Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Aug 2016, 06:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If S is the sum of the reciprocals of the consecutive

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Dec 2005
Posts: 95
Followers: 1

Kudos [?]: 50 [7] , given: 0

If S is the sum of the reciprocals of the consecutive [#permalink]

### Show Tags

23 Dec 2005, 02:19
7
KUDOS
18
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:02) correct 47% (01:07) wrong based on 729 sessions

### HideShow timer Statistics

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III. 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III
[Reveal] Spoiler: OA

_________________

JAI HIND!

Math Expert
Joined: 02 Sep 2009
Posts: 34456
Followers: 6277

Kudos [?]: 79628 [17] , given: 10022

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

### Show Tags

25 Nov 2013, 08:43
17
KUDOS
Expert's post
21
This post was
BOOKMARKED
JAI HIND wrote:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III. 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III

Given that $$S=\frac{1}{91}+\frac{1}{92}+\frac{1}{93}+\frac{1}{94}+\frac{1}{95}+\frac{1}{96}+\frac{1}{97}+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}$$. Notice that 1/91 is the larges term and 1/100 is the smallest term.

If all 10 terms were equal to 1/91, then the sum would be 10/91, but since actual sum is less than that, then we have that S<1/91.

If all 10 terms were equal to 1/100, then the sum would be 10/100=1/10, but since actual sum is more than that, then we have that S>1/10.

Therefore, 1/10 < S < 10/91.

Also, notice that 10/91 < 1/9 < 1/8, thus we have that 1/10 < S < 10/91 < 1/9 < 1/8.

Therefore only 1/10 is less than S.

Similar questions to practice:
m-is-the-sum-of-the-reciprocals-of-the-consecutive-integers-143703.html
if-k-is-the-sum-of-reciprocals-of-the-consecutive-integers-145365.html
_________________
Director
Joined: 17 Dec 2005
Posts: 548
Location: Germany
Followers: 1

Kudos [?]: 34 [12] , given: 0

### Show Tags

23 Dec 2005, 02:47
12
KUDOS
1
This post was
BOOKMARKED
I think it's C, but I'm not quite sure.

Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.

On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.

We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us C as the only possible answer.
Manager
Joined: 12 Nov 2005
Posts: 78
Followers: 1

Kudos [?]: 14 [10] , given: 0

### Show Tags

23 Dec 2005, 23:44
10
KUDOS
2
This post was
BOOKMARKED
This question is a repetition here.
Anyways lemme explain the solution

1/91+1/92+..........1/100 > 1/100+1/100......10 times
or Summation S >10/100
i.e S>1/10

Similarly
1/91+1/92+..........1/100 < 1/91+1/91......10 times
Summation < 10/91 <1/9

Hence summation is only greater than 1/10.........Hence C
Senior Manager
Joined: 15 Apr 2005
Posts: 417
Location: India, Chennai
Followers: 2

Kudos [?]: 13 [6] , given: 0

### Show Tags

23 Dec 2005, 05:26
6
KUDOS
JAI HIND wrote:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III. 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III

From the answer choice we get 1) 1/8 = .125
2) 1/9 = .11 (Approx)
3) 1/10 = .1

1/100 = .01 The other numbers from 1/91 to 1/99 will also be close to .01 but little greater than that . so approx .01 * 10 = .1 So its C.
VP
Joined: 06 Jun 2004
Posts: 1059
Location: CA
Followers: 2

Kudos [?]: 116 [2] , given: 0

### Show Tags

23 Dec 2005, 03:14
2
KUDOS
1
This post was
BOOKMARKED
JAI HIND wrote:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III. 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III

S = 1/91 + 1/92 + 1/93.....+ 1/100
S = (1/91 + 1/100)(10/2) = 191/1820 = approx 0.1049.....

I. 1/8 = 0.12...
II. 1/9 = 0.11....
III. 1/10 = 0.10
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Intern
Status: I'm trying to GMAT?
Joined: 12 Feb 2013
Posts: 26
Location: United States
Concentration: Finance, General Management
GMAT Date: 06-22-2013
WE: Engineering (Consulting)
Followers: 0

Kudos [?]: 13 [1] , given: 10

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

### Show Tags

10 Jan 2014, 11:40
1
KUDOS
JAI HIND wrote:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III. 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III

We know that there are 10 numbers in the sum: (100-91)+1=10
Take the mean of the sum and times it by 10 to get our sum: (1/ ((100+91)/2)) x 10 = 10/95.5 = 1/9.55

From here we know that the only number which will be smaller than our sum must be divisible by >9.55

Hence only III satisfies. Answer: C
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7170
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 312

Kudos [?]: 2125 [1] , given: 161

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

### Show Tags

21 Feb 2015, 23:50
1
KUDOS
Expert's post
Hi All,

The other explanations in this thread have properly explained the "math" behind this prompt - it's essentially about figuring out the "minimum" and "maximum" value that the sum COULD be, then realizing the sum is between those two values. Any time you find yourself reading a Quant question and you think "the math will take forever", then you're probably right AND there should be another way to get to the correct answer. The Quant section of the GMAT is NOT a "math test" (at least not in the way that you might be used to thinking about it). Yes, you will do plenty of small calculations and use formulas, but the Quant section is there to test you on LOTS of other non-math related skills: organization, accuracy, attention to detail, ability to prove that you're correct, pattern-matching, pacing, etc. To maximize your performance on Test Day, you have to be a stronger 'strategist' and 'pattern-matcher' than 'mathematician.'

