If $0 < t < 0.5 < u < 1.5$, which of the following... | Free GMAT Practice Question | GMAT Panda

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If 0 < t < 0.5 < u < 1.5, which of the following must be less than 1? I. t + t^{2}; II. u - t; III. \frac{t}{u}

Explanation	Calculations	Help
$We first consider "t + t^{2} " . Since t is less than 0.5 and its square is under 0.25, adding them shows the sum is under 1.$	$t < 0.5 t^{2} < 0.25 t + t^{2} < 0.5 + 0.25 = 0.75$	Theory & Tactics Method Card INEQ1-D Click to view full details
$We then examine "u - t" . Since u can be as large as 1.5 and t can be as small as 0, the difference can reach 1.5, which is more than 1.$	$u < 1.5 - t < 0 u - t < 1.5 + 0 = 1.5$	Theory & Tactics Method Card INEQ1-D Click to view full details
$Finally, we look at " \frac{t}{u} " . Because u exceeds 0.5 and t is below 0.5, dividing gives a result below 1.$	$t < 0.5 u > 0.5 \frac{t}{u} < \frac{0.5}{0.5} = 1$	Theory & Tactics Method Card INEQ1-A Click to view full details

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E

If 0 < t < 0.5 < u < 1.5, which of the following must be less than 1? I. t + t^{2}; II. u - t; III. \frac{t}{u}

Explanation	Calculations	Help
$We first consider "t + t^{2} " . Since t is less than 0.5 and its square is under 0.25, adding them shows the sum is under 1.$	$t < 0.5 t^{2} < 0.25 t + t^{2} < 0.5 + 0.25 = 0.75$	Theory & Tactics Method Card INEQ1-D Click to view full details
$We then examine "u - t" . Since u can be as large as 1.5 and t can be as small as 0, the difference can reach 1.5, which is more than 1.$	$u < 1.5 - t < 0 u - t < 1.5 + 0 = 1.5$	Theory & Tactics Method Card INEQ1-D Click to view full details
$Finally, we look at " \frac{t}{u} " . Because u exceeds 0.5 and t is below 0.5, dividing gives a result below 1.$	$t < 0.5 u > 0.5 \frac{t}{u} < \frac{0.5}{0.5} = 1$	Theory & Tactics Method Card INEQ1-A Click to view full details

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E