Last visit was: 09 Oct 2024, 22:40 It is currently 09 Oct 2024, 22:40
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
SORT BY:
Date
User avatar
Joined: 06 Feb 2010
Posts: 124
Own Kudos [?]: 3383 [362]
Given Kudos: 182
Concentration: Marketing, Leadership
Schools: University of Dhaka - Class of 2010
GPA: 3.63
WE:Business Development (Consumer Packaged Goods)
Send PM
Most Helpful Reply
Tutor
Joined: 16 Oct 2010
Posts: 15357
Own Kudos [?]: 68667 [238]
Given Kudos: 444
Location: Pune, India
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 96014
Own Kudos [?]: 666813 [124]
Given Kudos: 87567
Send PM
User avatar
Joined: 06 Sep 2013
Posts: 1328
Own Kudos [?]: 2518 [93]
Given Kudos: 355
Concentration: Finance
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
71
Kudos
22
Bookmarks
monirjewel
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 = 4x

where 'x' is the average of other 20 numbers

Then sum of other 20 numbers is 20x

So we get 4x/24x = 1/6

B is our answer

Cheers!
J :)
General Discussion
User avatar
Joined: 08 Jul 2011
Status:Bunuel's fan!
Posts: 104
Own Kudos [?]: 180 [1]
Given Kudos: 55
Concentration: Non-profit
Send PM
Re: A certain list consists [#permalink]
1
Kudos
VeritasPrepKarishma
monirjewel
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

When you have your answer in percentages/fractions and there are no values in the data given to you, assume values.
Here you do not have the value of any number. So assume 20 numbers are all 1. Their average is 1 and sum is 20.
Then n is 4 and sum of 21 numbers is 24.
4/24 = 1/6

For this solution, I thought all numbers have to be different?
Tutor
Joined: 16 Oct 2010
Posts: 15357
Own Kudos [?]: 68667 [10]
Given Kudos: 444
Location: Pune, India
Send PM
Re: A certain list consists [#permalink]
9
Kudos
1
Bookmarks
Expert Reply
gmatfighter12
VeritasPrepKarishma
monirjewel
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

When you have your answer in percentages/fractions and there are no values in the data given to you, assume values.
Here you do not have the value of any number. So assume 20 numbers are all 1. Their average is 1 and sum is 20.
Then n is 4 and sum of 21 numbers is 24.
4/24 = 1/6

For this solution, I thought all numbers have to be different?

It usually doesn't matter if the numbers don't need to be integers.
The numbers could be 0.999999999999999, 0.99999998, 1.00000000000000001, 1.000000000002 etc. Effectively, they are all 1 and our solution doesn't change at all.
User avatar
Tutor
Joined: 20 Aug 2015
Posts: 348
Own Kudos [?]: 1431 [15]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Send PM
A certain list consists of 21 different numbers. If n is in [#permalink]
11
Kudos
3
Bookmarks
Expert Reply
monirjewel
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

Given: 21 numbers in a list including n. n = 4 times the average of other 20 numbers.
Assume the average to be x
n = 4x - (i)

Average = Sum/20
Sum of other 20 numbers = 20x - (ii)

n/Sum of other 21 numbers = \(\frac{4x}{(4x + 20x)} = \frac{4x}{24x} = 1/6\)
Option B
User avatar
Joined: 18 Jan 2010
Posts: 209
Own Kudos [?]: 1030 [2]
Given Kudos: 9
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
2
Kudos
monirjewel
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


Suppose sum of 20 nos. (excluding n) is S

Then

n = 4 * (\(\frac{S}{20}\))

n = \(\frac{S}{5}\))
5n = S

If we add n to S, we get sum of all 21 nos.

5n+n = Sum of all 21 Nos.

6n = Sum of all 21 nos.

n = (1/6) S.

