a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (4/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?  Choose the correct answer
A) 2 / 5  B) 1 / 2  C) 11 / 16  D) 5 / 7  E) 3 / 4

Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )"
Answer: B