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 (5/8)*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 choice from the following choices:	A) 3 / 8	B) 1 / 2	C) 9 / 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 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c )
Answer: C