GmatKiss wrote:GMATGuruNY wrote:GmatKiss 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
When a set is SYMMETRICAL about the median, the mean = the median.
Since the given numbers are evenly spaced, there are only 3 options:
x = the smallest value:
0,4,8,12,16
x = the median,
halfway between 8 and 12:
4,8,
10,12,16
x = the greatest value:
4,8,12,16,
20
The correct answer is
D.
Hi Mitch,
why not between 12 and 16 (14) ? Am i missing anything!
TIA,
GK
If x is halfway between 12 and 16, the numbers will NOT be symmetrical about the median:
4,8,
12,14,16
The distances are 4-4-median-2-2.
Not symmetrical about the median.
Each of the sets in my post above is symmetrical about the median:
{0,4,8,12,16}
The distances are 4-4-median-4-4.
{4,8,10,12,16}
The distances are 4-2-median-2-4.
{4,8,12,16,20}
The distances are 4-4-median-4-4.
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