Last visit was: 19 Nov 2025, 08:02 It is currently 19 Nov 2025, 08:02
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,389
Own Kudos:
778,260
 [25]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,389
Kudos: 778,260
 [25]
When 15 is appended to a list of integers, the mean is increased by 2. 19 Mar 2019, 01:36
2
Kudos
Add Kudos
23
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

57% (03:12) correct 43% (02:49) wrong based on 195 sessions

History

Date
Time
Result
Not Attempted Yet
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [7]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [7]
When 15 is appended to a list of integers, the mean is increased by 2. Updated on: 17 Feb 2022, 00:13
Originally posted by KarishmaB on 13 Feb 2022, 22:38.
Last edited by KarishmaB on 17 Feb 2022, 00:13, edited 1 time in total.
3
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Show more

We can solve it in 30 secs using the basic concept of what mean is - the value that can replace all values in a list.
When a new value 15 is added, the mean increases by 2. It means 15 has enough extra (above mean) to give 2 to each member of the list and itself.
When a new value 1 is added, the mean decrease by 1. It means 1 has enough deficit (below mean) to take away 1 from each member of the list and still be 1 less.
Looking at the difference between 15 and 1, we can say that we will likely have 4 or 5 numbers in the original list.

Say if we have 4 numbers in the original list, 15 has 10 extra (2 for each of the 4 members and for itself) and hence original mean must be 5. When we add 15, the mean becomes 7 and now we have 5 numbers in the list.
Now when 1 is added to the list, it is 6 less than the mean 7 and hence all 5 numbers give 1 to it to bring it up to 6 and the avg reduces to 6. It works.
Hence, we had 4 numbers in the list. The numbers given are very manageable so that we don't need to do much calculation, the hallmark of a good GMAT question.

Answer (A)

rsrighosh
General Discussion
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Nov 2025
Posts: 8,422
Own Kudos:
4,981
 [4]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,422
Kudos: 4,981
 [4]
When 15 is appended to a list of integers, the mean is increased by 2. 19 Mar 2019, 05:45
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Show more

x = sum of integers
y= no of integers
x+15/y+1 = x/y + 2
and
x+15+1/y+2 = x/y+2-1
solve we get x=4
IMO A
User avatar
mt7777
User avatar
Joined: 11 Oct 2018
Last visit: 31 May 2019
Posts: 19
Own Kudos:
38
 [1]
Given Kudos: 40
Location: Germany
Posts: 19
Kudos: 38
 [1]
When 15 is appended to a list of integers, the mean is increased by 2. 19 Mar 2019, 16:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Show more

\(x=\) Sum of integers
\(y=\) number of integers

\(I. \frac{x+15}{y+1}=\frac{x}{y}+2\) or \(\frac{x+15}{y+1}-1=\frac{x}{y}+1\)

\(II. \frac{x+16}{y+2}=\frac{x}{y}+1\)

\(\frac{x+15}{y+1}-1=\frac{x+16}{y+2}\)

Cross-multiply

\((y+2)(x+15)-(y+2)(y+1)=(y+1)(x+16)\)
\(x=y^2+4y-12\)

Plug in in \(I\)

\(\frac{y^2+4y-12+15}{y+1}=\frac{y^2+4y-12}{y}+2\)

Simplify

\(\frac{(y+1)(y+3)}{(y+1)}=y+6-\frac{12}{y}\)

\(y+3-(y+6)=-\frac{12}{y}\)
\(y=4\)

IMO A

That approach is really time consuming. I hope there are some faster approaches.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Nov 2025
Posts: 21,713
Own Kudos:
26,995
 [4]
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,713
Kudos: 26,995
 [4]
When 15 is appended to a list of integers, the mean is increased by 2. 21 Mar 2019, 17:53
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Show more

We can let n = the number of integers in the original list and a = the average of these integers. We can create the equations:

(na + 15)/(n + 1) = a + 2

and

(na + 15 + 1)/(n + 2) = a + 2 - 1

Solving the first equation, we have:

na + 15= (n + 1)(a + 2)

na + 15 = na + 2n + a + 2

13 = 2n + a

13 - 2n = a

Solving the second equation, we have:

