SSC CGL 2024 Tier-I · 25 September 2024, Shift 1 · General Intelligence and Reasoning · Question 23 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.

11 is related to 121 following a certain logic. Following the same logic, 22 is related to 484. To which of the following is 31 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)943
(b)961
(c)957
(d)973

Answer

Why

Correct — B. Test the simplest whole-number operation on both given pairs.

11 × 11 = 121
22 × 22 = 484

Rule: the second number is the square of the first.

31 × 31 = 31 × 30 + 31 = 930 + 31 = 961 — option (b).

Why the others are wrong

(a)
943 — 943 = 23 × 41, so it is no square at all. It sits between 30 squared, which is 900, and 31 squared, which is 961.
(c)
957 — 957 = 3 × 11 × 29 — three distinct primes, so it cannot be a perfect square. It is four short of 961, which is close enough to survive a rushed multiplication.
(d)
973 — 973 = 7 × 139, again not a square, and it overshoots 31 × 31. The relation here lands exactly on the square, never above it.

Concept

The NOTE in the stem is doing real work: it forbids treating 31 as a 3 and a 1. Whatever the relation is, it acts on the whole number.

That narrows the search. Try, in order, adding a constant, multiplying by a constant, squaring, cubing, and the reverse of each.

Here 11 grows to 121 by a factor of 11 and 22 grows to 484 by a factor of 22 — the multiplier equals the number, which is squaring. One pair could be a coincidence, but two pairs settle it.

Squares up to 31 squared are worth knowing cold. Failing that, use 31 squared = 30 squared + 30 + 31, which is 900 + 61 = 961 and needs no long multiplication.

Key facts

11 squared is 121 and 22 squared is 484, which fixes the relation as squaring.
31 squared is 961, the keyed value.
The stem's NOTE forbids splitting 31 into the digits 3 and 1, so only whole-number operations are allowed.

Study next

Number analogies built on squares, cubes and their rootsSquares of 1 to 32 from memory, with the (n+1) squared = n squared + n + (n+1) shortcutReading the whole-number NOTE and knowing which rules it rules out

Common traps

Hunting for a digit-based rule in spite of the NOTE
Computing 31 × 31 as 900 + 31 and losing the extra 30
Accepting an option merely because it is close to 961, without checking it is a square

Power relations recur with the exponent and the direction changed. At 11 Sep 2024, 09:00, Reasoning Q.21 the pairs 8 : 512 and 12 : 1728 are cubes, and at 24 Sep 2024, 16:00, Reasoning Q.3 the pairs 64 : 4 and 216 : 6 run the same relation backwards as a cube root.

Related PYQs

No directly related past PYQ was found.