SOLUTION: S=( 11,12,13,14,15). The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T? A)1

Question 1143714: S=( 11,12,13,14,15). The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T?
A)19
B)18
C)17
D)16
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

median= the average of the first and the last terms
S=( 11,12,13,14,15).

The median of the set S is equal to the mean of the set T, which consists of 11 consecutive positive integers. What is the largest integer of the set T?
mean of the set T=
mean= median
the sum of the elements = the mean * # of elements
the sum of the elements =
the sum of the consecutive positive integers:

............smallest integer in the set T,
then the integer of the set T is
check the median
->which is true
so, answer is )

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

In any set of an odd number of consecutive positive integers, the mean and the median are the same.

So we have a set S consisting of 5 consecutive positive integers with a mean of 13; that means a middle number 13 with the 2 integers either side of 13.

We are looking for the largest number in a set T consisting of 11 positive integers with middle number 13. That means middle number 13 with 5 integers either side of 13.

That makes the largest integer in set T 13+5 = 18.
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