GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Jul 2020, 02:20

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A certain list consists of 21 different numbers. If n is in

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 14 Jun 2012
Posts: 110
Concentration: International Business
GMAT 1: 560 Q36 V31
GMAT 2: 580 Q39 V31
GMAT 3: 630 Q41 V35
GPA: 4
Reviews Badge
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 12 Jun 2016, 04:23
1
He just picked a random number for the average of the numbers which is 10 and then multiplied it my 20 to get the sum, then added the 21st number which is 4 times as big as the average of the other numbers.

vipul1702 wrote:
EMPOWERgmatRichC wrote:
Hi Silviax,

This question can be solved by TESTing VALUES; you'll have to make sure to take the proper notes and label your work to finish it in an efficient way though.

We're told that a list consists of 21 different numbers (N and 20 others) and that N is equal to 4 times the AVERAGE of the other 20 numbers.

Let's TEST:
Average of 20 numbers = 10
Sum of those 20 numbers = 20(10) = 200
N = 4(10) = 40

We're asked to calculate the fraction N/(sum of all 21 numbers) = 40/(200+40) = 40/240 = 1/6

Final Answer:

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


Sorry, I am a noob at this and my query could be a stupid one but can you please explain how did you conclude the following:
Average of 20 numbers = 10
Sum of those 20 numbers = 20(10) = 200
Current Student
User avatar
Joined: 18 Oct 2014
Posts: 770
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 12 Jun 2016, 08:17
1
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21


Let the total of 20 numbers other than 'n' = t

So, n= 4t/20= t/5

total including n= n + t= t/5 +t= 6t/5

ratio of n/total= t/5/6t/5= 1/6

B is the answer.
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Manager
Manager
avatar
B
Joined: 13 Dec 2013
Posts: 138
Location: United States (NY)
Concentration: General Management, International Business
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 23 Mar 2017, 15:13
List has 21 numbers, of which n is one.

Setting m as the average of the 20 numbers:

4m/(20m+4m)=4/24=1/6
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 27 Mar 2017, 16:31
1
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21


We can let x = the sum of the 21 numbers. Thus, x/21 = the average of the 21 numbers and (x - n)/20 = the average of the 20 numbers when n is removed from the list. Since n is 4 times the average of the other 20 numbers in the list:

n = 4(x - n)/20

n = (x - n)/5

5n = x - n

6n = x

n = (1/6)x

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

VP
VP
avatar
D
Joined: 07 Dec 2014
Posts: 1258
A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post Updated on: 14 Feb 2020, 10:35
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21


let s=sum of 21 numbers
n=4(s-n)/20→
n/s=4/24=1/6
B

Originally posted by gracie on 09 Sep 2017, 15:10.
Last edited by gracie on 14 Feb 2020, 10:35, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 14 Aug 2017
Posts: 39
Location: India
Concentration: Operations, Social Entrepreneurship
Schools: Price (A)
GMAT 1: 610 Q48 V26
GMAT ToolKit User
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 11 Nov 2017, 12:47
VeritasPrepKarishma - Going by your method, assuming if it would have been given in the premise as different integers? Would this method not be suitable to go forward with?

I did try and solve by taking consecutive integers from 1 to 21 but was not able to solve.

P.S Repeatedly kept on trying 6 times but did not succeed.
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10622
Location: Pune, India
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 11 Nov 2017, 20:41
2
siddyj94 wrote:
VeritasPrepKarishma - Going by your method, assuming if it would have been given in the premise as different integers? Would this method not be suitable to go forward with?

I did try and solve by taking consecutive integers from 1 to 21 but was not able to solve.

P.S Repeatedly kept on trying 6 times but did not succeed.


It will work for any set of values satisfying all given constraints.

You can assume 20 different integers as 1, 2, 3...20.
Their mean will be the average of middle two numbers 10 and 11 so it will be 10.5.
The 21st number then will be 4*10.5 = 42
Sum of all 21 numbers = 20*21/2 + 42 = 252

Required fraction = 42/252 = 1/6
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
B
Joined: 14 Aug 2017
Posts: 39
Location: India
Concentration: Operations, Social Entrepreneurship
Schools: Price (A)
GMAT 1: 610 Q48 V26
GMAT ToolKit User
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 11 Nov 2017, 21:01
Thanks Karishma!
For 6 times i just re-checked my calculations were wrong!

