SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · General Intelligence and Reasoning · Question 17 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 5 $ 2 = 27 and 7 $ 3 = 64, what is 6 $ 4?

(a)10
(b)12
(c)8
(d)14

Answer

Why

Correct — C.
Rule: a $ b = (a − b)³.

5 $ 2: (5 − 2)³ = 3³ = 27, as given
7 $ 3: (7 − 3)³ = 4³ = 64, as given

6 $ 4: (6 − 4)³ = 2³ = 8 → option (c).

Why the others are wrong

(a)
10 — 10 is 6 + 4, the plain sum. The sum fails the examples: 5 + 2 is 7, not 27. It is not a cube either, and both examples give cubes.
(b)
12 — 12 is not a cube. Both given results are cubes (27 = 3³, 64 = 4³), so the answer must be one too, and 12 lies between 2³ = 8 and 3³ = 27.
(d)
14 — 14 is not a cube, so no difference cubed produces it. With a − b = 2, the result has to be 2³ = 8.

Concept

A symbol puzzle hides an arithmetic rule. Find a rule that fits every example, then apply it once.

The results here, 27 and 64, are 3³ and 4³, and 3 and 4 are exactly the differences 5 − 2 and 7 − 3. Recognising the results as cubes is the fastest way in.

Test a candidate rule on both examples before using it. a² + b fits 5 $ 2 (25 + 2 = 27) but gives 52 for 7 $ 3, so it is out.

Key facts

Cubes to memorise: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
A rule is confirmed when it reproduces every given example, not just the first.

Study next

Symbol puzzles built on a² + b² or (a + b)²Rules that combine two operations, such as (a − b) × bRecognising squares up to 20² and cubes up to 10³

Common traps

Stopping at a rule that fits the first example, such as a² + b, without testing the second.
Picking 10 because it is the sum 6 + 4, a rule neither example supports.

14 Sep 2025, 12:30, Reasoning Q.18 asks for the same 6 $ 4 from different examples (9 $ 3 = 18, 8 $ 2 = 12). Its rule is (a − b) × b, and it is also keyed 8.

12 Sep 2025, 12:30, Reasoning Q.20 uses a² + b²: 7 $ 3 = 58 and 6 $ 2 = 40, keyed 26 for 5 $ 1.

Related PYQs

No directly related past PYQ was found.

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