GATE CH 2022 | GA Question: 8

Question

​​​​​​​Consider the following inequalities.

1. $3p \:– q < 4$
2. $3q \:– p < 12$

Which one of the following expressions below satisfies the above two inequalities?

• A. $p + q < 8$
• B. $p + q = 8$
• C. $8 \leq p + q < 16$
• D. $p + q \geq 16$

Answer 1

Given that, 

• $3p-q<4 \quad \longrightarrow (1)$
• $3q-p<12 \quad \longrightarrow (2)$

Adding the equation $(1)\; \& \; (2).$

$3p-q + 3q-p < 4 + 12$

$\Rightarrow 2p + 2q < 16$

$\Rightarrow 2(p + q) < 16$

$\Rightarrow {\color{Green} {\boxed{p + q < 8}}}$

Correct Answer $:\text{A}$