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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
Joined: 16 Aug 2015
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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
2
7
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Difficulty:

35% (medium)

Question Stats:

69% (01:19) correct 31% (01:41) wrong based on 110 sessions

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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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Ask GMAT Experts Forum Moderator Status: Preparing for GMAT Joined: 25 Nov 2015 Posts: 1028 Location: India GPA: 3.64 Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the [#permalink] ### Show Tags 26 Oct 2017, 01:08 2 2 (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 Answer E. Please give kudos, if u liked my post! _________________ Please give kudos, if you like my post When the going gets tough, the tough gets going... Intern Joined: 31 Jul 2017 Posts: 7 Location: United States GMAT 1: 620 Q44 V31 GMAT 2: 710 Q49 V37 GPA: 3.44 WE: Research (Other) Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r [#permalink] ### Show Tags 26 Oct 2017, 12:52 1 1 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7603 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r [#permalink] ### Show Tags 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. Therefore, the answer is E. Answer : E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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06 Jan 2019, 01:41
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Re: (1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following r   [#permalink] 06 Jan 2019, 01:41
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