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

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Senior Manager
Joined: 12 May 2010
Posts: 289

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Location: United Kingdom
Concentration: Entrepreneurship, Technology
GMAT Date: 10-22-2011
GPA: 3
WE: Information Technology (Internet and New Media)
If 0 < r < 1 < s < 2, which of the following must be less [#permalink]

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25 Oct 2010, 11:56
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Difficulty:

15% (low)

Question Stats:

66% (00:22) correct 34% (00:19) wrong based on 721 sessions

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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

Kudos [?]: 77 [5], given: 12

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Joined: 02 Sep 2010
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Re: GMAT Prep - If 0 < r < 1 < s < 2, which of the following..?? [#permalink]

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25 Oct 2010, 12:07
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n2739178 wrote:
GMAT Prep question... What's the easiest way to solve this using MGMAT style case-charts?

Attachment:
q2.jpg

Not sure what you mean by MGMAT style case charts. But this question is quite straight forward

For r,s positive : r/s is less than 1, when r<s. which we know

rs : No need for this to be less than 1 (r could be almost 1 and s could be 1.5 or 1.7)

s-r : No need for this to be less than 1 (r could be almost 0 and s could be 1.5 or 1.7)

Think of extreme cases in such questions, you should always be able to find the exception like that
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Kudos [?]: 1186 [4], given: 25

Senior Manager
Joined: 12 May 2010
Posts: 289

Kudos [?]: 77 [0], given: 12

Location: United Kingdom
Concentration: Entrepreneurship, Technology
GMAT Date: 10-22-2011
GPA: 3
WE: Information Technology (Internet and New Media)
Re: GMAT Prep - If 0 < r < 1 < s < 2, which of the following..?? [#permalink]

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25 Oct 2010, 14:28
aaa yes of course - extreme cases - that's what I remember MGMAT going on about for these sorts of questions - awesome, thanks!

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Re: GMAT Prep - If 0 < r < 1 < s < 2, which of the following..?? [#permalink]

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10 May 2012, 06:03
Is the following true:

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

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Re: GMAT Prep - If 0 < r < 1 < s < 2, which of the following..?? [#permalink]

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10 May 2012, 06:14
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honsmos wrote:
Is the following true:

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.

Answer: A (I only).

Check our new Must or Could be True Questions to practice more: 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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Kudos [?]: 128888 [8], given: 12183

Re: GMAT Prep - If 0 < r < 1 < s < 2, which of the following..??   [#permalink] 10 May 2012, 06:14
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# If 0 < r < 1 < s < 2, which of the following must be less

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