Thanks!


Sent from my iPhone using GMAT Club Forum
Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 628
Location: India
A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 11 Nov 2017, 21:24
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21

We need to find n/(sum of the 20 numbers + n)
Sum of the 20 numbers = 20*Ave
We have Ave=n/4
So sum of 20 numbers = 20*(n/4) = 5n
n/(sum of the 20 numbers +n)=n/(5n+n) = 1/6
_________________
Srinivasan Vaidyaraman
Magical Logicians
Holistic and Holy Approach
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4952
Location: Canada
GMAT 1: 770 Q49 V46
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 21 Apr 2018, 06:04
Top Contributor
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21


A quick solution here is to plug in some values that meet the given criteria.

Aside: I'm going to ignore the part about the numbers being different, since I have a feeling that this is the author's way of eliminating the possibility that all of the values equal zero (which would ruin the question).

So, the first 20 values (excluding n) could all equal 1, in which case their average (mean) would be 1.
Since n is 4 times the average, n would equal 4.
So, the sum of all 21 values is 24.

Question: n is what fraction of the sum of the 21 numbers in the list?
Answer: 4/24
= 1/6

Answer: B

IMPORTANT: Keep in mind that I broke the rule about all of the numbers being different. What's important here is that we COULD replace the 1's with 20 different numbers that still have a mean of 1, in which case the sum of the first 20 numbers would still be 20, which means the answer will remain B.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 19 Aug 2016
Posts: 2
Location: United States
GMAT 1: 670 Q28 V56
GPA: 3.5
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 08 Sep 2018, 09:37
Bunuel wrote:
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?


Given: \(average_{20}=\frac{sum_{20}}{20}=\frac{n}{4}\)--> \(sum_{20}=5n\) --> \(sum_{21}=sum_{20}+n=5n+n=6n\);

Question: \(n\) is what fraction of the sum of the 21 numbers in the list?
\(\frac{n}{sum_{21}}=\frac{n}{6n}=\frac{1}{6}\).

Answer: B.


For the part highlighted why would this be n/4 versus 4n, given the problem states that n is equal to 4x(Avg of 20 other numbers)?
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6420
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 09 Jan 2019, 00:45
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21



n= (4*(sum of 20 no))/ 20
or say sum of 20 no= x
x/5= n

so , x/5/ ( x/5+x)
; x/5 * 5/6x ; 1/6 IMO B
Intern
Intern
avatar
B
Joined: 20 Jul 2018
Posts: 16
A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 15 Jan 2020, 01:55
1. Average of 20 nos = Sum of 20 nos/20.

2. n= 4* Average of 20 nos.

n= 4* (Sum of 20 nos/20) = Sum of 20 nos/5.

5n = Sum of 20 nos.

3. Sum of 21 nos = Sum of 20 nos+n = 5n + n = 6n.

4. n = Sum of 21 nos/6.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11028
Location: United States (CA)
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 13 Feb 2020, 05:49
monirjewel wrote:
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21


We can let x = the sum of the 21 numbers. Thus, (x - n)/20 = the average of the 20 numbers when n is removed from the list. Since n is 4 times the average of the other 20 numbers in the list:

n = 4(x - n)/20

n = (x - n)/5

5n = x - n

6n = x

n = (1/6)x

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Manager
Manager
avatar
B
Joined: 27 Mar 2017
Posts: 171
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 19 May 2020, 19:13
Bunuel EMPOWERgmatRichC VeritasKarishma chetan2u

Why can't we solve this using AP formulae. I am consistently getting (D) as the answer. Where am I going wrong ?

\(a_{11} (avg) = a_1 + 10d\)
\(n = 4(a_{11}) = 4(a_1 + 10d)\)
\(S (sum) = \frac{21}{2}(2a_1 + 20d)\)

Putting in any dummy values in resulting expression for \(\frac{n}{S}\) will give (D) as the fraction.

