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Set S consists of 5 values, not necessarily in ascending

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Set S consists of 5 values, not necessarily in ascending [#permalink] New post 12 Dec 2012, 13:36
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Dec 2012, 01:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Set S consists of 5 values, not necessarily [#permalink] New post 12 Dec 2012, 23:15
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mun23 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)0
(B)1
(C)2
(D)3
(E)More than 3

Need details explanation.............

There could be 3 medians of this set.
8 , when x <8
x , when 8<=x<=12
and
12, when x>12

There could be 1 mean = (40+x)/5

Now, we can solve (40+x)/5 = 8 , x, 12 to find out values.. and if valid values are found that solution counts.
We get x= 0 ,10, 20. Hence 3 solutions.

Ans D it is.
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Re: Set S consists of 5 values, not necessarily in ascending [#permalink] New post 13 Dec 2012, 01:21
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mun23 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


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Hope it helps.
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Re: Set S consists of 5 values, not necessarily in ascending [#permalink] New post 14 Dec 2012, 01:12
Expert's post
@vips and @bunuel:
Since mean and median are the same for evenly spaced sets, so to make the entire set an evenly spaced set x can be made either 0 or 20.
Can this concept be used to find x=10 as the mean and median?
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Re: Set S consists of 5 values, not necessarily in ascending [#permalink] New post 14 Dec 2012, 01:22
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Marcab wrote:
@vips and @bunuel:
Since mean and median are the same for evenly spaced sets, so to make the entire set an evenly spaced set x can be made either 0 or 20.
Can this concept be used to find x=10 as the mean and median?


Actually that (such numbers) could be a trap in this question.

You might remember -
If set is evenly spaced then for sure mean=median
But, if mean=median, it doesnt mean that set is evenly spaced. It may or may not be.

So, if we make x=0 and x=20, and find mean and median =10. We are pratically limiting our scope only to evenly spaced sets. And thus we get a few solutions-but not all.

We still need to look for solution for the other case where set is not evenly spaced. (Also x=10 doesnt give u an evenly spaced set.. so concept cant be applied directly, it would be more evident if the number of elements in set is even).

One easy concept that u can use though is, if median =mean then numbers in the set will be symmetrical around median. Why it helps is that finding median is usually very simple,without calculation.
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Re: Set S consists of 5 values, not necessarily in ascending   [#permalink] 14 Dec 2012, 01:22
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