SSC CGL 2024 Tier-I · 13 September 2024, Shift 2 · General Intelligence and Reasoning · Question 10 of 99

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.

16 is related to 30 following a certain logic. Following the same logic, 81 is related to 110. To which of the following is 49 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)60
(b)64
(c)90
(d)72

Answer

Why

Correct — D. Rule: take the square root, then multiply the next two whole numbers. If the number is k squared, its partner is (k + 1) × (k + 2).

16: k = 4, so 5 × 6 = 30.
81: k = 9, so 10 × 11 = 110.

49: k = 7, so 8 × 9 = 72, option (d).

The same numbers read another way: 30 is 5 squared plus 5 and 110 is 10 squared plus 10, so 49 gives 8 squared plus 8, which is 72 again.

Why the others are wrong

(a)
60 — 60 is not a product of two consecutive whole numbers at all, since 7 × 8 = 56 and 8 × 9 = 72. Both worked pairs land on such a product, 30 = 5 × 6 and 110 = 10 × 11.
(b)
64 — 64 is 8 squared, the square of the next whole number, with the extra 8 dropped. Test it on the example: 16 would give 5 squared, which is 25 and not 30.
(c)
90 — 90 is 9 × 10, a product of consecutive numbers but the wrong pair — it steps two past the root instead of one. On 16 that rule would give 6 × 7 = 42, not 30.

Concept

A number analogy is solved by finding an operation that works on both given pairs, then applying it once.

16, 81 and 49 are all perfect squares, which is the signal to work through the root rather than through the number itself.

From the root k, the partner here is (k + 1)(k + 2), the product of the next two whole numbers. Written as (k + 1) squared plus (k + 1), it also reads as the next square plus that square's own root.

The printed note bars you from splitting 16 into 1 and 6. That closes off the digit tricks which sometimes rescue these items and forces the square-root reading.

Key facts

16, 81 and 49 are the squares of 4, 9 and 7.
30 = 5 × 6, 110 = 10 × 11 and 72 = 8 × 9, each the product of the two whole numbers after the root.
The same rule reads as the next square plus its root, since 5 × 6 equals 25 + 5.

Study next

Spotting perfect squares as the cue to work through the rootProducts of consecutive integers and the equivalent form k squared plus kTesting a candidate rule on the second given pair before answering

Common traps

Stopping at the next square, which gives 64.
Overshooting the root by two, which gives 90.
Working on the digits of 49 despite the printed note.

Number analogies and triads both hang on a single relation that has to fit every worked pair. Reasoning Q.2 of the same 13 Sep 2024, 12:30 paper puts a constant ratio on a triad, and Reasoning Q.24 of that paper puts a constant difference on one.

Related PYQs

No directly related past PYQ was found.