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(1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following

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(1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 01:28
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(1/11)+(1/12)+……+(1/19)+(1/20) is including in which of
the following ranges?

A. 0 ~ (1/5)
B. (1/5) ~ (1/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1
[Reveal] Spoiler: OA

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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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MathRevolution wrote:
(1/11)+(1/12)+……+(1/19)+(1/20) is including in which of
the following ranges?

A. 0 ~ (1/5)
B. (1/5) ~ (1/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1



Hi..
You don't have to start Adding..
Just find the ATLEAST value..
Here the SUM has to be GREATER than 10 times lowest value= 10*1/20=1/2
So sum >1/2

Only E fits in..
E
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(1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 03:12
Expression that we need to find the range is \({(\frac{1}{11})+(\frac{1}{12})+……+(\frac{1}{19})+(\frac{1}{20})}\)

The minimum range of that expression is \(\frac{1}{20}+\frac{1}{20}\)... total 10 times
Therefore the value of that minimum expression is greater than \(\frac{10}{20}\) or \(\frac{1}{2}\)

Similarly the range for maximum value is \(\frac{10}{11} = 0.91\)(approximately)

Hence the range for the expression must be \(\frac{1}{2}\) < expression < 1(Option E)
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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 05:51
pushpitkc wrote:
Expression that we need to find the range is \({(\frac{1}{11})+(\frac{1}{12})+……+(\frac{1}{19})+(\frac{1}{20})}\)

The minimum range of that expression is \(\frac{1}{20}+\frac{1}{20}\)... total 10 times
Therefore the value of that minimum expression is greater than \(\frac{10}{20}\) or \(\frac{1}{2}\)

Similarly the range for maximum value is \(\frac{10}{11} = 0.91\)(approximately)

Hence the range for the expression must be \(\frac{1}{2}\) < expression < 1(Option E)



Hi,

How are you deriving the minimum range as 1/20+1/20... ?

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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 06:17
kunalsinghNS wrote:

Hi,

How are you deriving the minimum range as 1/20+1/20... ?



We have a total of 10 elements in the expression.
The minimum range can be got by adding the smallest number
10 times.

Since 1/20 is the smallest number in the expression,
adding the number to the itself 10 times will give you the
smallest number possible(1/20 = 0.05)
When added 10 times to itself, 0.05*10 = 0.5 = 1/2!

Hope that helps!
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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 22:22
Thank you for your response !

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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 30 Aug 2017, 22:43
This explained method is not bad ..we can extract result from by multiply 10/20 for higher range and 10/11 for lower range...but it is a tricky solution

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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following [#permalink]

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New post 01 Sep 2017, 10:05
=> (1/20) < (1/11), (1/20) < (1/12), …, (1/20) < (1/19).
(1/20) + (1/20) + … + (1/20) < (1/11)+(1/12)+……+(1/19)+(1/20)
(1/20)*10 < (1/11)+(1/12)+……+(1/19)+(1/20)
(1/2) < (1/11)+(1/12)+……+(1/19)+(1/20)

(1/11) < (1/10), (1/12) < (1/10), … , (1/20) < (1/10)
(1/11)+(1/12)+……+(1/19)+(1/20) < (1/10) + (1/10) + … + (1/10) = 1

Thus, 1/2 < (1/11)+(1/12)+……+(1/19)+(1/20) < 1

Ans: E
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Re: (1/11)+(1/12)+……+(1/19)+(1/20) is including in which of the following   [#permalink] 01 Sep 2017, 10:05
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