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0<r<1<s<2

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Capthan
 Post subject: 0<r<1<s<2
 Post Posted: Wed Sep 03, 2008 3:46 pm 
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
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TP
 Post subject: Re: 0<r<1<s<2
 Post Posted: Wed Sep 03, 2008 4:59 pm 
Capthan wrote:
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
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RonPurewal
 Post subject:
 Post Posted: Fri Sep 26, 2008 4:47 am 
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ManhattanGMAT Staff


Posts: 7146
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.
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