SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · General Intelligence and Reasoning · Question 18 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 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.

Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (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.) 13 : 55 23 : 105

(a)29 : 113
(b)7 : 26
(c)11 : 51
(d)31 : 145

Answer

Why

Correct — D. Rule: multiply by 5, then subtract 10 — that is, 5 × (n − 2).

13 × 5 = 65, and 65 − 10 = 55 ✓
23 × 5 = 115, and 115 − 10 = 105 ✓
31 × 5 = 155, and 155 − 10 = 145

145 is the second number of option (d).

Why the others are wrong

(a)
29 : 113 — 29 × 5 − 10 = 135, not the 113 printed here, so the pair breaks the rule.
(b)
7 : 26 — 7 × 5 − 10 = 25, one short of the 26 printed here.
(c)
11 : 51 — 11 × 5 − 10 = 45, not 51, so this pair fails on the same test.

Concept

This analogy hands you two solved pairs, and that is deliberate: a rule fitted to one pair is a guess. Test every candidate rule on both.

'13 : 55' on its own also fits 4n + 3. The second pair kills that reading at once, because 4 × 23 + 3 = 95, not 105.

The bracketed note forbids digit-level work, so the operation must act on the whole number — multiply, add, subtract, square, or a combination of those.

Written as 5(n − 2) the rule is faster to apply than 5n − 10: subtract 2 first, then take five times the result.

Key facts

5n − 10 factorises as 5(n − 2), so 31 − 2 = 29 and 29 × 5 = 145.
4n + 3 fits 13 : 55 but fails 23 : 105, which is why a second worked pair is given.
Both given pairs must be satisfied by any rule you propose.

Study next

Linear rules of the form an + b tested against two worked examplesNumber analogies built on squares and cubes rather than linear rulesThe same analogy frame at Reasoning Q.8 and Q.22 of this shift

Common traps

Fitting the rule to the first pair only and then choosing the option that matches that partial rule.
Adding a constant that changes between the examples, such as +3 and then +13, and calling it a rule.
Working on the digits of the number, which the stem's note rules out.

Two solved pairs are given before the question, so the rule can be confirmed on both pairs before you use it. Reasoning Q.8 and Q.22 of this shift set the same frame with different arithmetic inside it.

Related PYQs

No directly related past PYQ was found.