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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

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.

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

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05 Nov 2012, 15:18

I got 0.2 too (B). Please help. Here is my approach (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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12 Aug 2014, 15:28

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08 Nov 2015, 20:48

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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

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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15 Dec 2016, 04:00

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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

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14 Feb 2017, 16:55

1

This post received KUDOS

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:

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.

Answer: B
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Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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

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