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If 0 < r < 1 < s < 2, which of the following

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Intern
Joined: 10 Oct 2008
Posts: 14
Followers: 0

Kudos [?]: 4 [0], given: 0

If 0 < r < 1 < s < 2, which of the following [#permalink]  10 Oct 2008, 10:29
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
Manager
Joined: 09 Oct 2008
Posts: 94
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: o,r.1,2 [#permalink]  10 Oct 2008, 17:14
IMO A:

s = 1.5 < 2
r = 0.5 < 1

s-r =1.5 -0.5 = 1 which is not <1

* we are asked 'must be' in question
VP
Joined: 30 Jun 2008
Posts: 1048
Followers: 11

Kudos [?]: 344 [1] , given: 1

Re: o,r.1,2 [#permalink]  10 Oct 2008, 19:20
1
KUDOS
Pick up two numbers for r and s. I picked up r=1/2 and s=3/2

I. r/s = 1/3 this is < 1 true.
II. rs = 3/4 this is < 1 true.
III. s-r = 3/2-1/2 = 1 this is NOT < 1 false

lets try with r=2/3 and 3/2 as well.

I. r/s = 1/3 this is < 1 true.
II. rs = 1 this is NOT < 1 false
III. s-r = 3/2-1/2 = 5/6 this is < 1 true.

Only the first equation seems to be ALWAYS true. So A must be the answer.
_________________

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Re: o,r.1,2   [#permalink] 10 Oct 2008, 19:20
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