If $1< u<4$ and $2< v<5$, which of the following m... | Free GMAT Practice Question | GMAT Panda

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If 1 < u < 4 and 2 < v < 5, which of the following must be less than 2? I . v - u II . \frac{u + v}{3} III . \frac{u}{v}

Explanation	Calculations	Help
$We test whether " v - u " is always less than 2 by finding a counterexample.$	$u = 1.5 v = 4.1 v - u = 4.1 - 1.5 = 2.6 > 2$
$We test whether " \frac{u + v}{3} " is always less than 2 by finding a counterexample.$	$u = 3.5 v = 4.5 \frac{u + v}{3} = \frac{3.5 + 4.5}{3} = \frac{8}{3} \approx 2.67 > 2$
$We use the bounds on u and v to see that " \frac{u}{v} " must be less than 2.$	$u < 4 v > 2 \frac{u}{v} < \frac{4}{v} \frac{4}{v} < 2 \frac{u}{v} < 2$	Theory & Tactics Method Card INEQ1-A Click to view full details Theory & Tactics Method Card INEQ1-C Click to view full details

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C

If 1 < u < 4 and 2 < v < 5, which of the following must be less than 2? I . v - u II . \frac{u + v}{3} III . \frac{u}{v}

Explanation	Calculations	Help
$We test whether " v - u " is always less than 2 by finding a counterexample.$	$u = 1.5 v = 4.1 v - u = 4.1 - 1.5 = 2.6 > 2$
$We test whether " \frac{u + v}{3} " is always less than 2 by finding a counterexample.$	$u = 3.5 v = 4.5 \frac{u + v}{3} = \frac{3.5 + 4.5}{3} = \frac{8}{3} \approx 2.67 > 2$
$We use the bounds on u and v to see that " \frac{u}{v} " must be less than 2.$	$u < 4 v > 2 \frac{u}{v} < \frac{4}{v} \frac{4}{v} < 2 \frac{u}{v} < 2$	Theory & Tactics Method Card INEQ1-A Click to view full details Theory & Tactics Method Card INEQ1-C Click to view full details

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C