SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · General Intelligence and Reasoning · Question 18 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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If 9 $ 3 = 18, 8 $ 2 = 12, then what is 6 $ 4?

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

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 = 6 × 3 = 18, as given
8 $ 2: (8 − 2) × 2 = 6 × 2 = 12, as given
6 $ 4: (6 − 4) × 4 = 2 × 4 = 8

That is option (a).

Why the others are wrong

(b)
10 — 10 is 6 + 4, the rule a + b. It fails the first example: 9 + 3 = 12, not 18.
(c)
12 — 12 is 2 × 6, the rule 2a. That fits 9 $ 3 = 18 but gives 16 for 8 $ 2, where the paper prints 12.
(d)
14 — 14 is 6 + 2 × 4, the rule a + 2b. On the first example it gives 9 + 6 = 15, not 18.

Concept

An operator item defines a symbol only through examples. Find a rule, then test it on every example before using it: 2a fits 9 $ 3 = 18 and fails at 8 $ 2.

Here both results are multiples of b: 18 = 6 × 3 and 12 = 6 × 2. The 6 is a − b in both examples, which gives (a − b) × b, the same as ab − b².

Both examples have a − b = 6, so on their own they also fit a plain 6 × b. That gives 6 $ 4 = 24, which is not an option.

Reading the 6 as a − b is what the options support.

Key facts

(a − b) × b turns 9 $ 3 into 6 × 3 = 18 and 8 $ 2 into 6 × 2 = 12.
(a − b) × b is the same as ab − b², so 6 $ 4 = 24 − 16 = 8.
A plain 6 × b also fits both examples but gives 24, which no option offers.

Study next

Operator rules built from a difference, such as (a − b)²Operator items with three examples that rule out look-alike formulasMissing-number grids that hide the same kind of rule

Common traps

Taking 2a from the first example alone and answering 12.
Adding the two numbers, as if $ meant +, and answering 10.

Reasoning Q.15 of this shift uses the companion rule (a + b) × b: 9 @ 3 = 36, so 8 @ 2 = 20.

At 17 Sep 2025, 16:00, Reasoning Q.5, 3 @ 2 = 7, 6 @ 3 = 21 and 8 @ 2 = 22 fit a × b + (a − b), so 5 @ 4 = 21.

Related PYQs

No directly related past PYQ was found.

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