0<r<1<s<2

[Capthan]

If 0<r<1<s<2, which one is less than 1

I. r/s
II. rs
III. s-r

1) I only
2) II only
3) III only
4) I & II
5 I & III

Please explain why the correct answer is 1)
Thanks

[TP]

If 0<r<1<s<2, which one is less than 1

I. r/s
II. rs
III. s-r

1) I only
2) II only
3) III only
4) I & II
5 I & III

Please explain why the correct answer is 1)
Thanks

I. Any number between 0 & 1 divided by any number between 1 & 2, will always be < 1
II. 2 cases: Consider r = 0.9 and s = 1.5, rs = 1.35. Consider r = 0.1 and s = 1.1, then rs = 0.11, so not true
III. 2 cases: 1.9 - 0.1 = 1.8 (this is > 1), 1.1 - 0.9 = 0.2 (< 1)

hence only I

[RonPurewal]

when you consider a problem like this, in which you are GIVEN INEQUALITIES, you should always CONSIDER THE EXTREMES of the given inequalities.

this technique is very simplistic, yet very powerful: consider the extremes to find the extremes.
therefore, it's sufficient to think about, say, 0.1 and 0.9 for r, and 1.1 and 1.9 for s.

statement (i): 0.1/1.1, 0.9/1.1, 0.1/1.9, and 0.9/1.9 are all less than 1, so you're good.
statement (ii): works for (0.1)(1.1), (0.9)(1.1), and (0.1)(1.9), but NOT (0.9)(1.9).
statement (iii): only works for 1.1 - 0.9, doesn't work for any of the other pairs.

notice that this method is systematic: you don't just generate numbers at random, you generate numbers at the extremes of the intervals dictated by the inequality/ies.

good stuff.