GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 May 2018, 09:54

### 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 10 consecutive integers from

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3405
If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

25 Jul 2017, 11:33
4
KUDOS
Top Contributor
8
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:56) correct 25% (01:36) wrong based on 353 sessions

### HideShow timer Statistics

If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 45423
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

25 Jul 2017, 23:30
5
KUDOS
Expert's post
7
This post was
BOOKMARKED
carcass wrote:
If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

$$S = \frac{1}{21} + \frac{1}{22} + \frac{1}{23} + \frac{1}{24} + \frac{1}{25} + \frac{1}{26} + \frac{1}{27} + \frac{1}{28} + \frac{1}{29} + \frac{1}{30}$$. Notice that 1/21 is the largest term and 1/30 is the smallest term.

If all 10 terms were equal to 1/30, then the sum would be 10*1/30 = 1/3, but since the actual sum is more than that, then we have that S > 1/3.

If all 10 terms were equal to 1/21, then the sum would be 10*1/21 = 10/21, but since the actual sum is less than that, then we have that S < 10/21.

Therefore, $$\frac{1}{3} < S < \frac{10}{21}$$ (notice that 10/21 < 1/2, so 1/3 < S < 10/21 < 1/2).

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 45423
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

25 Jul 2017, 23:31
Bunuel wrote:
carcass wrote:
If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

$$S = \frac{1}{21} + \frac{1}{22} + \frac{1}{23} + \frac{1}{24} + \frac{1}{25} + \frac{1}{26} + \frac{1}{27} + \frac{1}{28} + \frac{1}{29} + \frac{1}{30}$$. Notice that 1/21 is the largest term and 1/30 is the smallest term.

If all 10 terms were equal to 1/30, then the sum would be 10*1/30 = 1/3, but since the actual sum is more than that, then we have that S > 1/3.

If all 10 terms were equal to 1/21, then the sum would be 10*1/21 = 10/21, but since the actual sum is less than that, then we have that S < 10/21.

Therefore, $$\frac{1}{3} < S < \frac{10}{21}$$ (notice that 10/21 < 1/2, so 1/3 < S < 10/21 < 1/2).

Similar questions to practice:
https://gmatclub.com/forum/m-is-the-sum ... 43703.html
https://gmatclub.com/forum/if-k-is-the- ... 45365.html
https://gmatclub.com/forum/if-s-is-the- ... 32690.html
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2638
Location: United States (CA)
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

26 Jul 2017, 16:21
Expert's post
2
This post was
BOOKMARKED
carcass wrote:
If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

Let's first analyze the question. We are trying to find a potential range for S in which S is the sum of the 10 reciprocals from 21 to 30 inclusive. Thus, S is:

1/21 + 1/22 + 1/23 + … + 1/30

Since we probably would not be expected to do such time-consuming arithmetic (i.e., to add 10 fractions, each with a different denominator), that is exactly why each answer choice is given as a range of values. Thus, we do not need to know the EXACT value of S. The easiest way to determine the RANGE of values for S is to use easy numbers that can be quickly manipulated.

Notice that 1/20 is greater than each of the addends and that 1/30 is less than or equal to each of the addends. Therefore, instead of trying to add 1/21 + 1/22 + 1/23 + … + 1/30, we are going to add 1/20 ten times and 1/30 ten times. These two sums will give us a high estimate of S and a low estimate of S. Again, we are adding 1/20 ten times and 1/30 ten times because there are 10 numbers from 1/21 to 1/30.

Instead of actually adding each one of these values ten times, we will simply multiply each value by 10:

1/30 x 10 = ⅓. This value is the low estimate of S.

1/20 x 10 = ½. This value is the high estimate of S.

We see that M is between 1/3 and 1/2.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 14 Sep 2016
Posts: 151
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

10 Nov 2017, 05:24
can we use mean = median ideology here ?

using this i got the sum and answer as A.
Math Expert
Joined: 02 Sep 2009
Posts: 45423
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

10 Nov 2017, 05:41
kunalsinghNS wrote:
can we use mean = median ideology here ?

using this i got the sum and answer as A.

No. The set {1/21, 1/22, 1/23, …, 1/30} is NOT evenly spaced but the formula you apply is for an evenly spaced set.
_________________
Manager
Joined: 02 Jan 2017
Posts: 81
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
WE: Business Development (Accounting)
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

18 Dec 2017, 05:12
carcass wrote:
If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

Easier way at least for me was this method.