B is the answer.
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21831
Own Kudos [?]: 11921 [5]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
4
Kudos
1
Bookmarks
Expert Reply
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
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3033
Own Kudos [?]: 6973 [4]
Given Kudos: 1646
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
4
Kudos
Expert Reply
monirjewel
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
Joined: 14 Aug 2017
Posts: 33
Own Kudos [?]: 10 [0]
Given Kudos: 38
Location: India
Concentration: Operations, Social Entrepreneurship
Schools: (A)
GMAT 1: 610 Q48 V26
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
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.
Tutor
Joined: 16 Oct 2010
Posts: 15357
Own Kudos [?]: 68667 [2]
Given Kudos: 444
Location: Pune, India
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
2
Kudos
Expert Reply
siddyj94
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
Joined: 17 Dec 2012
Posts: 584
Own Kudos [?]: 1614 [1]
Given Kudos: 20
Location: India
Send PM
A certain list consists of 21 different numbers. If n is in [#permalink]
1
Bookmarks
Expert Reply
monirjewel
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
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6797
Own Kudos [?]: 31599 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
Expert Reply
Top Contributor
monirjewel
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 [spoiler]B[/spoiler].

Cheers,
Brent
Joined: 27 Mar 2017
Posts: 269
Own Kudos [?]: 77 [0]
Given Kudos: 406
Location: Saudi Arabia
GMAT 1: 700 Q47 V39
GPA: 3.36
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
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.
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11498
Own Kudos [?]: 36699 [1]
Given Kudos: 333
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
1
Kudos
Expert Reply
altairahmad
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.
Tutor
Joined: 16 Oct 2010
Posts: 15357
Own Kudos [?]: 68667 [0]
Given Kudos: 444
Location: Pune, India
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
Expert Reply
altairahmad
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.
Joined: 11 Feb 2018
Posts: 35
Own Kudos [?]: 17 [1]
Given Kudos: 3
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
1
Bookmarks
hi VeritasKarishma

Thanks for the this quick and effective way to solve.

Just to be sure this won't work if in the question it is given that the numbers are NOT same.
Any guide on how to assume numbers in this type of questions

Thanks

VeritasKarishma
monirjewel
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

When you have your answer in percentages/fractions and there are no values in the data given to you, assume values.
Here you do not have the value of any number. So assume 20 numbers are all 1. Their average is 1 and sum is 20.
Then n is 4 and sum of 21 numbers is 24.
4/24 = 1/6


P.S. - The question requires the number to be different but note that they needn't be integers. So the numbers could be 0.999999999999999, 0.99999998, 1.00000000000000001, 1.000000000002 etc. Effectively, they are all 1 and our solution doesn't change.
Joined: 17 Dec 2012
Posts: 584
Own Kudos [?]: 1614 [0]
Given Kudos: 20
Location: India
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
Expert Reply
monirjewel
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
variables :
n,
a=ave of other 20 numbers,
s = sum of the 21 numbers
question :n/s

relationships:
n = 4*a
s= 20a +n

n/s= 4a/(20a+4a) =1/6
Tutor
Joined: 16 Oct 2010
Posts: 15357
Own Kudos [?]: 68667 [1]
Given Kudos: 444
Location: Pune, India
Send PM
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
1
Kudos
Expert Reply
cruiseav
hi VeritasKarishma

Thanks for the this quick and effective way to solve.

Just to be sure this won't work if in the question it is given that the numbers are NOT same.
Any guide on how to assume numbers in this type of questions

Thanks

VeritasKarishma
monirjewel
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

When you have your answer in percentages/fractions and there are no values in the data given to you, assume values.
Here you do not have the value of any number. So assume 20 numbers are all 1. Their average is 1 and sum is 20.
Then n is 4 and sum of 21 numbers is 24.
4/24 = 1/6


P.S. - The question requires the number to be different but note that they needn't be integers. So the numbers could be 0.999999999999999, 0.99999998, 1.00000000000000001, 1.000000000002 etc. Effectively, they are all 1 and our solution doesn't change.

Note that the question here mentions that the numbers are distinct but they needn't be integers so we assume them all to be very very close to 1 just to make things easier in our head.
If the question were to talk about distinct integers and then their average and sum etc, one could just assume that the average is still 1 (numbers could just as well be ... -6, -4, -2, 0, 2, 4, 6, 8, ... such that 0 and 2 are the middle two numbers).
Since average of the 20 numbers is 1, their sum would be 20.
n would still be 4 and the sum of 21 numbers would be 24.
4/24 = 1/6
GMAT Club Bot
Re: A certain list consists of 21 different numbers. If n is in [#permalink]
 1   2   
Moderator:
Math Expert
96014 posts