Since S contains only consecutive integers, its median is the average of the extreme
values a and b. We also know that the median of S is 3/4b. We can set up and simplify
the following equation:
Since set Q contains only consecutive integers, its median is also the average of the
extreme values, in this case b and c. We also know that the median of Q is 7/8c . We can
set up and simplify the following equation:
We can find the ratio of a to c as follows:
Taking the first equation
2a =b→8a = 4b
and the second equation, 4b = 3c
and setting them equal to each other, yields the following:
Since set R contains only consecutive integers, its median is the average of the extreme
values a and c:
. We can use the ratio
to substitute 3c/8 for a:
Thus the median of set R is 11/16c. The correct answer is C.