If 5 3 = 19 and 7 2 = 17 , what is 9 1 ?

Question

If 5 3 = 19 and 7 2 = 17 , what is 9 1 ?

1. A. 12
2. B. 10
3. C. 8
4. D. 11 (Correct answer)

Correct Answer

Option D — 11

Detailed Solution & Explanation

The correct answer is 11.

Key Points

• Find a rule satisfying both worked pairs. Here a # b = b × (a + 1) + 1.
• Check: 5 # 3 = 3 × (5 + 1) + 1 = 3 × 6 + 1 = 19 ✓
• Check: 7 # 2 = 2 × (7 + 1) + 1 = 2 × 8 + 1 = 17 ✓
• Apply it: 9 # 1 = 1 × (9 + 1) + 1 = 10 + 1 = 11.

Additional Information

• Equivalently the rule is ab + b + 1, which is often quicker to evaluate mentally.
• A rule fitting only the first pair is worthless. Testing on the second pair is what separates the correct definition from the several that coincidentally produce 19.
• Definitions frequently used in this question type: a + 2b, 2a + b, ab + a + b, a² + b, a² − b², and b(a + 1). Work through them in order rather than guessing, and stop as soon as one satisfies both examples.

प्रश्न (हिन्दी में)

यदि 5 3 = 19 और 7 2 = 17 , तो 9 1 क्या है?

1. A. 12
2. B. 10
3. C. 8
4. D. 11