GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Apr 2019, 07:32

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

When 15 is appended to a list of integers, the mean is increased by 2.

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54371
When 15 is appended to a list of integers, the mean is increased by 2.  [#permalink]

Show Tags

New post 19 Mar 2019, 01:36
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (03:13) correct 50% (02:36) wrong based on 26 sessions

HideShow timer Statistics

CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 2998
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: When 15 is appended to a list of integers, the mean is increased by 2.  [#permalink]

Show Tags

New post 19 Mar 2019, 05:45
2
Bunuel wrote:
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


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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Intern
avatar
B
Joined: 11 Oct 2018
Posts: 20
CAT Tests
Re: When 15 is appended to a list of integers, the mean is increased by 2.  [#permalink]

Show Tags

New post 19 Mar 2019, 16:31
Bunuel wrote:
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


\(x=\) 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.
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5784
Location: United States (CA)
Re: When 15 is appended to a list of integers, the mean is increased by 2.  [#permalink]

Show Tags

New post 21 Mar 2019, 17:53
Bunuel wrote:
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 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
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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
G
Joined: 01 Feb 2017
Posts: 211
Re: When 15 is appended to a list of integers, the mean is increased by 2.  [#permalink]

Show Tags

New post 27 Mar 2019, 11:49
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
GMAT Club Bot
Re: When 15 is appended to a list of integers, the mean is increased by 2.   [#permalink] 27 Mar 2019, 11:49
Display posts from previous: Sort by

When 15 is appended to a list of integers, the mean is increased by 2.

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.