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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, 09:35
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Difficulty:

35% (medium)

Question Stats:

66% (00:54) correct 34% (00:58) wrong based on 501 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, 03:12, 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, 09:42
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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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05 Nov 2012, 15:18
(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]

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06 Nov 2012, 13:47
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, 03:59
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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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09 Nov 2015, 03:15
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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13 Feb 2017, 05:20
TeamGMATIFY 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

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

Hi,

aren't there 10 terms and not 20 ?

regards

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

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14 Feb 2017, 16:55
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Expert's post
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

We need to determine the approximate value of the sum of the reciprocals from 45 to 54 inclusive; thus, we need the approximate value of the following:

1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54

Rather than adding each of these numbers (which would be incredibly time-consuming), let’s strategically select one of the fractions in our list and add it to itself 10 times. That sum will give us an approximate value for S.

Scanning the list, we see the best number to add to itself 10 times is 1/50. However, instead of actually adding 1/50 ten times, we will simply multiply it by 10:

1/50 x 10 = 10/50 = 1/5 = 0.2

Thus, we see that S is approximately 0.2.

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Re: If S is the sum of reciprocals of a list of consecutive   [#permalink] 14 Feb 2017, 16:55
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