(na + 16)/(n + 2) = a + 1

na + 16 = (n + 2)(a + 1)

na + 16 = na + n + 2a + 2

14 = n + 2a

Substituting a = 13 - 2n into 14 = n + 2a, we have:

14 = n + 2(13 - 2n)

14 = n + 26 - 4n

3n = 12

n = 4

Answer: A
avatar
Shobhit7
avatar
Joined: 01 Feb 2017
Last visit: 29 Apr 2021
Posts: 240
Own Kudos:
426
Given Kudos: 148
Posts: 240
Kudos: 426
When 15 is appended to a list of integers, the mean is increased by 2. 27 Mar 2019, 11:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Change in Average = value added above old average / n+1

1st Case: Original set (Avg A) to Enlarged set
2= (15-A) / (n+1)
A+2n = 13

2nd Case: Enlarged set (Avg A') to Super Enlarged set
-1= (1-A') / (n+2)
A'-n= 3

We are given that A'=A+2
So,
Equation 1: A+2n = 13
Equation 2: A'-n = A+2-n = 3 >>> A-n = 1
Solving, we get 3n = 12 and so n=4

Ans A
User avatar
rsrighosh
User avatar
Joined: 13 Jun 2019
Last visit: 11 Dec 2022
Posts: 188
Own Kudos:
132
Given Kudos: 645
GMAT 1: 490 Q42 V17
GMAT 2: 550 Q39 V27
GMAT 3: 630 Q49 V27
GMAT 3: 630 Q49 V27
Posts: 188
Kudos: 132
When 15 is appended to a list of integers, the mean is increased by 2. 16 Feb 2022, 09:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi KarishmaB

I also tried to approach a similar method earlier but took algebraic approach later. Doing so, i got the answer in -ve. I am unable to understand where I am going wrong. I am pretty sure I made mistake in the second equation

Let us consider original mean of the list as m.
Then we can consider the list as {m, m, m, m....... (n times)}

When 15 is appended to a list of integers, the mean is increased by 2.
Hence list becomes
{m, m, m, ..... (n times), 15}
As this list has mean as m+2, hence going by your approach, I can say that total of 2ns (2 + 2+ 2 +.... (n times)) is carry forwarded from ms to 15
Hence, 15+2n=m+2

When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1
hence the list becomes
{m, m, m, ..... (n times), 15, 1} and its mean is m+2-1=m+1
Again following the same rule, I can say that n (1+1+1...(n times)) is carry forwarded from all ms to 15 and m is carry forwarded from 1 to 15.
Hence we can otherwise say 15 + n - m = m+1

So if i solve for n using the equations 15+2n=m+2 and 15 + n - m = m+1, i am getting the answer as n = -4
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [1]
When 15 is appended to a list of integers, the mean is increased by 2. 17 Feb 2022, 00:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rsrighosh
Hi KarishmaB

I also tried to approach a similar method earlier but took algebraic approach later. Doing so, i got the answer in -ve. I am unable to understand where I am going wrong. I am pretty sure I made mistake in the second equation

Let us consider original mean of the list as m.
Then we can consider the list as {m, m, m, m....... (n times)}

When 15 is appended to a list of integers, the mean is increased by 2.
Hence list becomes
{m, m, m, ..... (n times), 15}
As this list has mean as m+2, hence going by your approach, I can say that total of 2ns (2 + 2+ 2 +.... (n times)) is carry forwarded from ms to 15
Hence, 15+2n=m+2

When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1
hence the list becomes
{m, m, m, ..... (n times), 15, 1} and its mean is m+2-1=m+1
Again following the same rule, I can say that n (1+1+1...(n times)) is carry forwarded from all ms to 15 and m is carry forwarded from 1 to 15.
Hence we can otherwise say 15 + n - m = m+1

So if i solve for n using the equations 15+2n=m+2 and 15 + n - m = m+1, i am getting the answer as n = -4
Show more


The equations will be
15 - 2n = m + 2
(15 gives away 2 to each of the n elements so that it becomes m + 2 which is the new average)

and
1 + (n + 1) = m + 1
(All the n+1 elements (including 15) give 1 to 1 so that it comes up to the new average which is m+1)

