is trying to hold the row in your head, so write it down.

The given terms sit between 672 and 716 while all four options sit between 737 and 757, so the size of the answer eliminates nothing. The step has to be computed.

Key facts

The first differences are 5, 9, 13 and 17.
Each difference exceeds the previous one by 4, so the second difference is constant.
The next difference is 21, giving 716 + 21 = 737.

Study next

Series with constant second differences and how to spot them in one passSeries where the differences multiply rather than addSeries built on squares or cubes with a constant added or subtracted

Common traps

Adding the next difference to the wrong term, usually the second-last one.
Extending the difference row twice and landing a full term ahead.
Hunting for a multiplication rule before the differences are written out.

Difference-of-differences series are set in other shifts too.

17 Sep 2024, 12:30, Reasoning Q.24 runs 949, 1006, 1066, 1129, 1195 with differences rising by 3, and 9 Sep 2024, 12:30, Reasoning Q.14 runs 99, 123, 150, 180, 213 the same way. The rise is small and constant, so the row is quick to confirm.

Related PYQs

No directly related past PYQ was found.