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

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

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20 Mar 2011, 03:04
1
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Difficulty:

35% (medium)

Question Stats:

64% (00:54) correct 36% (00:49) wrong based on 121 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
Manager
Joined: 03 Mar 2011
Posts: 87
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

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20 Mar 2011, 03:09
1
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

So, the answer is A
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Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.  [#permalink]

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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.

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]

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20 Apr 2015, 03:30
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 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]

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08 Oct 2018, 04:20
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Re: If 0 < r < 1 < s < 2, which of the following must be less than 1? I.   [#permalink] 08 Oct 2018, 04:20
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# If 0 < r < 1 < s < 2, which of the following must be less than 1? I.

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