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inequality

by selfmade » Mon Sep 27, 2010 3:28 pm
0<r<1<s<2 which of the following must be less than 1

1) r/s
2) rs
3) s-r

Answer Choices
1) I only
2) II only
3) III only
4) I and II
5) I and III

I picked numbers and came to answer choice 4 . Can someone explain their strategies to solve these kind of problems.
OA is 1
----------
Aiming for 780
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Source: — Data Sufficiency |
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by tlt2372 » Mon Sep 27, 2010 4:34 pm
selfmade wrote:0<r<1<s<2 which of the following must be less than 1

1) r/s
2) rs
3) s-r

Answer Choices
1) I only
2) II only
3) III only
4) I and II
5) I and III

I picked numbers and came to answer choice 4 . Can someone explain their strategies to solve these kind of problems.

I also tested cases.
r=1/2, s=3/2-------------this scenario gave me answer choice 4. Then I tested a more extreme case r=9/10,s=3/2-----this gave me rs=27/20...
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by shovan85 » Mon Sep 27, 2010 11:09 pm
In this kind of problem I generally draw a number line and put the values. Here 0,1 and 2. Now r and s are to be put between 0 and 1, and between 1 and 2 respectively.

We are asked to find Result < 1 (MUST) so consider the EXTREME cases to prove it wrong (I mean make the Result >= 1)

1. r/s: take r the max value(Numerator) and s the least value(Denominator) (say r = 0.9999999.... and s=1.00000000001) still r/s < 1 [Suffice]
2. rs: take max value for r and that for s also. (say r=0.99999... and s=1.9999... => rs >1) [Does not Suffice]
3. s-r: take max s and least r (say r=0.1 and s=1.9 => s-r = 1.8 ) [Does not Suffice]

The key is As result MUST be < 1 if we can prove single case is wrong (Result > 1) then the choice is wrong and immediately discarded .

This works for me but the idea varies from person to person.
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by gmatmachoman » Wed Sep 29, 2010 12:57 am
selfmade wrote:0<r<1<s<2 which of the following must be less than 1

1) r/s
2) rs
3) s-r

Answer Choices
1) I only
2) II only
3) III only
4) I and II
5) I and III

I picked numbers and came to answer choice 4 . Can someone explain their strategies to solve these kind of problems.
OA is 1
@selfmade : The stem asks "must be true". There is a distinction between Must be & could be true".

II can be / cannot be true depending on plugged numbers. But I will ALWAYS BE true for ALL the numbers in that range.

SO OA is very much 1
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