Problem Solving

A list of measurements in increasing order is 4, 5, 6, 8, 10, and x. If median of the measurements is 6/7 times the mean, what is the value of x?
a. 16
b. 10
c. 12
d. 13
e. 15

Since the set of numbers 4,5,6,8,10, and x are in increasing order, the median of the set would be 6+8/2=14/2=7. The mean of the set would be 4+5+6+8+10+x/6=(33+x)/6. The problem tells us that the median is 6/7 the mean, so we can set up an equation to find the value x:

(33+x)/6*6/7=7
The 6's would cancel and you'd be left with:

(33+x)/7=7
33+x=49
x=16 A.

We can calculate 7 as the median here.

7 = 6/7 [(33 + x)/6]

We get x = 16

(A)