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# M13-04

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Math Expert
Joined: 02 Sep 2009
Posts: 48109

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16 Sep 2014, 00:48
1
4
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:47) correct 25% (00:25) wrong based on 71 sessions

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Which of the following is closest to $$\frac{1}{1.001}$$?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001

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Math Expert
Joined: 02 Sep 2009
Posts: 48109

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16 Sep 2014, 00:48
2
1
Official Solution:

Which of the following is closest to $$\frac{1}{1.001}$$?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001

If $$a$$ is small, $$\frac{1}{(1 + a)}$$ is close to $$1 - a$$. This is because $$(1 - a)*(1 + a) = 1 - a^2$$, which is close to 1 if $$a$$ is small. So, $$\frac{1}{1.001} = \frac{1}{(1 + 0.001)}$$ is approximately $$1 - 0.001 = 0.999$$.

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Joined: 30 Dec 2016
Posts: 160

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16 Dec 2017, 08:37
Hi Bunuel. My question is what is one supposed to learn from this question?

Am I supposed to learn the property that is mentioned in the solution? Will this property come handy in any other questions?
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SandySilva

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Intern
Joined: 19 May 2016
Posts: 14
Location: Pakistan
Concentration: Marketing, Strategy
GPA: 3.1

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05 May 2018, 07:40
cannot understand this! can someone post another explanation?
Manager
Joined: 20 Feb 2017
Posts: 140
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)

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05 May 2018, 08:04
1
anum23 wrote:
cannot understand this! can someone post another explanation?

Multiply (1-0.001) on denominator and numerator.
We get 1-0.001/(1+0.001)(1-0.001)
We have (a+b)(a-b) = a^2-b^2
We get 1-(0.001)^2 in denominator which is very close to 1. Hence we assume denominator as 1.
In numerator we have 1-0.001 = 0.999
I hope you underatand it now

Posted from my mobile device
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Intern
Joined: 19 May 2016
Posts: 14
Location: Pakistan
Concentration: Marketing, Strategy
GPA: 3.1

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05 May 2018, 08:17
Raksat wrote:
anum23 wrote:
cannot understand this! can someone post another explanation?

Multiply (1-0.001) on denominator and numerator.
We get 1-0.001/(1+0.001)(1-0.001)
We have (a+b)(a-b) = a^2-b^2
We get 1-(0.001)^2 in denominator which is very close to 1. Hence we assume denominator as 1.
In numerator we have 1-0.001 = 0.999
I hope you underatand it now

Posted from my mobile device

Got it! Thanks a lot!
Re: M13-04 &nbs [#permalink] 05 May 2018, 08:17
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# M13-04

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