SSC CGL 2024 Tier-I · 17 September 2024, Shift 1 · General Intelligence and Reasoning · Question 12 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.

30 is related to 41 following certain logic. Following the same logic, 14 is related to 21. To which of the following numbers is 54 related, following the same logic? (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 /deleting /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)69
(b)63
(c)53
(d)59

Answer

Why

Correct — A. Every number given sits five above a perfect square, so read each one as a square plus 5.

30 = 5² + 5, and 41 = 6² + 5.
14 = 3² + 5, and 21 = 4² + 5.

Rule: k² + 5 becomes (k + 1)² + 5.

54 = 7² + 5, so k = 7.
(7 + 1)² + 5 = 64 + 5 = 69, which is option (a).

Why the others are wrong

(b)
63 — 63 is 54 + 9. The step is not a fixed addition — it is +11 from 30 to 41 and +7 from 14 to 21 — because the square advances, not the total.
(c)
53 — 53 keeps the square at 7² and drops the constant to 4. Both halves are wrong: the constant stays at +5 and the square has to move to 8².
(d)
59 — 59 adds the constant 5 to 54 instead of stepping the square. The rule sends 7² + 5 to 8² + 5, which is 69.

Concept

Number analogies carrying the whole-numbers NOTE are usually built on squares, cubes or primes rather than on a difference. The difference here changes — +11 for the first pair and +7 for the second — which is the signal to stop looking for a fixed step.

Subtract a small constant from each number and see whether a square appears. Take 5 away: 30 becomes 25, 41 becomes 36, 14 becomes 9, 21 becomes 16. All four are squares, and each pair advances the root by exactly one.

So 54 has to be read the same way: 54 − 5 = 49 = 7².

Two independent pairs confirm the rule before you apply it, which is what makes it safe.

A single pair, 30 to 41, could just as well be read as a jump of 11.

Key facts

30 = 5² + 5 and 41 = 6² + 5.
14 = 3² + 5 and 21 = 4² + 5.
54 = 7² + 5, so its partner is 8² + 5 = 69.

Study next

Number analogies built on k² plus or minus a fixed constantCube-based analogies, where the same subtract-and-test method worksKnowing the squares up to 20² on sight

Common traps

Assuming a fixed difference, which the two given pairs already contradict.
Splitting 54 as 6² + 18 or some other combination, when +5 is the constant both pairs share.
Advancing the constant instead of the root, which gives 54 + 5 = 59.

The same square-plus-a-constant analogy is set at 10 Sep 2024, 16:00, Reasoning Q.17, where 62 = 8² − 2 goes to 79 = 9² − 2, and at 26 Sep 2024, 16:00, Reasoning Q.7, where 80 = 9² − 1 goes to 99 = 10² − 1.

Related PYQs

No directly related past PYQ was found.