If \(6\ \\ 2 = 20\) and \(4\ \\ 3 = 19\) , then \(5\ \\ 2 = ?\)

Question

If \(6\ \\ 2 = 20\) and \(4\ \\ 3 = 19\) , then \(5\ \\ 2 = ?\)

1. A. 18
2. B. 17 (Correct answer)
3. C. 16
4. D. 15

Correct Answer

Option B — 17

Detailed Solution & Explanation

The correct answer is 17.

Key Points

• Test a rule against both given pairs before using it. Here a $ b = ab + a + b.
• Check: 6 $ 2 = 12 + 6 + 2 = 20 ✓ and 4 $ 3 = 12 + 4 + 3 = 19 ✓.
• Applying it: 5 $ 2 = 10 + 5 + 2 = 17.
• Note ab + a + b = (a + 1)(b + 1) − 1, which is often quicker: 6 × 3 − 1 = 17.
• A rule that fits only the first pair is worthless — always validate on the second.

Additional Information

• Symbol-definition questions supply a made-up operator and expect you to infer its rule from worked examples.
• Test candidate rules in a fixed order — a + b, a − b, ab, ab + a + b, a² + b, a² − b² — and reject any that fails the second pair.
• Note that ab + a + b = (a + 1)(b + 1) − 1, a factored form that turns the arithmetic into a single multiplication.

प्रश्न (हिन्दी में)

यदि \(6\ \\ 2 = 20\) और \(4\ \\ 3 = 19\) है, तो \(5\ \\ 2 = ?\)

1. A. 18
2. B. 17
3. C. 16
4. D. 15