SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · General Intelligence and Reasoning · Question 21 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 2 @ 3 = 13, 3 @ 4 = 25, then what is 4 @ 5?

(a)36
(b)39
(c)41
(d)33

Answer

Why

Correct — C.
Rule: a @ b = a² + b² (square each number, then add).

Check 2 @ 3: 4 + 9 = 13 ✓
Check 3 @ 4: 9 + 16 = 25 ✓
Apply 4 @ 5: 16 + 25 = 41 → option (c)

Why the others are wrong

(a)
36 — 36 falls 5 short of 4² + 5² = 41. It fits a 'next square' guess from 25 = 5², but 13 is not a square, so that guess is not the rule.
(b)
39 — 39 is 2 × 4 × 5 − 1. The examples need +1, not −1: 2 × 2 × 3 + 1 = 13, so 4 @ 5 = 40 + 1 = 41.
(d)
33 — 33 falls 8 short of 16 + 25 = 41. The results rise from 13 to 25 by 12; 33 would mean the next rise shrinks to 8.

Concept

Operator puzzles hide a rule in two worked examples. Test what the example numbers could produce, such as a sum of squares or a product plus a constant, and keep the rule that fits both.

Here 13 = 4 + 9 and 25 = 9 + 16, a sum of squares. Note that 3 @ 4 = 25 is the familiar 3² + 4² = 5².

Because each pair is consecutive (b = a + 1), a² + b² equals 2 × a × b + 1 here: 13 = 12 + 1, 25 = 24 + 1, and 4 @ 5 = 40 + 1 = 41. The key holds under either reading.

Key facts

The rule here: a @ b = a² + b².
For consecutive numbers, a² + (a + 1)² = 2a(a + 1) + 1, so both readings give 41.
Squares to know by heart: 4, 9, 16, 25, 36.

Study next

Operator puzzles built on a² + b, a² + b² and a × (a + b)Squares up to 30² for quick pattern spottingPythagorean triples such as 3-4-5 and 5-12-13

Common traps

Reading 3 @ 4 = 25 as 5² and guessing that the next result is the next square, 36.
Getting the form right but the constant wrong: 2 × 4 × 5 − 1 = 39.

At 12 Sep 2025, 16:00, Reasoning Q.19, 5 @ 3 = 28 and 4 @ 2 = 18 fix a different rule, a² + b (25 + 3, 16 + 2), and 6 @ 4 is keyed 40.

Reasoning Q.20 of this paper, 6 * 3 = 54, is solved by the same method, testing the rule on both examples, but its rule is different: 3 × a × b.

Related PYQs

No directly related past PYQ was found.

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