3 r 4 s+5 |s| 5...

Question

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

GMAT Panda · Accepted Answer

20 We turn the absolute value condition on s into a range for s. |s| 5[[LB]]-5 s[[LB]]s 5 We isolate r by dividing the inequality 3r 4s + 5 by the positive number 3. 3r 4s + 5 r 4s + 5/3 We find the highest bound for r by using the largest s=5. r 4 5 + 5/3 = 25/3 8.33 We compare this bound to each choice and see that 20 exceeds about 8.33. 20 > 25/3 8.33

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

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