Median problem

psm12se wrote:4, 8, 12, y, 5, 10, 15

If y is a positive integer such that 3 < y < 16, but y does not equal 9, the median of the list above must be:

a. either 5 or 8
b. either 10 or 12
c. either 8 or 10
d. y
e. 9

Source: Grockit
OA: C

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

First list the numbers in ascending order {4, 5, 8, 10, 12, 15}
We need to add y to this set.

When we add y to the set, the median will be the middlemost value (since there is an odd number of values in the set)

Since y is an integer, and since y cannot equal 9, we need only consider two cases.
case 1: y < 8
case 2: y > 10

case 1: If y < 8, then the median = 8
case 2: If y > 10, then the median = 10

So, the median must be either 8 or 10

Answer: C

Cheers,
Brent

psm12se wrote:Thank you Brent for the solution.

Also I will take care to use the spoiler next time.

No problem.
FYI, you can still go back and add the spoiler to your original post. Just go to that post and click EDIT

Cheers,
Brent