BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

mean median

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Sat Dec 01, 2007 4:19 pm
Thanked: 5 times

mean median

by vscid » Fri Feb 12, 2010 6:38 am
Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 am
Thanked: 19 times
Followed by:1 members
GMAT Score:690

by sreak1089 » Fri Feb 12, 2010 8:34 am
IMO C?

Mean and median of set equal if they are equally-spaced. So the problem can be re-stated as "for how many values
of x, the set is equally-spaced." I see two possibilities:

4,8,12,16,20
0,4,8,12,16

Am I correct?
Top
GMAT Instructor
Posts: 1578
Joined: Thu May 28, 2009 8:02 am
Thanked: 128 times
Followed by:34 members
GMAT Score:760

by Osirus@VeritasPrep » Fri Feb 12, 2010 8:37 am
sreak1089 wrote:IMO C?

Mean and median of set equal if they are equally-spaced. So the problem can be re-stated as "for how many values
of x, the set is equally-spaced." I see two possibilities:

4,8,12,16,20
0,4,8,12,16

Am I correct?
Wouldn't it be 3? If x equals 10 wouldn't the mean equal 10 and ten would be the middle number so it would equal 10 as well
https://www.beatthegmat.com/the-retake-o ... 51414.html

Brandon Dorsey
GMAT Instructor
Veritas Prep

Buy any Veritas Prep book(s) and receive access to 5 Practice Cats for free! Learn More.
Top
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 am
Thanked: 19 times
Followed by:1 members
GMAT Score:690

by sreak1089 » Fri Feb 12, 2010 8:48 am
Perfect. Missed that one.
sreak1089 wrote:IMO C?

Mean and median of set equal if they are equally-spaced. So the problem can be re-stated as "for how many values
of x, the set is equally-spaced." I see two possibilities:

4,8,12,16,20
0,4,8,12,16

Am I correct?
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pm
Location: India
Thanked: 4 times
Followed by:1 members

by abhi332 » Thu Feb 18, 2010 2:09 am
is there any other strategies to solve this kind of problems?
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Sat Dec 01, 2007 4:19 pm
Thanked: 5 times

by vscid » Thu Feb 18, 2010 6:01 am
OA is D
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 10:32 am
vscid wrote:Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
The Condition we have is:-Mean of set S equal the median of set S.
Imp. concept to be kept in mind:-Median is the middle most value .(i.e. the 3rd term) and
Mean is the average of all the 5 terms.
Case 1:- x>16 , x should be 20 to satisfy the condition.[median=mean is 12]
Case 2:- 16>x>12 not possible.
Case 3 :-12>x>8 ,x=10 would satisfy the condition.[median=mean 10]
Case 4:-8>x>4 ,not possible
Case 5:-x<4 , x=0 would satisfy the condition.[median=mean is 8]

Thus the answer is three.D
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
GMAT Instructor
Posts: 1578
Joined: Thu May 28, 2009 8:02 am
Thanked: 128 times
Followed by:34 members
GMAT Score:760

by Osirus@VeritasPrep » Thu Feb 18, 2010 10:37 am
You added nothing to the conversation troll. WHy would you up and old thread in which the correct solution has already been posted just to post no new information? You are just a blatant troll.
harsh.champ wrote:
vscid wrote:Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
The Condition we have is:-Mean of set S equal the median of set S.
Imp. concept to be kept in mind:-Median is the middle most value .(i.e. the 3rd term) and
Mean is the average of all the 5 terms.
Case 1:- x>16 , x should be 20 to satisfy the condition.[median=mean is 12]
Case 2:- 16>x>12 not possible.
Case 3 :-12>x>8 ,x=10 would satisfy the condition.[median=mean 10]
Case 4:-8>x>4 ,not possible
Case 5:-x<4 , x=0 would satisfy the condition.[median=mean is 8]


Thus the answer is three.D
https://www.beatthegmat.com/the-retake-o ... 51414.html

Brandon Dorsey
GMAT Instructor
Veritas Prep

Buy any Veritas Prep book(s) and receive access to 5 Practice Cats for free! Learn More.
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 10:40 am
sreak1089 wrote:IMO C?

