Comparative - maximum value of p x q
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?
Options
Value-I < Value-II
Value-II < Value-I
Value-I = Value-II
Cannot be determined due to insufficient data
Explanation
We need to maximize p × q given p + q = 10. For Value-I, p and q are positive integers. The product of two numbers with a constant sum is maximized when the numbers are as close to each other as possible. Thus, p=5 and q=5, yielding a max product of 25. For Value-II, the constraints are p \ge -6 and q \ge -4. The unconstrained maximum occurs at p=5, q=5. Since these values perfectly satisfy the boundary conditions (5 \ge -6 and 5 \ge -4), the maximum product remains exactly 25.
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q56
Section
Data Interpretation & Sufficiency
Sub-topic
Comparative Quantitative
Type
Comparative quantitative
Difficulty
Medium
Source hint
Quantitative comparison
Same sub-topic — other years
Comparative Quantitative has appeared in multiple CSAT papers:
See all questions on Comparative Quantitative
Browse every tagged question across all years