Statistics

[amit803]

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
(7/8)c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set

R

?
(A) 3/8
(B) 1/2
(C) 11/16
(D) 5/7

(E) 3/4

OA -

SPOILER: C

[manuuuu]

since the sets contain all integers in between, the median just represents the mid-point. So we have (a+b)/2=0.75b, which you can simplify to b=2a. Similarly (b+c)/2=7c/8, so 3c=4b=8a and a=3c/8. Now, the mid-point of ac would just be (c+3c/8)/2, which comes down to 11c/16. Answer should be C.