AAPL wrote:In a particualr course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?
A. 52%
B. 64%
C. 72%
D. 76%
E. 80%
Let the whole course = 100 points.
Since the midterm is worth 1/4 of the total grade, the midterm = (1/4)(100) = 25 points, while the final = 100-25 = 75 points.
Since Lindsay's grade was 88%, the total number of points earned by Lindsay in the 100-point course = (88/100)(100) = 88 points.
To MINIMIZE the score needed on the midterm, we must MAXIMIZE the score earned on the final.
If Lindsay scores 100% on the 75-point final -- implying that she earns all 75 points -- the number points needed on the midterm = (total number of points earned) - (points earned on the final) = 88-75 = 13.
Since Lindsay must 13 points on the 25-point midterm, her score on the midterm = 13/25 = 52/100 = 52%.
The correct answer is
A.
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