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?

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

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?

is there any other strategies to solve this kind of problems?

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

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

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]

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.

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.

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.