Last visit was: 27 Jul 2024, 07:13 It is currently 27 Jul 2024, 07:13
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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

A set of 13 integers has a median of 10 and an average of 15.

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
S
benejo
Intern
Intern
Joined: 17 Jan 2017
Posts: 47
Own Kudos [?]: 120 [15]
Given Kudos: 4
Send PM
A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   12 May 2018, 09:38
15
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

38% (02:41) correct 62% (02:59) wrong based on 146 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
A set of 13 integers has a median of 10 and an average of 15. If the highest term in the set is a unique, non-repeating integer, what is the lowest possible value of the highest integer in the set?
A. 81
B. 25
C. 22
D. 21
E. 20

Source:ExpertsGlobal
ShowHide Answer
Official Answer
C
User avatar
G
Hero8888
Senior Manager
Senior Manager
Joined: 29 Dec 2017
Posts: 302
Own Kudos [?]: 311 [1]
Given Kudos: 273
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE:Marketing (Telecommunications)
Send PM
A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   12 May 2018, 11:47
1
Kudos
benejo wrote:
A set of 13 integers has a median of 10 and an average of 15. If the highest term in the set is a unique, non-repeating integer, what is the lowest possible value of the highest integer in the set?
A. 81
B. 25
C. 22
D. 21
E. 20

Source:ExpertsGlobal


To make X- the last 13th member of the set, we have to maximize other values in the set.

1) Median (7th member) = 10, then we can max 1-6th values also to 10
2) Numbers in the set are integers, so X will be unique min, when 8-12th numbers = X-1
3) Sum of the set = avarage*number of set members = 15*13
We got an uquality:

10*7 + 5*(x-1) + x = 13*15
3x=65
x= 21.7
Since x- is integer we can say it is 21 or 22,
so 3x=66 or 3x=63. In second case (63) we have to give extra 2 points to any number/numbers of the set which will a)move median b) will make other numbers = or > than the X. So the only scenario is possible to "take" extra 1 point from any other number of the set. Hence Answer is 22 (C)
User avatar
P
SSM700plus
Manager
Manager
Joined: 01 Aug 2017
Posts: 165
Own Kudos [?]: 163 [0]
Given Kudos: 420
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S) IIMA PGPX"20 (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE:Information Technology (Computer Software)
Send PM
Reviews Badge
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   12 May 2018, 12:22
benejo wrote:
A set of 13 integers has a median of 10 and an average of 15. If the highest term in the set is a unique, non-repeating integer, what is the lowest possible value of the highest integer in the set?
A. 81
B. 25
C. 22
D. 21
E. 20

Source:ExpertsGlobal


To make X- the last member of the set, we have to maximize other values in the set.

We know that median is the middle value. 7th term is 10. We need to minimize the 13th term.

1) 6 terms below Median can be not more than 10. So, 10 is the maximum value.
2) 7th term is 10. Given in question.
3) From 8th to 12th term can take maximum value of - One less than 13th term.

Numbers in the set are integers, Let X will be unique min 13th term, and 8th -12th numbers be X-1 each
Sum of the set = average*number of set members = 15*13

10*7 + 5*(x-1) + x = 13*15
5*(x-1) + x = 195 - 70
5*(x-1) + x = 125---------------------------> 1
5x-5+x = 195 - 70
6x = 125+5

x = 130/6 = 21.7

Since x- is integer we can say it is 21 or 22,

Let's assume x =21,

8th term - 12th term is 20. And 13th term is 21. Sum is 20*5 + 21= 121. But it should add up to 125. See eq 1

4 less than the value it should add up to. This 4 can be adjusted by increasing the values of last four terms ( 10th, 11th, 12th and 13th term).

So now, 10th term is 21, 11th term is 21, 12th term is 21 and 13th term is 22.

So Ans is - 22. C
avatar
B
arijitd
Intern
Intern
Joined: 24 Aug 2013
Posts: 6
Own Kudos [?]: 1 [0]
Given Kudos: 135
Send PM
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   12 May 2018, 13:59
I used the smaller number as 9. Such a dumb ?

Posted from my mobile device
User avatar
B
rahulbanerjee1992
Intern
Intern
Joined: 10 Dec 2015
Posts: 23
Own Kudos [?]: 17 [1]
Given Kudos: 55
GMAT 1: 680 Q45 V38
Send PM
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   16 May 2018, 06:05
1
Kudos
Here's my method of finding it via concepts:
13 integers are present, and the median is 10.
In order to minimize the value of X, the largest integer, we have to maximize the value of all integers till 10.
The max value for each integer till the median is 10. So, our list has 7 integers, with value, '10'.
The sum of our list is 195.
10*number of integers till median = 10*7=70. Apart from these, we have 6 remaining integers.
Substract 70 from 195, we get 125.
So, the sum of the remaining 6 integers must be 125.
Now, in order to minimize the highest unique value, we must maximize the integers.
If we assume these to be 20, we have 6*20=120 which is less than 125.
Now assume them to be 21, we have 6*21=126, which is greater than 125.
Now write,
20 20 20 20 20 25(X) ...Matches our answer choice, but let's see if we can lessen the value of X, somehow.
20 20 20 20 21 24
20 20 20 20 22 23
20 20 20 21 21 22
After this, we will not be able to minimize the value of X, because then X would not be a UNIQUE integer in the list.
Hence, Option C is our answer.
User avatar
G
Maxximus
Experts' Global Representative
Joined: 19 Feb 2010
Posts: 261
Own Kudos [?]: 232 [1]
Given Kudos: 90
Send PM
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   25 May 2019, 09:18
1
Kudos
Expert Reply
Interesting discussion.

Here is the video explanation by us-



Hope this helps.

All the best!
Experts' Global team

benejo wrote:
A set of 13 integers has a median of 10 and an average of 15. If the highest term in the set is a unique, non-repeating integer, what is the lowest possible value of the highest integer in the set?
A. 81
B. 25
C. 22
D. 21
E. 20

Source:ExpertsGlobal
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34121
Own Kudos [?]: 854 [0]
Given Kudos: 0
Send PM
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink] A set of 13 integers has a median of 10 and an average of 15.   22 Apr 2024, 22:10
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.
GMAT Club Bot
gmatclubot
Re: A set of 13 integers has a median of 10 and an average of 15. [#permalink]
22 Apr 2024, 22:10
Moderator:
Bunuel
Math Expert
94625 posts