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# If k is the sum of the reciprocals of the consecutive intege

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If k is the sum of the reciprocals of the consecutive intege [#permalink]  13 Sep 2017, 12:56
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If k is the sum of the reciprocals of the consecutive integers from 41 to 60 inclusive, which of the following are less than k?

Indicate all such statements.

❑ $$\frac{1}{4}$$

❑ $$\frac{1}{3}$$

❑ $$\frac{1}{2}$$

[Reveal] Spoiler: OA
A,B
[Reveal] Spoiler: OA

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Re: If k is the sum of the reciprocals of the consecutive intege [#permalink]  13 Sep 2017, 18:47
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Sum up 1/60 20 times to get 1/3.
Answer is definitely more than 1/3. Therefore answer is 1/2, as it is the only option greater than 1/3.
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Re: If k is the sum of the reciprocals of the consecutive intege [#permalink]  24 Oct 2017, 01:35
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If k is the sum of the reciprocals of the consecutive integers from 41 to 60 inclusive, which of the following are less than k?

Indicate all such statements.

❑ \frac{1}{4}

❑ \frac{1}{3}

❑ \frac{1}{2}

Since K is the sum of 1/41 to 1/60 and it is a evenly spaced set, we can easily calculate the sum of set k as follows:

(1/41 + 1/60)/(2) * 20 = 0,41

We multiply by 20 since we have 20 values in our set.

Hence A an B are the correct answers as they are < 0,41

I hope this helped !
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Re: If k is the sum of the reciprocals of the consecutive intege [#permalink]  25 Apr 2018, 11:20
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S = 1/41 +1/42 + ... + 1/60
There are 40 elements >= 1/60 in that set => S > 20 * 1/60 = 1/3
Since 1/3 > 1/4 => S > 1/4 also

There are 40 elements < 1/40 in that set => S < 20 *1/40 = 1/2 => Eliminate C

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Re: If k is the sum of the reciprocals of the consecutive intege [#permalink]  24 May 2018, 08:50
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For max value 1/41 * 20 = 0.48
For least value 1/60 * 20 = 1/3

Hence, K will be less than 1/2 but more than 1/3.

Answer: 1/3 and 1/4 are less than k. (A & B)
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Re: If k is the sum of the reciprocals of the consecutive intege [#permalink]  08 Aug 2018, 22:21
Carcass wrote:

If k is the sum of the reciprocals of the consecutive integers from 41 to 60 inclusive, which of the following are less than k?

Indicate all such statements.

❑ $$\frac{1}{4}$$

❑ $$\frac{1}{3}$$

❑ $$\frac{1}{2}$$

[Reveal] Spoiler: OA
A,B

Re: If k is the sum of the reciprocals of the consecutive intege   [#permalink] 08 Aug 2018, 22:21
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