If $0<r<1<\mathrm{s}<2$, which of the following mu... | Free GMAT Practice Question | GMAT Panda

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If 0 < r < 1 < s < 2, which of the following must be less than 1 ? I. \frac{r}{s} II. rs III. s - r

Explanation	Calculations	Help
$Determine whether \frac{r}{s} is always less than 1 by comparing numerator and denominator$	$r < 1 s > 1 \frac{r}{s} < \frac{1}{s} < 1$
$Check whether rs must be less than 1 by testing with sample values$	$r = \frac{3}{4}, s = \frac{3}{2} rs = \frac{3}{4} \times \frac{3}{2} = \frac{9}{8} > 1$
$Check whether s - r must be less than 1 by testing with sample values$	$s = \frac{9}{5}, r = \frac{1}{2} s - r = \frac{9}{5} - \frac{1}{2} = \frac{18}{10} - \frac{5}{10} = \frac{13}{10} > 1$

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I only (A)

If 0 < r < 1 < s < 2, which of the following must be less than 1 ? I. \frac{r}{s} II. rs III. s - r

Explanation	Calculations	Help
$Determine whether \frac{r}{s} is always less than 1 by comparing numerator and denominator$	$r < 1 s > 1 \frac{r}{s} < \frac{1}{s} < 1$
$Check whether rs must be less than 1 by testing with sample values$	$r = \frac{3}{4}, s = \frac{3}{2} rs = \frac{3}{4} \times \frac{3}{2} = \frac{9}{8} > 1$
$Check whether s - r must be less than 1 by testing with sample values$	$s = \frac{9}{5}, r = \frac{1}{2} s - r = \frac{9}{5} - \frac{1}{2} = \frac{18}{10} - \frac{5}{10} = \frac{13}{10} > 1$

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I only (A)