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# If S is the sum of reciprocals of a list of consecutive

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If S is the sum of reciprocals of a list of consecutive [#permalink]  16 May 2012, 08:35
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Question Stats:

68% (01:39) correct 32% (00:49) wrong based on 114 sessions
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Aug 2014, 02:12, edited 1 time in total.
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  16 May 2012, 08:42
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gmihir wrote:
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Sorry, don't have an official answer.

We need to find the approximate value of 1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54. Now, the sum of these 10 terms will be very close to 10 times 1/50, which is 0.02*10=0.2.

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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  24 Aug 2012, 03:27
Are these kind of progressions tested on the GMAT?
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  24 Aug 2012, 09:09
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+1 B

All those numbers are close to 0.02.

Amogh: yes, that would be a GMAT question. You don't have to calculate, just estimate.
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  05 Nov 2012, 14:18
(1/45) + (1/46) + .....+(1/54) = (45-44)/45 +(46-45)/46 +.....+(54-53)/54
= 10 -(44/45 + 45/46 + ...53/54). Each term in the bracket is > 0.977, and there are ten of them. Then their sum is roughly 9.8
10-9.8 = 0.2. But is this doable in 2 mn under stress and heat?
Brother Karamazov

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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  06 Nov 2012, 12:47
my method was 1/45 + 1/46 + ... => 10/45 ~ 2/9 ~ .2
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  19 Dec 2012, 02:59
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gmihir wrote:
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Sorry, don't have an official answer.

Solved this using Bunuel's technique that I saw on another similar problem.

S = $$\frac{1}{45}+\frac{1}{46}+...+\frac{1}{54}$$

Get number of terms: $$54 - 45 + 1 = 10$$

Get lower limit: $$10*\frac{1}{54}=\frac{5}{27}=0.18$$
Get upper limit: $$10*\frac{1}{45}=\frac{2}{9}=0.22$$

$$0.18<S<0.22$$

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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  12 Aug 2014, 14:28
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  12 Aug 2014, 20:39
1
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gmihir wrote:
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Sorry, don't have an official answer.

Bunuel, Kindly update OA for this question (Answer = B)
Thanks
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]  13 Aug 2014, 02:14
Expert's post
PareshGmat wrote:
gmihir wrote:
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Sorry, don't have an official answer.

Bunuel, Kindly update OA for this question (Answer = B)
Thanks

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Done. Thank you.
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Re: If S is the sum of reciprocals of a list of consecutive   [#permalink] 13 Aug 2014, 02:14
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