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If r and s are positive numbers and s > r, then r/s will always be < 1.

If given that r>0, s>0 and s>r then divide s>r by s (we can safely do that since s>0): 1>r/s.

Complete solution:

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

A. I only B. II only C. III only D. I and II E. I and III

Notice that we are asked "which of the following MUST be lees than 1, not COULD be less than 1. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: \(0 < r < s\) --> divide by \(s\) (we can safely do this since we know that \(s>0\)) --> \(\frac{r}{s}<1\), so I must be true;

II. rs: if \(r=\frac{9}{10}<1\) and \(1<(s=\frac{10}{9})<2\) then \(rs=1\), so this statement is not alway true;

III. s-r: if \(r=0.5<1\) and 1\(<(s=1.5)<2\) then \(s-r=1\), so this statement is not alway true.

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