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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 setof 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)
    ½
  • c)
    11/16
  • d)
    5/7
  • e)
    3/4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
a, b, and c are integers and a < b < c. S is the set of all inte...
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

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 . 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  The correct answer is C
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a, b, and c are integers and a < b < c. S is the set of all inte...
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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 setof 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)½c)11/16d)5/7e)3/4Correct answer is option 'C'. Can you explain this answer?
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