Terrible ACT Problem

Question

The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is 420. What is the sum of the 4 scores that are NOT the median?

F. 315

G. 320

H. 336

J. 350

K. 360

Answer 1

The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is 420. What is the sum of the 4 scores that are NOT the median?

F. 315

G. 320

H. 336

J. 350

K. 360

The scores are distinct. That is important.

There are five (an odd number) scores, so the median is the distinct middle score (not the average of the two middle scores).

Let the scores be: A, B, C, D, E in ascending order. Find (A+B+D+E)

Average of 5 scores = (A+B+C+D+E)/5 = 420/5 = 84 = C

(A+B+D+E) = (A+B+C+D+E) - C

(A+B+D+E) = 420 - 84

(A+B+D+E) = 336

Answer 2

The average is 84, that is also the median. So the other four sum to 420 - 84.

What is that sum?