SSC CGL 2025 Tier-I · 17 September 2025, Shift 2 · General Intelligence and Reasoning · Question 17 of 99

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.

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If 4 @ 3 = 19 and 2 @ 5 = 9, then 5 @ 2 = ?

(a)21
(b)23
(c)25
(d)27

Answer

Why

Correct — D.
Rule: a @ b = a² + b (square the first number, add the second).

Check: 4 @ 3 = 16 + 3 = 19 ✓
Check: 2 @ 5 = 4 + 5 = 9 ✓

Apply: 5 @ 2 = 25 + 2 = 27 → option (d).

Why the others are wrong

(a)
21 — 21 is 5² − 2² = 25 − 4. That rule fails the first example: 4² − 3² = 16 − 9 = 7, not 19.
(b)
23 — 23 is 5² − 2 = 25 − 2. That rule fails the first example: 4² − 3 = 13, not 19.
(c)
25 — 25 is 5² alone, dropping the second number. The examples need it added: 4² = 16, and only 16 + 3 gives 19.

Concept

In a defined-operation item the symbol stands for a formula you recover from the examples. Try the simple candidates, such as a sum, a product, or a square plus or minus the other number, and keep one that fits every example.

Here a² + b fits both lines. The operation is not symmetric: 2 @ 5 = 9, but 5 @ 2 = 27, because the number being squared changes.

Another rule also fits both examples: 5a − 1 gives 19 for a = 4 and 9 for a = 2. It predicts 5 @ 2 = 24, which is not an option, so a² + b is the rule the options support.

Key facts

4 @ 3 = 4² + 3 = 19 and 2 @ 5 = 2² + 5 = 9.
5 @ 2 = 5² + 2 = 27.
Swapping the numbers changes the result: 2 @ 5 = 9 but 5 @ 2 = 27.

Study next

Defined operations built on a² + b²Defined operations built on ab + a + bOdd-one-out items where one equation breaks the operation's rule

Common traps

Checking a rule against one example and stopping, when it must fit both 4 @ 3 and 2 @ 5
Assuming 5 @ 2 equals 2 @ 5 because the same two numbers appear

12 Sep 2025, 16:00, Reasoning Q.19 uses the same a² + b rule: 5 @ 3 = 28, 4 @ 2 = 18, keyed 6 @ 4 = 40.

17 Sep 2025, 09:00, Reasoning Q.21 changes it to a² + b²: 2 @ 3 = 13, 3 @ 4 = 25, keyed 4 @ 5 = 41.

Related PYQs

No directly related past PYQ was found.

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