21-30 are 10 consecutive integers ( AP)

sum of terms S= Mean * No of terms

Therefore: $$\frac{(31+20)}{2}$$ *10= 255 ( S)

Now take reciprocal of this and it becomes : $$\frac{1}{255}$$

by long division within few seconds, you will estimate the value to be .003 something.
Only Option A went with this.

Correct me if this method was wrong.

Regards
Director
Joined: 09 Mar 2016
Posts: 536
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

24 Feb 2018, 13:42
ScottTargetTestPrep wrote:
carcass wrote:
If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?

A. $$\frac{1}{3}$$ and $$\frac{1}{2}$$

B. $$\frac{1}{4}$$ and $$\frac{1}{3}$$

C. $$\frac{1}{5}$$ and $$\frac{1}{4}$$

D. $$\frac{1}{6}$$ and $$\frac{1}{5}$$

E. $$\frac{1}{7}$$ and$$\frac{1}{6}$$

Let's first analyze the question. We are trying to find a potential range for S in which S is the sum of the 10 reciprocals from 21 to 30 inclusive. Thus, S is:

1/21 + 1/22 + 1/23 + … + 1/30

Since we probably would not be expected to do such time-consuming arithmetic (i.e., to add 10 fractions, each with a different denominator), that is exactly why each answer choice is given as a range of values. Thus, we do not need to know the EXACT value of S. The easiest way to determine the RANGE of values for S is to use easy numbers that can be quickly manipulated.

Notice that 1/20 is greater than each of the addends and that 1/30 is less than or equal to each of the addends. Therefore, instead of trying to add 1/21 + 1/22 + 1/23 + … + 1/30, we are going to add 1/20 ten times and 1/30 ten times. These two sums will give us a high estimate of S and a low estimate of S. Again, we are adding 1/20 ten times and 1/30 ten times because there are 10 numbers from 1/21 to 1/30.

Instead of actually adding each one of these values ten times, we will simply multiply each value by 10:

1/30 x 10 = ⅓. This value is the low estimate of S.

1/20 x 10 = ½. This value is the high estimate of S.

We see that M is between 1/3 and 1/2.

Hello
Why are you adding 1/20 ten times instead of 1/21 ? And how can 1/30 be equal to each of the addends thank you for your explanation
Intern
Joined: 01 Aug 2017
Posts: 9
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

15 Mar 2018, 01:50
My approach to this question was a little bit different. I thought it was worth to comment.

I considered a normal sequence: 1,2,3,4,5,6,7,8,9,10. So I added the first two extreme values (1,10) and did that for all the other pairs (2,9), (3,8) .... So what can we take from this?? All the pairs are equal 11. Then i thought that this should apply to reciprocals.

I did the first calculation and approximated 1/21 to 1/20. So 0.05 + 0.033=0.083. There is no need for more calculations but if you wanted you could have calculated the next pair to be sure. Then i multiplied by 5 because we have 5 pairs and got S=0.4. Which is between 1/3 and 1/2.

Just as an extra info. The real value of S, if all the calculations were done would be 0.79.

Hope it helps someone
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1240
Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

26 Mar 2018, 05:27
Expert's post
1
This post was
BOOKMARKED

Solution

$$S$$= $$\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+…………….+ \frac{1}{30}$$

The greatest value of $$S$$:

We know,
• $$\frac{1}{20}>\frac{1}{21}$$.
Hence,
• $$\frac{1}{20}+\frac{1}{20}+……+\frac{1}{20}> \frac{1}{21}+\frac{1}{22}+\frac{1}{23}+…….+\frac{1}{30}$$
• $$\frac{10}{20}>S$$
• $$S<\frac{1}{2}$$

Hence, $$S$$ is always smaller than $$\frac{1}{2}$$.

The least value of S:

We know,
• $$\frac{1}{29}>\frac{1}{30}$$

Hence,
•$$\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+…………+\frac{1}{29}+\frac{1}{30}> \frac{1}{30}+\frac{1}{30}+…..+1\frac{}{30}$$
•$$S> \frac{10}{30}$$
•$$S$$>$$\frac{1}{3}$$

Hence, $$S$$ is always greater than $$\frac{1}{3}$$.

Thus, $$\frac{1}{3}< S<\frac{1}{2}$$.
Hence $$A$$ is the correct answer.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: If S is the sum of the reciprocals of the 10 consecutive integers from   [#permalink] 26 Mar 2018, 05:27
Display posts from previous: Sort by

# If S is the sum of the reciprocals of the 10 consecutive integers from

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.