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# If 0 < r < 1 < s < 2, which of the following must be less than 1? I.

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If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink]  20 Mar 2011, 03:04
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-0-r-1-s-2-which-of-the-following-must-be-less-than-128112.html
[Reveal] Spoiler: OA
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Kudos [?]: 110 [1] , given: 12

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink]  20 Mar 2011, 03:09
1
KUDOS
We could solve this easily using contrexamples.
I is true since r<s and both are positive
II is false. Take r=2/3, s=3/2. rs=1
III is false. Take r=0.1, s=1.9. s-r=1.8

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Kudos [?]: 487 [0], given: 39

Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink]  17 Jun 2011, 03:56
nikhilsrl wrote:
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

OA is provided.

[Reveal] Spoiler:
I am not able to eliminate II.

Let 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

Now let, 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.
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Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink]  19 Apr 2015, 21:47
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Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I. [#permalink]  20 Apr 2015, 03:30
Expert's post
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.

Check our Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-0-r-1-s-2-which-of-the-following-must-be-less-than-128112.html
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Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.   [#permalink] 20 Apr 2015, 03:30
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