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The tricky set

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by vivek1110 » Mon Apr 05, 2010 4:58 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


Any help?

OA: D
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by thephoenix » Mon Apr 05, 2010 5:08 am
ans is three
for x=0,10 and 20 mean and median are equal
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by ajith » Mon Apr 05, 2010 5:32 am
vivek1110 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


Any help?

OA: D
The mean = (4+8+12+16 +x)/5 = 8 +x/5

if x is greater than 12, 12 will be the median
so 8+x/5 =12
x/5 = 4
x = 20

If x is in between 8 and 12 x will be the median

8+x/5 = x
4/5x =8
x =10

If x is less than 8; 8 will be the median

8 = 8+x/5
x = 0

So, there are clearly 3 values of x which satisfy the condition mean = median
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