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Question

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

GMAT Panda · Accepted Answer

I only (A) Determine whether r/s is always less than 1 by comparing numerator and denominator r < 1 s > 1 r/s < 1/s < 1 Check whether rs must be less than 1 by testing with sample values r = 3/4, s = 3/2 rs = 3/4 3/2 = 9/8 > 1 Check whether s - r must be less than 1 by testing with sample values s = 9/5, r = 1/2 s - r = 9/5 - 1/2 = 18/10 - 5/10 = 13/10 > 1

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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