GMAT Inequalities Explained — 3 r \leq 4 s+5 |s| \leq 5...

3 r \leq 4 s + 5 ∣ s ∣ \leq 5 Given the inequalities above, which of the following CANNOT be the value of r ?

inequalitiesabsolute valuessimultaneous equations

Explanation	Calculations	Help
$We turn the absolute value condition on s into a range for s .$	$∣ s ∣ \leq 5 - 5 \leq s s \leq 5$	Theory & Tactics Method Card INEQ3 Click to view full details
$We isolate r by dividing the inequality 3 r \leq 4 s + 5 by the positive number 3.$	$3 r \leq 4 s + 5 r \leq \frac{4 s + 5}{3}$	Theory & Tactics Method Card INEQ1-A Click to view full details
$We find the highest bound for r by using the largest s = 5 .$	$r \leq \frac{4 \times 5 + 5}{3} = \frac{25}{3} \approx 8.33$
$We compare this bound to each choice and see that 20 exceeds about 8.33.$	$20 > \frac{25}{3} \approx 8.33$

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