Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers.

Question

Let p + q = 10, where p, q are integers.

Value-I = Maximum value of p × q when p, q are positive integers.

Value-II = Maximum value of p × q when p ≥ −6, q ≥ −4.

Which one of the following is correct?

1. A. Value-I < Value-II
2. B. Value-II < Value-I
3. C. Value-I = Value-II (Correct answer)
4. D. Cannot be determined due to insufficient data

Correct Answer

Option C — Value-I = Value-II

Detailed Solution & Explanation

The correct answer is Value-I = Value-II.

Key Points

• p+q=10. Value-I: max p×q for positive integers: p=5,q=5 → 25. Value-II: max p×q for p≥−6, q≥−4, p+q=10. q = 10−p. f(p) = p(10−p).
• If p=−6: (−6)(16)=−96. If q=−4: p=14, 14×(−4)=−56. Max is still at p=5: 5×5=25. Value-I = Value-II = 25. Answer: Value-I = Value-II.