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# 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)3/8b)1/2c)11/16d)5/7e)3/4Correct answer is option 'C'. Can you explain this answer? Related Test: GMAT Full Mock Test- 1

## GMAT Question

 DEVASYA SACHAN Apr 11, 2020
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.