If \(5\ @\ 3 = 28\) and \(4\ @\ 2 = 18\) , then what is \(6\ @\ 4\) ?

Question

If \(5\ @\ 3 = 28\) and \(4\ @\ 2 = 18\) , then what is \(6\ @\ 4\) ?

1. A. 40 (Correct answer)
2. B. 52
3. C. 64
4. D. 76

Correct Answer

Option A — 40

Detailed Solution & Explanation

The correct answer is 40.

Key Points

• Look for a rule satisfying both pairs. Here a @ b = a² + b.
• Check: 5 @ 3 = 25 + 3 = 28 ✓ and 4 @ 2 = 16 + 2 = 18 ✓.
• Applying it: 6 @ 4 = 36 + 4 = 40.
• When the outputs grow much faster than the inputs, try squaring one operand before trying more elaborate combinations.
• Verify a candidate rule on both given pairs before applying it; a rule fitting only one pair will usually still produce one of the wrong options, which is how the distractors are designed.
• Common patterns in these questions: a² + b, a² − b, ab + a + b, (a + b)², and a² − b².

Additional Information

• Where outputs grow far faster than inputs, suspect a squared or cubed term before trying additive combinations.
• Validate every candidate rule on both worked pairs; a rule fitting only one pair will usually still land on a distractor, which is precisely how they are built.
• Frequently used definitions: a² + b, a² − b, ab + a, ab − b, (a + b)² and (a − b)².

प्रश्न (हिन्दी में)

यदि \(5\ @\ 3 = 28\) और \(4\ @\ 2 = 18\) है, तो \(6\ @\ 4\) क्या है?

1. A. 40
2. B. 52
3. C. 64
4. D. 76