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 31 Oct 2015 Posts: 37 Followers: 0 Kudos [?]: 2 [1] , given: 53 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 20 Jan 2016, 18:30 1 This post received KUDOS See attachment for response. Attachments SmartSelectImage_2016-01-20-20-29-20.png.png [ 56.1 KiB | Viewed 5251 times ] Senior Manager Joined: 07 Dec 2014 Posts: 363 Followers: 1 Kudos [?]: 44 [1] , given: 1 If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 18 Jul 2016, 14:55 1 This post received KUDOS 1/91+1/100=.021 .021/2=.011 10*.011=.11 only 1/10<.11 C. III only GMAT Club Legend Joined: 09 Sep 2013 Posts: 11095 Followers: 511 Kudos [?]: 134 [0], given: 0 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 25 Nov 2013, 08:12 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 30 Jan 2014 Posts: 4 Followers: 0 Kudos [?]: 0 [0], given: 8 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 20 Feb 2014, 16:30 some person solved this with an Arithmetic progression formula, is that possible, or just a coincidence? GMAT Club Legend Joined: 09 Sep 2013 Posts: 11095 Followers: 511 Kudos [?]: 134 [0], given: 0 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 21 Feb 2015, 23:20 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 22 Jan 2014 Posts: 138 WE: Project Management (Computer Hardware) Followers: 0 Kudos [?]: 44 [0], given: 122 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 22 Mar 2015, 12:10 JAI HIND wrote: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S? I. 1/8 II. 1/9 III. 1/10 A. None B. I only C. III only D. II and III only E. I, II, and III S = 1/91 + 1/92 + ... + 1/100 or S > 1/100 + 1/100 +... + 1/100 S > 1/10 or S < 10/91 S < 0.109 => 0.1 < S < 0.109 hence C. _________________ Illegitimi non carborundum. BSchool Forum Moderator Status: I Declare War!!! Joined: 02 Apr 2014 Posts: 257 Location: United States Concentration: Finance, Economics GMAT Date: 03-18-2015 WE: Asset Management (Investment Banking) Followers: 7 Kudos [?]: 85 [0], given: 529 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 17 Jul 2016, 04:27 hey! callig all experts... bunnuel / chetan4u / egmat etc to help in solving this with some less math richi do help plz EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 7170 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 312 Kudos [?]: 2125 [0], given: 161 Re: If S is the sum of the reciprocals of the consecutive [#permalink] ### Show Tags 18 Jul 2016, 12:10 Hi Celestial09, Based on the wording of the prompt, you might think that you should add up the fractions 1/91 + 1/92 + .... 1/100, but the GMAT would NEVER require that you do that math. Instead, lets do some real basic estimation of what that sum would be LESS than and GREATER than.... There are 10 total fractions and 9 of them are GREATER than 1/100. So, at the 'lower end', let's just say that all 10 fractions are equal to 1/100.... (10)(1/100) = 10/100 = 1/10 Thus, we know that the sum of those 10 fractions will be GREATER than 1/10. Similarly, we know that all 10 of those fractions are LESS than 1/90. So, at the 'higher end', let's just say that all 10 fractions are equal to 1/90... (10)(1/90) = 10/90 = 1/9 Thus, we know that the sum of those 10 fractions will be LESS than 1/9. With those two deductions, there's only one answer that 'fits'... Final Answer: [Reveal] Spoiler: C GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 26 Mar 2016
Posts: 22
Location: Greece
Concentration: General Management, Finance
GMAT 1: 600 Q44 V27
Followers: 0

Kudos [?]: 1 [0], given: 12

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

### Show Tags

18 Jul 2016, 16:41
1/91 + 1/92 +...+ 1/100..
I took 1/95 as the median of the sequence (approximately, the real median is 1/95.5).
So 10*1/95= approximately 1/9.5.
So the only answer possible is C.
It took me like 15 seconds for this question approaching the problem this way.
Senior Manager
Joined: 15 Sep 2011
Posts: 351
Location: United States
WE: Corporate Finance (Manufacturing)
Followers: 6

Kudos [?]: 258 [0], given: 45

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

### Show Tags

18 Jul 2016, 18:10
Top Contributor
C. The sum of the reciprocals is 10/955, which is derived from the sum of consecutive integers formula n(n+1)/2, and that number is less than 1/8 and 1/9, both. Tested via cross multiplication.

Sent from my iPhone using Tapatalk
Re: If S is the sum of the reciprocals of the consecutive   [#permalink] 18 Jul 2016, 18:10
Similar topics Replies Last post
Similar
Topics:
50 If K is the sum of reciprocals of the consecutive integers 20 07 Jan 2013, 03:05
163 M is the sum of the reciprocals of the consecutive integers 25 06 Dec 2012, 09:42
15 M is the sum of the reciprocals of the consecutive integers 2 07 Jun 2012, 01:14
17 If S is the sum of reciprocals of a list of consecutive 11 16 May 2012, 09:35
33 Which of the following could be the sum of the reciprocals 15 31 Mar 2009, 21:29
Display posts from previous: Sort by