The GATE Grind

GATE 2023 ME – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Consider the following inequalities
$p^2 - 4q < 4$
$3p + 2q < 6$
where $p$ and $q$ are positive integers.

The value of $(p + q)$ is _______.

  1. 2
  2. 1
  3. 3
  4. 4

Practise this question in The GATE Grind →

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 $p + q = 2$.