SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · General Intelligence and Reasoning · Question 20 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 7 $ 3 = 58 and 6 $ 2 = 40, what is 5 $ 1?

(a)26
(b)24
(c)28
(d)22

Answer

Why

Correct — A. Compare each result with the square of the first number.

Rule: a $ b = a² + b².

7 $ 3 = 49 + 9 = 58
6 $ 2 = 36 + 4 = 40
Both samples fit.

5 $ 1 = 25 + 1 = 26, option (a).

Why the others are wrong

(b)
24 — 24 = 5² − 1², a difference of squares. Tried on the first sample it gives 49 − 9 = 40, not 58, so subtraction is the wrong operation.
(c)
28 — 28 is 2 more than the rule's 26. Adding 2 breaks the first sample: 49 + 9 + 2 = 60, not 58.
(d)
22 — 22 is less than 5² = 25 on its own, but both samples add a positive square to the first square: 58 = 49 + 9 and 40 = 36 + 4.

Concept

In a defined-operation puzzle the symbol stands for a rule you rebuild from the samples. Try simple candidates on the first pair, then keep one only if it fits every sample.

Here each result sits just above the square of the first number: 58 is 49 plus 9, and 40 is 36 plus 4. The extra is the square of the second number.

Another form fits the samples too: 2 × a × b + 16 gives 58 and 40. It also gives 26 for 5 $ 1, because a − b is 4 in all three pairs and a² + b² = (a − b)² + 2ab. The answer does not depend on which form you find.

Key facts

7² + 3² = 58 and 6² + 2² = 40.
5² + 1² = 26.
A candidate rule must reproduce every given sample, not just the first.

Study next

Defined operations built on squares, such as (a + b)²Defined operations mixing product and sum, such as a × b + a + bSquares of 1 to 30 by sight

Common traps

Testing a rule on one sample only, when it has to give both 58 and 40.
Adding before squaring: (7 + 3)² = 100, not 58.

The two-sample format is also set at 12 Sep 2025, 16:00, Reasoning Q.16, where 6 $ 2 = 20 and 4 $ 3 = 19 fit a × b + a + b, giving 5 $ 2 = 17. Same symbol, different rule, so rebuild it from the samples.

12 Sep 2025, 12:30, Reasoning Q.24 defines its operation, A % B, inside the question instead.

Related PYQs

No directly related past PYQ was found.

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