When you solve these, you get m = 5, n = 4
User avatar
Tejassharmaa
User avatar
Joined: 23 Jun 2024
Last visit: 19 Nov 2025
Posts: 7
Own Kudos:
1
Given Kudos: 39
Location: India
Schools: Booth '27 Haas '27 INSEAD '26 Johnson '27 LBS '26 Rotman '27 Tepper '27
GMAT Focus 1: 645 Q83 V85 DI79
GPA: 3.1
Schools: Booth '27 Haas '27 INSEAD '26 Johnson '27 LBS '26 Rotman '27 Tepper '27
GMAT Focus 1: 645 Q83 V85 DI79
Posts: 7
Kudos: 1
When 15 is appended to a list of integers, the mean is increased by 2. 26 Jun 2024, 02:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
KarishmaB

Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
We can solve it in 30 secs using the basic concept of what mean is - the value that can replace all values in a list.
When a new value 15 is added, the mean increases by 2. It means 15 has enough extra (above mean) to give 2 to each member of the list and itself.
When a new value 1 is added, the mean decrease by 1. It means 1 has enough deficit (below mean) to take away 1 from each member of the list and still be 1 less.
Looking at the difference between 15 and 1, we can say that we will likely have 4 or 5 numbers in the original list.

Say if we have 4 numbers in the original list, 15 has 10 extra (2 for each of the 4 members and for itself) and hence original mean must be 5. When we add 15, the mean becomes 7 and now we have 5 numbers in the list.
Now when 1 is added to the list, it is 6 less than the mean 7 and hence all 5 numbers give 1 to it to bring it up to 6 and the avg reduces to 6. It works.
Hence, we had 4 numbers in the list. The numbers given are very manageable so that we don't need to do much calculation, the hallmark of a good GMAT question.

Answer (A)

rsrighosh
Show more
­Can you please explain how mean came out to be 5?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
When 15 is appended to a list of integers, the mean is increased by 2. 26 Jun 2024, 04:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Tejassharmaa

KarishmaB

Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
We can solve it in 30 secs using the basic concept of what mean is - the value that can replace all values in a list.
When a new value 15 is added, the mean increases by 2. It means 15 has enough extra (above mean) to give 2 to each member of the list and itself.
When a new value 1 is added, the mean decrease by 1. It means 1 has enough deficit (below mean) to take away 1 from each member of the list and still be 1 less.
Looking at the difference between 15 and 1, we can say that we will likely have 4 or 5 numbers in the original list.

Say if we have 4 numbers in the original list, 15 has 10 extra (2 for each of the 4 members and for itself) and hence original mean must be 5. When we add 15, the mean becomes 7 and now we have 5 numbers in the list.
Now when 1 is added to the list, it is 6 less than the mean 7 and hence all 5 numbers give 1 to it to bring it up to 6 and the avg reduces to 6. It works.
Hence, we had 4 numbers in the list. The numbers given are very manageable so that we don't need to do much calculation, the hallmark of a good GMAT question.

Answer (A)

rsrighosh
­Can you please explain how mean came out to be 5?
Show more
­
Assuming there were 4 people,
15 has 2 extra for each of the 4 people and for itself (that is why mean goes up by 2). So 15 has 10 more than mean. This tells us that mean must be 5 (that is how 15 has 10 more than mean)

 
User avatar
PS31
User avatar
Joined: 18 Feb 2024
Last visit: 16 Sep 2025
Posts: 6
Own Kudos:
7
Given Kudos: 43
Posts: 6
Kudos: 7
When 15 is appended to a list of integers, the mean is increased by 2. 07 Aug 2024, 06:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Show more

Posted from my mobile device
Attachments

File comment: Try this sum method
17230390331808598877508226059274.jpg
17230390331808598877508226059274.jpg [ 3.07 MiB | Viewed 2455 times ]

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
When 15 is appended to a list of integers, the mean is increased by 2. 25 Sep 2025, 23:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105389 posts
Krunaal
Tuck School Moderator
805 posts