Test madness
Joe's test scores for a physics course were 72, 78, 80, , and . The professor decides to replace the lowest test score with the average (arithmetic mean) of the remaining four test scores. After this transition, the average of Joe's test scores is 75. Find the larger of and .
The answer is 70.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Without loss of generality, let x≤y. We have two cases:
Case 1: 72 is the lowest test score. In this case, we only need to look at the remaining four test scores. Hence 78+80+x+y=300. However, if x and y are both greater than or equal to 72, 78+80+x+y>300, a contradiction.
Case 2: x is the lowest test score. Then 72+78+80+y=300⟺y=70. Therefore the answer is 70.