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GATE 2022 CY – Question 8

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

Consider (i) $3p-q<4$ and (ii) $3q-p<12$. Which expression satisfies the above two inequalities?

  1. $p+q<8$
  2. $p+q=8$
  3. $8\le p+q<16$
  4. $p+q\ge16$

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Show answer and explanation

Correct answer: (A) $p+q<8$

Explanation

Add the inequalities to obtain 2p+2q<16. Dividing by positive 2 preserves the inequality, giving **p+q<8, A**. This is a necessary consequence of both given inequalities, even though it does not alone imply them separately.