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GATE 2022 IN – 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 follows from the two inequalities?

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

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

Explanation

Adding 3p−q<4 and 3q−p<12 gives 2p+2q<16. Divide by two to obtain **p+q<8, A**. The bound is strict because both premises are strict.