SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · General Intelligence and Reasoning · Question 15 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

If 9 @ 3 = 36 and 6 @ 2 = 16, then 8 @ 2 = ?

(a)20
(b)18
(c)19
(d)17

Answer

Why

Correct — A. Find one rule that fits both examples, then apply it.

Rule: a @ b = (a + b) × b.

9 @ 3: (9 + 3) × 3 = 12 × 3 = 36, as given
6 @ 2: (6 + 2) × 2 = 8 × 2 = 16, as given
8 @ 2: (8 + 2) × 2 = 10 × 2 = 20

That is option (a).

Why the others are wrong

(b)
18 — 18 is 8 × 2 + 2, the rule a × b + b. Test it on the first example: 9 × 3 + 3 = 30, not 36.
(c)
19 — 19 is one short of the rule's value, (8 + 2) × 2 = 20. With b = 2 the rule always gives an even number, so an odd result cannot come from it.
(d)
17 — 17 is 8 × 2 + 1. The same pattern on the first example gives 9 × 3 + 1 = 28, not 36.

Concept

An operator item hides a formula behind a symbol and shows it only through examples. Test each candidate rule on every example before applying it: a × 4 gives 9 @ 3 = 36 but 6 @ 2 = 24, so it fails.

Here both results are multiples of b: 36 = 12 × 3 and 16 = 8 × 2. The multipliers 12 and 8 are a + b, which gives (a + b) × b, the same as ab + b².

A second rule also fits both examples: (a − b)² gives (9 − 3)² = 36 and (6 − 2)² = 16. For 8 @ 2 it gives (8 − 2)² = 36, which is not among the options.

So the options, not the examples alone, settle the rule as (a + b) × b.

Key facts

(a + b) × b turns 9 @ 3 into 12 × 3 = 36 and 6 @ 2 into 8 × 2 = 16.
(a + b) × b is the same as ab + b².
(a − b)² also fits both examples but gives 36 for 8 @ 2, which no option offers.

Study next

Operator items with three examples, where the third rules out a rival ruleRules that mix a square with a sum, such as a² + bOdd-one-out items built on a hidden operator rule

Common traps

Stopping at a rule that fits the first example alone, such as a × 4, which gives 24 for 6 @ 2.
Finding (a − b)², reaching 36, and guessing when 36 is not offered, instead of looking for a second rule.

The companion rule (a − b) × b decides Reasoning Q.18 of this shift, where 9 $ 3 = 18 and 8 $ 2 = 12 give 6 $ 4 = 8.

At 12 Sep 2025, 16:00, Reasoning Q.19, 5 @ 3 = 28 and 4 @ 2 = 18 fit a² + b, so 6 @ 4 = 40.

Related PYQs

No directly related past PYQ was found.

Topic: Symbolic/Number Analogy — all 169 SSC CGL questions on it, every solved shift.