SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · General Intelligence and Reasoning · Question 22 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 13 September 2026.

Where this paper and its answers come from

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 3 @ 4 = 19, 5 @ 6 = 41, then what is 6 @ 7?

(a)49
(b)55
(c)61
(d)65

Answer

Why

Correct — B.
Rule: a @ b = a × b + a + b.

Check: 3 @ 4 = 12 + 3 + 4 = 19 ✓
Check: 5 @ 6 = 30 + 5 + 6 = 41 ✓

6 @ 7 = 42 + 6 + 7 = 55 → option (b).

Why the others are wrong

(a)
49 — 49 is 6 × 7 + 7, which drops the first number. The rule adds both: 3 @ 4 needs 12 + 3 + 4 to reach 19.
(c)
61 — 61 would need 19 added to 6 × 7 = 42. The rule adds only the two numbers, 6 + 7 = 13, which gives 55.
(d)
65 — 65 is 10 above the rule's value. 6 × 7 = 42, and adding 6 and 7 gives 55, just as 5 @ 6 gave 30 + 11 = 41.

Concept

Operator puzzles define a new symbol through examples. Test simple combinations, such as product, sum and squares, on both given pairs before trusting one.

a × b + a + b is the same as (a + 1)(b + 1) − 1: 4 × 5 − 1 = 19, 6 × 7 − 1 = 41, 7 × 8 − 1 = 55.

A second rule, b² + a, also fits: 16 + 3 = 19 and 36 + 5 = 41, and it too gives 49 + 6 = 55.

Key facts

a × b + a + b = (a + 1)(b + 1) − 1.
3 @ 4 = 19 and 5 @ 6 = 41 fit both a × b + a + b and b² + a.
Both rules give 6 @ 7 = 55.

Study next

Operator puzzles built on squares: (a + b)² and a² + b²Rewriting ab + a + b as (a + 1)(b + 1) − 1Number analogies where both examples must fit one rule

Common traps

Testing a rule on the first pair only: a² + 2b + 2 gives 19 for 3 @ 4 but 39 for 5 @ 6
Dropping one of the two added numbers in the last step: 42 + 7 = 49

The same @ format hides different rules: at 14 Sep 2025, 16:00, Reasoning Q.20 it is (a + b)², keyed 81 for 4 @ 5, and at 17 Sep 2025, 09:00, Reasoning Q.21 it is a² + b², keyed 41 for 4 @ 5.

Related PYQs

No directly related past PYQ was found.

Topic: Symbolic/Number Analogy — all 210 SSC CGL questions on it, every solved shift.