Mean and median of set equal if they are equally-spaced. So the problem can be re-stated as "for how many values
of x, the set is equally-spaced." I see two possibilities:

4,8,12,16,20
0,4,8,12,16

Am I correct?
Well,you are correct that Mean and median of set equal if they are equally-spaced.
But I am afraid, you committed a very common mistake.
You left out the case when x itself becomes the mean = median when x=10
This can lead ppl to choose C instead of D.
I hope it is clear to you now.
[spoiler]The set will be {4,8,10,12,16}[/spoiler]
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 10:45 am
osirus0830 wrote:You added nothing to the conversation troll. WHy would you up and old thread in which the correct solution has already been posted just to post no new information? You are just a blatant troll.
harsh.champ wrote:
vscid wrote:Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
The Condition we have is:-Mean of set S equal the median of set S.
Imp. concept to be kept in mind:-Median is the middle most value .(i.e. the 3rd term) and
Mean is the average of all the 5 terms.
Case 1:- x>16 , x should be 20 to satisfy the condition.[median=mean is 12]
Case 2:- 16>x>12 not possible.
Case 3 :-12>x>8 ,x=10 would satisfy the condition.[median=mean 10]
Case 4:-8>x>4 ,not possible
Case 5:-x<4 , x=0 would satisfy the condition.[median=mean is 8]


Thus the answer is three.D
Hey osirus,
The OA was D but nobody had posted how we get the answer as 3.
On the other hand,sreak1089 had also done a mistake in solving the problem.
So,I added 2 things to the conversation:-
1)The soln. approach as to how stepwise we need to solve the problem.[I guess it is better to show the 5 cases ,take the 3 possible cases and how to formally approach the soln. so that even if we have 7 no.s instead of 5 no-one who reads this post makes any mistake]
2)Pointed out an imp. mistake that ppl leave the case x=10 in which x itself becomes the mean and the median.

Well,just carefully check my 2 posts above and still if you feel that the above posts were useless then you can notify me.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Mon Jul 13, 2009 4:25 pm
Thanked: 1 times

by ymach3 » Tue Apr 13, 2010 5:49 am
Mean of Set S= (40+x)/5

Possible medians = 8,x,12.

From the Qn,

Mean = Median

(40+x)/5=Median (probable medians 8,x,12 and i think 16 or 4 cannot be median of the Set)

Therfore, X can take 0,10,20 values for median to be 8,10,12. --> 3 Values.

Hence D.

Thanks to Osirus and Harsh for "You left out the case when x itself becomes the mean = median when x=10 " -
Initially i dint consider this case, which made me to select option C, i.e 2 values.


Let me know if i have messed it up.
Top
User avatar
GMAT Instructor
Posts: 22
Joined: Mon Mar 15, 2010 2:42 pm
Location: Brooklyn, NY
Thanked: 14 times
Followed by:4 members

by stephen@knewton » Tue Apr 13, 2010 12:07 pm
Nope, you've done a good job!

The mean will ALWAYS be (40+x)/5

The median can have three values:
8 for all X<=8
X for all 8<X<12
12 for all X>=12

(For the sake of completeness, I'll point out that even for X=8 or X=12 the set becomes {4, 8, 8, 12, 16} or {4, 8, 12, 12, 16} respectively, and thus the median is still 8 or 12).

This sets up three possible equations describing the condition in the question prompt (mean = median):

(40+x)/5 = 8
(40+x)/5 = X
(40+x)/5 = 12

Each one has a unique solution (as stated 0, 10 and 20 respectively) so the correct answer is D.

Great work!

Cheers, Steve P.
Stephen
GMAT Instructor
Knewton Inc.
Top
Post new topic Post Reply
• Page 1 of 1