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Sum of reciprocals

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by rahulvsd » Thu May 03, 2012 9:12 am
If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?

A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
[spoiler]
OA: C. Source: GMAT Prep[/spoiler]
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by cypherskull » Thu May 03, 2012 9:31 am
I think the answer would be 1/6 (D).

1/40 equals 0.025.

0.025 times 6 (number of reciprocals including and between 43-48) is 0.015 which is approximately equal to 1/6.
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by Brent@GMATPrepNow » Thu May 03, 2012 11:02 am
rahulvsd wrote:If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?
A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
There are six fractions to add here.

Now make the following observations using some upper and lower bounds:
1. (1/42)+(1/42)+(1/42)+(1/42)+(1/42)+(1/42) = 6/42 = 1/7
2. (1/48)+(1/48)+(1/48)+(1/48)+(1/48)+(1/48) = 6/48 = 1/8

From this we can conclude that 1/8 < K < 1/7

If K is between 1/8 and 1/7, then K must be closer to 1/8 than it is to 1/6

Answer = C

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by GMATGuruNY » Thu May 03, 2012 11:10 am
rahulvsd wrote:If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?

A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
[spoiler]
OA: C. Source: GMAT Prep[/spoiler]
Determine the RANGE of the sum.

If all of the fractions were 1/43, the sum = 6(1/43) ≈ 6/42 = 1/7.
If all of the fractions were 1/48, the sum = 6(1/48) = 6/48 = 1/8.
Thus, the sum must be between 1/7 and 1/8.

The correct answer is C.
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by Scott@TargetTestPrep » Sun Oct 20, 2019 8:45 am
rahulvsd wrote:If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?

A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
[spoiler]
OA: C. Source: GMAT Prep[/spoiler]
We see that K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48. We see that K is a sum of 6 numbers. Since each number is less than 1/42 and greater than or equal to 1/48, a lower estimate for K is 6 x 1/48 = 6/48 = ⅛, and an upper estimate for K is 6 x 1/42 = 6/42 = 1/7. In other words, K is between 1/7 and 1/8. Therefore, K is closest to 1/8.

Answer: C

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