If S is the sum of reciprocals of a list of consecutive : GMAT Problem Solving (PS)
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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]

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16 May 2012, 08:35
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Question Stats:

69% (01:49) correct 31% (00:52) wrong based on 245 sessions

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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]

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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]

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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]

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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]

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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?
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]

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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]

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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]

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12 Aug 2014, 14:28
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]

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12 Aug 2014, 20:39
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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]

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13 Aug 2014, 02:14
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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]

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08 Nov 2015, 19:48
Hello from the GMAT Club BumpBot!

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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]

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09 Nov 2015, 02:15
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

Such questions do not test your calculations. (In fact most of GMAT questions) They test your logic and how easily can you simplify a problem.
That is why an approximate result is asked and not the absolute value.

Out of the given numbers, from 45 to 54, carrying out calculations with 50 would be easiest.

Hene instead of 1/45 + 1/46 + ... 1/50 + ... + 1/54,
We can increase some terms and decrease some terms by changing the numbers with 50

Hence we have a sequence = 1/50 + 1/50 + ... + 1/50 (Total 20 terms)
= 10/50 = 1/5 = 0.2 approximately
Option B
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Re: If S is the sum of reciprocals of a list of consecutive [#permalink]

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15 Dec 2016, 03:00
Hello from the GMAT Club BumpBot!

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Re: If S is the sum of reciprocals of a list of consecutive   [#permalink] 15 Dec 2016, 03:00
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