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# Which of the following is closest to \frac{1}{9} +

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Manager
Joined: 22 May 2007
Posts: 211
Which of the following is closest to \frac{1}{9} +  [#permalink]

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02 Aug 2008, 21:37
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

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Director
Joined: 27 May 2008
Posts: 530

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02 Aug 2008, 21:42
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Manager
Joined: 22 May 2007
Posts: 211

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02 Aug 2008, 21:45
durgesh79 wrote:
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Durgesh,

How does one solve this quickly ? Did you calculate each fraction? IS there a way to quickly do this?
Director
Joined: 27 May 2008
Posts: 530

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02 Aug 2008, 21:49
aaron22197 wrote:
durgesh79 wrote:
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

Durgesh,

How does one solve this quickly ? Did you calculate each fraction? IS there a way to quickly do this?

my experiance in comparing fraction says .... do one of two things
covert everything to common denominator
OR
covert everything to decimals

in this case converting to common denominator is tough ... and these fractions are simple ones ... we know 1/10 and 1/9
all you need todo is convert 1/99, 1/999 and 1/8 .... option D and E are already eliminated ....
VP
Joined: 17 Jun 2008
Posts: 1279

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02 Aug 2008, 21:54
aaron22197 wrote:
Which of the following is closest to $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$ ?

* 1/10
* 1/9
* 1/8
* 1/6
* 1/5

Closest options for the above question are :
(A) and (B)

now say x=$$\frac{1}{9} + \frac{1}{99} + \frac{1}{999}$$
x-1/9=$$\frac{1}{99} + \frac{1}{999}$$
x-1/10 = $$\frac{1}{90} + \frac{1}{99} + \frac{1}{999}$$

hence x-1/10 > x-1/9 => 1/9 is closest
good question
_________________

cheers
Its Now Or Never

Manager
Joined: 22 May 2007
Posts: 211

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03 Aug 2008, 02:14
Q = 0.111111 + 0.010101 + 0.001001001 = 0.122

A = 0.1
B = 0.11111111
C = 0.125
D = 0.14...
E = 0.16.....

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: 1/999 &nbs [#permalink] 03 Aug 2008, 02:14
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