GATE 2022 MN – Question 7

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

Consider the following inequalities.

(i) $2x-1>7$

(ii) $2x-9<1$

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

$x\le-4$
$-4<x\le4$
$4<x<5$
$x\ge5$

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Show answer and explanation

Correct answer: (C) $4<x<5$

Explanation

Solve each inequality separately. From 2x−1>7, add one and divide by two to obtain x>4. From 2x−9<1, add nine and divide by two to obtain x<5. Their intersection is $4<x<5$, option C. Both endpoints are excluded because the original inequalities are strict.

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