If 0<r<1<s<2. Which of the following must be less than 1.

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If 0<r<1<s<2. Which of the following must be less than 1. [#permalink]

25 Feb 2012, 02:06

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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

What is a quick and fool proof way of solving ques like these. I picked numbers and got the wrong answer as D

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Re: less than 1 [#permalink]

25 Feb 2012, 02:16

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.
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Manager

Joined: 25 Aug 2011

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Location: India

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WE: Operations (Insurance)

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Kudos [?]: 20 [0], given: 11

Re: less than 1 [#permalink]

25 Feb 2012, 02:32

So the best strategy is to pick numbers in these ques?

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Re: less than 1 [#permalink]

25 Feb 2012, 02:43

devinawilliam83 wrote:

So the best strategy is to pick numbers in these ques?

Number picking is a good strategy for such kind of questions, though as you can see we proved that I is true with algebra (so to prove that a statement MUST be true you might need an algebraic or logical/conceptual approach).

Generally it really depends on the problem to pick the way of handling it. Check the link in my previous post to see bunch of Must or Could be True Questions solved using different approaches.
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Re: less than 1 [#permalink] 25 Feb 2012, 02:43

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If 0<r<1<s<2. Which of the following must be less than 1.

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If 0<r<1<s<2. Which of the following must be less than 1.

If 0<r<1<s<2. Which of the following must be less than 1.

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