Please help.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8750
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 19 May 2020, 19:30
1
altairahmad wrote:
Bunuel EMPOWERgmatRichC VeritasKarishma chetan2u

Why can't we solve this using AP formulae. I am consistently getting (D) as the answer. Where am I going wrong ?

\(a_{11} (avg) = a_1 + 10d\)
\(n = 4(a_{11}) = 4(a_1 + 10d)\)
\(S (sum) = \frac{21}{2}(2a_1 + 20d)\)

Putting in any dummy values in resulting expression for \(\frac{n}{S}\) will give (D) as the fraction.

Please help.



Hi
As you yourself have mentioned the word AP, so you cannot use the formula here as it is only for AP.
An AP is set where all terms differ by a common number from the previous element.

Here it is not given that it is an AP, that is Arithmetic Progression.
_________________
Manager
Manager
avatar
B
Joined: 27 Mar 2017
Posts: 171
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 19 May 2020, 22:34
chetan2u wrote:
Hi
As you yourself have mentioned the word AP, so you cannot use the formula here as it is only for AP.
An AP is set where all terms differ by a common number from the previous element.

Here it is not given that it is an AP, that is Arithmetic Progression.


Thanks for the response.

The solutions suggested above where Total = Avg x Number of values, doesn't that signify a set of numbers which is evenly spaced or AP ?
Senior Manager
Senior Manager
User avatar
G
Status: Today a Reader; Tomorrow a Leader.
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 19 May 2020, 23:16
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

let,the average(arithmetic mean) of the other 20 numbers in the list = a
so, sum of the other 20 numbers in the list = 20a
n=4a
now,sum of the other 21 numbers in the list = 20a+4a = 24a
so,n is 4a/24a=1/6 fraction of the sum of the 21 numbers in the list.

correct answer B
Manager
Manager
avatar
B
Joined: 27 Mar 2017
Posts: 171
A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 28 May 2020, 06:11
chetan2u wrote:
altairahmad wrote:
Bunuel EMPOWERgmatRichC VeritasKarishma chetan2u

Why can't we solve this using AP formulae. I am consistently getting (D) as the answer. Where am I going wrong ?

\(a_{11} (avg) = a_1 + 10d\)
\(n = 4(a_{11}) = 4(a_1 + 10d)\)
\(S (sum) = \frac{21}{2}(2a_1 + 20d)\)

Putting in any dummy values in resulting expression for \(\frac{n}{S}\) will give (D) as the fraction.

Please help.


Hi
As you yourself have mentioned the word AP, so you cannot use the formula here as it is only for AP.
An AP is set where all terms differ by a common number from the previous element.

Here it is not given that it is an AP, that is Arithmetic Progression.


Bunuel EMPOWERgmatRichC VeritasKarishma chetan2u

Can someone please help me with this basic confusion. Will be obliged.
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10622
Location: Pune, India
Re: A certain list consists of 21 different numbers. If n is in  [#permalink]

Show Tags

New post 29 May 2020, 00:12
altairahmad wrote:
Bunuel EMPOWERgmatRichC VeritasKarishma chetan2u

Why can't we solve this using AP formulae. I am consistently getting (D) as the answer. Where am I going wrong ?

\(a_{11} (avg) = a_1 + 10d\)
\(n = 4(a_{11}) = 4(a_1 + 10d)\)
\(S (sum) = \frac{21}{2}(2a_1 + 20d)\)

Putting in any dummy values in resulting expression for \(\frac{n}{S}\) will give (D) as the fraction.

Please help.


You are not given that the numbers in the list are in arithmetic progression. You are only given that n is 4 times the avg of other 20 numbers.
The numbers could be 1, 5, 6, 6, 6, 6, ... 6, 12
with an average of 6. Then n would be 24.

1, 5, 6, 6, 6, 6, 6, 6, .. 6, 12, 24 is not an AP.

Also, you are given that n = 4 * avg of other 20 numbers.
Even if this were an AP in which n were the last term, a11 is not the avg of first 20 numbers. The avg of first 20 numbers would be avg of 10th and 11th numbers.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: A certain list consists of 21 different numbers. If n is in   [#permalink] 29 May 2020, 00:12

Go to page   Previous    1   2   3    Next  [ 43 posts ] 

A certain list consists of 21 different numbers. If n is in

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





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne