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Question

Consider the following inequalities: p^2 - 4q < 4, and 3p + 2q < 6, where p and q are positive integers. The value of (p+q) is _______.

Accepted Answer

The correct answer is (A) 2. For positive integers, the smallest possible values are p=1,q=1. Checking: p^2-4q=1-4=-3<4 (satisfied), and 3p+2q=3+2=5<6 (satisfied). Trying p=1,q=2 gives 3+4=7, not <6 (fails); p=2,q=1 gives 6+2=8, not <6 (fails). So (p,q)=(1,1) is the only valid pair, giving p+q=2.

Explanation