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Set S consists of 5 values, not necessarily in ascending [#permalink]

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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

Re: Set S consists of 5 values, not necessarily [#permalink]

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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.

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

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]

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14 Dec 2012, 01:12

@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]

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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]

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23 Aug 2016, 03:13

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

Set S consists of 5 values, not necessarily in ascending [#permalink]

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24 Nov 2017, 10:26

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

The mean is always equal to median when numbers in a set have equal deviation. For instance, in our case if deviation is 4, the x should 0 or 20. Another case when a set is ascending from the mean out both sides. x should be 10. Please, look the atachments. Hope, it helps.

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]

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24 Nov 2017, 19:19

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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

if mean=(x+40)/5, then x must be an even multiple of 5 let x=0: mean=8; median=8 yes let x=10: mean=10; median=10 yes let x=20; mean=12; median=12 yes let x=30; mean=14; median=12 no 3 values of x work D