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# (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r

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Math Revolution GMAT Instructor
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(1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r [#permalink]

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26 Oct 2017, 00:48
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[GMAT math practice question]

(1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following ranges?

A. (1/6)~(1/5)
B. (1/5)~91/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1
[Reveal] Spoiler: OA

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Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the [#permalink]

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26 Oct 2017, 01:08
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(1/26)+(1/27)+……+(1/49)+(1/50)
There are 25 terms in this series.
Smallest sum will be in the case when all terms are equal to $$\frac{1}{50}$$
Smallest sum = $$\frac{25}{50}$$ =$$\frac{1}{2}$$
Largest sum will be in the case when all terms are equal to $$\frac{1}{26}$$
Largest sum =$$\frac{25}{26}$$ ~ 1
Only option E is in this range

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Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r [#permalink]

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26 Oct 2017, 12:52
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MathRevolution wrote:
[GMAT math practice question]

(1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following ranges?

A. (1/6)~(1/5)
B. (1/5)~91/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1

First you need to figure out how many numbers there are in the set. I took the 50 from 1/50 and the 26 from 1/26:

50-26+1 will give you 25 total. That is the formula for to count a given set that is inclusive.

Next, you can take the largest number in the set and assume all the numbers were that (1/26) , if you multiply 25 by 1/26 you end up with 25/26. This is greater than what our actual sum will be so lets say X = the sum of the set provided. Then X < 25/26.

You need to find the lower end of the range by assuming that all the numbers are the lowest possible value (1/50). Multiply that by 25 to get 1/2. This is the bottom end of the range so X > 1/2.

Put both of these together to get 1/2 < X < 25/26, the only answer that fits would be E.

Hopefully that makes sense.

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Math Revolution GMAT Instructor
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Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r [#permalink]

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29 Oct 2017, 18:05
=>
1/26 > 1/50, 1/27 > 1/50, …, 1/49 > 1/50
(1/26)+(1/27)+……+(1/49)+(1/50) > 1/50 + 1/50 + … + 1/50 = (1/50)*25 = 1/2.
1/26 < 1/25, 1/27 < 1/25, … , 1/49 < 1/25, 1/50 < 1/25.
(1/26)+(1/27)+……+(1/49)+(1/50) < 1/25 + 1/25 + … + 1/25 = (1/25)*25 = 1.

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Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r   [#permalink] 29 Oct 2017, 18:05
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