It is currently 13 Dec 2017, 03:27

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### 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

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3420

Kudos [?]: 9486 [0], given: 1202

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

### Show Tags

25 Jul 2017, 10:33
Top Contributor
3
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:03) correct 24% (01:25) wrong based on 175 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$$\frac{1}{6}$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 9486 [0], given: 1202

Math Expert
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135462 [2], given: 12695

Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

25 Jul 2017, 22:30
2
KUDOS
Expert's post
4
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).

_________________

Kudos [?]: 135462 [2], given: 12695

Math Expert
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135462 [0], given: 12695

Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

25 Jul 2017, 22:31
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
_________________

Kudos [?]: 135462 [0], given: 12695

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1931

Kudos [?]: 1015 [0], given: 3

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, 15:21
Expert's post
1
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

Kudos [?]: 1015 [0], given: 3

Manager
Joined: 14 Sep 2016
Posts: 148

Kudos [?]: 5 [0], given: 36

Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

10 Nov 2017, 04:24
can we use mean = median ideology here ?

using this i got the sum and answer as A.

Kudos [?]: 5 [0], given: 36

Math Expert
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135462 [0], given: 12695

Re: If S is the sum of the reciprocals of the 10 consecutive integers from [#permalink]

### Show Tags

10 Nov 2017, 04:41
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.
_________________

Kudos [?]: 135462 [0], given: 12695

Re: If S is the sum of the reciprocals of the 10 consecutive integers from   [#permalink] 10 Nov 2017, 04:41
Display posts from previous: Sort by