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M13-08

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M13-08  [#permalink]

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New post 16 Sep 2014, 00:48
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A
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D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:11) correct 49% (01:20) wrong based on 94 sessions

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Re M13-08  [#permalink]

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New post 16 Sep 2014, 00:48
Official Solution:


(1) \(r \gt 1\) and \(s \gt 1\). Since both variables are positive, we can rewrite the question as follows: is \(\frac{r+s}{rs} \lt 2\)? Or: is \(\frac{1}{s}+\frac{1}{r} \lt 2\)? Since it is given that \(r \gt 1\) and \(s \gt 1\), then both \(\frac{1}{s}\) and \(\frac{1}{r}\) are less than 1. Therefore, their sum is definitely less than 2. Sufficient.

(2) \(r \gt 2\) and \(s \gt 0\). The same here: is \(\frac{1}{s}+\frac{1}{r} \lt 2\)? If \(r=3\) and \(s=1\), then the answer is YES but if \(r=3\) and \(s=0.1\), then the answer is NO. Not sufficient.


Answer: A
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Re: M13-08  [#permalink]

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New post 11 Sep 2016, 17:26
Why you wrote down (r+s/rs)<2? I couldn't understand the logic used.
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Re: M13-08  [#permalink]

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New post 30 Sep 2016, 15:23
mounirbr wrote:
Why you wrote down (r+s/rs)<2? I couldn't understand the logic used.



I am very certain that was a typo. He meant for 2 to be (1/2)
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M13-08  [#permalink]

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New post 30 Sep 2016, 19:45
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ddb123 wrote:
mounirbr wrote:
Why you wrote down (r+s/rs)<2? I couldn't understand the logic used.



I am very certain that was a typo. He meant for 2 to be (1/2)


Hi,
It isn't a typo....
The original equation was rs/(r+s)>1/2....
Since both r and s are > than 1, they are positive..
So, you can cross multiply..
2*rs>1*(r+s)....
2/1>(r+s)/rs ....
(r+s)/rs<2...

Hope it is clear
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Re: M13-08  [#permalink]

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New post 30 Sep 2016, 20:17
chetan2u wrote:
ddb123 wrote:
mounirbr wrote:
Why you wrote down (r+s/rs)<2? I couldn't understand the logic used.



I am very certain that was a typo. He meant for 2 to be (1/2)


Hi,
It isn't a typo....
The original equation was rs/(r+s)>1/2....
Since both r and s are > than 1, they are positive..
So, you can cross multiply..
2*rs>1*(r+s)....
2/1>(r+s)/rs ....
(r+s)/rs<2...

Hope it is clear



Thanks for the clarification! I obviously wasn't looking at the information closely enough. Cheers.
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Re: M13-08  [#permalink]

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New post 03 Oct 2018, 17:26
let simplify the equation

2rs>r+s
rs-r>s-rs
r(s-1)>s(1-r)
r/s<(r-1)/(s-1)

stat-1

if r=3 and s=4 .... not true

but if r= 99 and s=2 ..... true

So can some one expain how the statement one itself sufficient.

Error detection will be appriciated on my expaination.......
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Re: M13-08  [#permalink]

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New post 03 Oct 2018, 21:17
rinkumaa4 wrote:
let simplify the equation

2rs>r+s
rs-r>s-rs
r(s-1)>s(1-r)
r/s<(r-1)/(s-1)


stat-1

if r=3 and s=4 .... not true

but if r= 99 and s=2 ..... true

So can some one expain how the statement one itself sufficient.

Error detection will be appriciated on my expaination.......


What is the point of algebraic manipulations you've done?

\(\frac{rs}{r + s} \gt \frac{1}{2}\) is true for r=3 and s=4 as well as for r= 99 and s=2.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M13-08 &nbs [#permalink] 03 Oct 2018, 21:17
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