Consider the following inequalities p^2 - 4q < 4 3p + 2q < 6 where p and q are positive integers. The value of (p + q) is __________. A. 2 B. 1 C. 3 D. 4

GATE 2023 · General Aptitude · Inequality · medium

Answer: The unique positive integer solution is (p, q) = (1, 1), giving p + q = 2.

1. Bound p using Constraint 2: Since p is a positive integer and p < 4/3 ~ 1.33, we must have p = 1.
2. Bound q using Constraint 2 with p = 1: Since q is a positive integer and q < 1.5, we must have q = 1.
3. Verify (p, q) = (1, 1) against both constraints: Constraint 1: (1)^2 - 4(1) = 1 - 4 = -3 < 4. TRUE. Constraint 2: 3(1) + 2(1) = 5 < 6. TRUE. Both satisfied.
4. Compute p + q: p + q = 2.