SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · 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 11 September 2026.

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If 10 @ 2 = 120 and 5 @ 5 = 100, what is 8 @ 3?

(a)80
(b)96
(c)108
(d)110

Answer

Why

Correct — D.
Rule: a @ b = (a + b) × 10.

10 @ 2: (10 + 2) × 10 = 120 ✓
5 @ 5: (5 + 5) × 10 = 100 ✓

8 @ 3: (8 + 3) × 10 = 11 × 10 = 110 → option (d).

Why the others are wrong

(a)
80 — 80 is 8 × 10: it drops the 3. The rule multiplies the sum, 8 + 3 = 11, by 10, which gives 110.
(b)
96 — 96 = 8 × 3 × 4 copies the × 4 that turns 5 × 5 into 100. But 10 × 2 × 4 = 80, not 120, so a product rule fails the first example.
(c)
108 — 108 would need the sum, 11, multiplied by about 9.8. Both examples fix the multiplier at exactly 10, so 8 @ 3 is 110.

Concept

@ is a made-up operation. Find one rule that turns both examples into their results, then apply it to the question.

The sums are the clue: 10 + 2 = 12 and 5 + 5 = 10, and the results are those sums times ten, 120 and 100. So @ adds the two numbers and multiplies by 10.

(a + b) × a also gives 120 for 10 @ 2, because a happens to be 10 there. It fails 5 @ 5, which would come to 50, so the multiplier is a fixed 10, not the first number.

Key facts

Test a candidate rule on every example before applying it.
(10 + 2) × 10 = 120 and (5 + 5) × 10 = 100.
A product rule cannot work here: 10 × 2 = 20 and 5 × 5 = 25 would need different multipliers, 6 and 4.

Study next

Symbol operations of the form (a + b) × a or (a + b) × bSymbol operations built on squares, such as a² + bPicking the odd equation out among several a @ b results

Common traps

Trying (a + b) × a because it fits 10 @ 2: it gives 50 for 5 @ 5, so it cannot be the rule
Settling on a product rule from one example: 5 × 5 × 4 = 100 fits, but 10 × 2 × 4 = 80 does not

15 Sep 2025, 12:30, Reasoning Q.21 also adds and then multiplies, by the first number, (a + b) × a, and keys 60 for 6 and 4.

14 Sep 2025, 12:30, Reasoning Q.15 multiplies the sum by the second number, (a + b) × b, and keys 20 for 8 @ 2.

Related PYQs

No directly related past PYQ was found.

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