Problem Solving

150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235


A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

So here's our set.

150
200
250
n

Depending on what n is, will affect what the median is.

If n < 150, then the median would be calculated with 150 and 200, leading to a value of 175. Statement 1 is a possibility.

If 150 < n < 200, then median would be calculated with n and 200. No choice is here.

If 200 < n < 250, then median would be calculated with 200 and n. There is a choice here, 215, that could be the median if n = 230. Statement 2 is a possibility.

If 250 < n, then median would be calculated with 200 and 250. The median is 225 in that case, and this is the maximum value. Statement 3 can not be the median.

So my answer is (C), statements 1 and 2.

Stuart Kovinsky wrote:

dikku07 wrote:150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235


A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

The median of an set with an even number of terms is the average of the two middle terms. So, we need to think about where n could fit in the current set. There are 4 cases to consider.

First, the two simple cases:

{n, 150, 200, 250}: median is 175

{150, 200, 250, n}: median is 225

Second, the two more complicated cases:

{150, n, 200, 250}: median could be anything between 175 (if n=150) and 200 (if n=200)

{150, 200, n, 250}: median could be anything between 200 (if n=200) and 225 (if n=250)

Putting them together:

175 <= median <= 225

So, 175 and 215 are both possible, 235 is not: choose C, I and II only.

Thanks Stuart, thats a cleaner and quicker method