SSC CGL 2024 Tier-I · 18 September 2024, Shift 3 · General Intelligence and Reasoning · Question 7 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 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 option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 10 : 110 :: 7 : 56 :: 9 : ? (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)90
(b)85
(c)91
(d)81

Answer

Why

Correct — A. Rule: second number = first² + first, which is the same as n × (n + 1).

10 : 10² + 10 = 100 + 10 = 110
7 : 7² + 7 = 49 + 7 = 56
9 : 9² + 9 = 81 + 9 = 90

Both given pairs obey it, so the fifth number pairs with 90 — option (a).

Why the others are wrong

(b)
85 — 85 is 81 + 4. What is added after squaring is the starting number itself, so 9 must be added to 81, not 4.
(c)
91 — 91 is 9 × 10 + 1. The rule gives 9 × 10 exactly, with nothing added on top of the product.
(d)
81 — 81 is 9² on its own — the squaring step done and the adding step forgotten, as 110 = 100 + 10 shows it should not be.

Concept

n² + n factorises as n(n + 1), so these are products of consecutive integers: 110 = 10 × 11, 56 = 7 × 8, 90 = 9 × 10. Recognising 110 and 56 in that form is quicker than squaring.

Two pairs are supplied so the rule can be tested twice. 10 : 110 alone fits several rules — × 11, +100, n² + n — and only 7 : 56 rules the others out.

The NOTE bars digit-splitting, so every operation runs on 10, 7 and 9 as whole numbers.

Three of the four options sit within ten of the answer, so an approximate method will not separate them. The arithmetic has to be finished.

Key facts

n² + n = n(n + 1), giving 110 = 10 × 11, 56 = 7 × 8 and 90 = 9 × 10.
Products of consecutive integers worth knowing on sight: 12, 20, 30, 42, 56, 72, 90, 110.
The NOTE bars breaking a number into its digits, so 110 stays 110.

Study next

Recognising products of consecutive integers instantlyNumber analogies built on n² - n and on n² + 1Settling a rule from two given pairs rather than from one

Common traps

Answering 81 by squaring and forgetting the second step
Fixing the rule from 10 : 110 alone, where several rules fit
Splitting 110 into 1, 1 and 0, which the NOTE forbids

The same five-number frame runs on 2n + 2 at 19 Sep 2024, 9:00, Reasoning Q.16, and on 17n at 25 Sep 2024, 9:00, Reasoning Q.25 — so derive the rule from both given pairs every time.

Related PYQs

No directly related past PYQ was found.

Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 10 : 110 :: 7 : 56 :: 9 : ? (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)90
(b)85
(c)91
(d)81