GATE 2023 AR — Architecture – Question 7
Consider the following inequalities
$p^2 - 4q < 4$
$3p + 2q < 6$
where $p$ and $q$ are positive integers.
The value of $(p + q)$ is _______.
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Show answer and explanation
Correct answer: (A) 2
Explanation
From $3p + 2q < 6$ with $q \ge 1$ we get $3p < 4$, so $p = 1$. Then $2q < 3$, which gives $q = 1$. Check the first inequality: $1 - 4 = -3 < 4$, true. So $p + q = 2$.
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