GMAT Focus EditionQuantitative ReasoningMedium
A student has grades of 88, 75, and 92 on three exams. The final exam counts as two regular exams. What score does the student need on the final exam to achieve an average score of 85 for the course?
- A87.5
- B85
- C80
- D90
Show answer & explanationAnswer & explanation
Correct answer: B. 85
Let X be the score on the final exam. Since the final exam counts as two regular exams, the total number of 'exam units' is 3 (for the regular exams) + 2 (for the final) = 5. The desired total score is 85 * 5 = 425. The sum of current scores is 88 + 75 + 92 = 255. So, 255 + 2X = 425. 2X = 425 - 255 = 170. X = 170 / 2 = 85.
Why the other options are wrong
- A. Incorrect calculation.
- C. If final score is 80, (88+75+92+80+80)/5 = 415/5 = 83.
- D. If final score is 90, (88+75+92+90+90)/5 = 435/5 = 87.
Weighted Average
A weighted average is an average where some values contribute more than others to the final mean. Each value is multiplied by a weight, and the sum of these products is divided by the sum of the weights.
- Used when data points have different levels of importance.
- Formula: (Σ(value × weight)) / (Σweights).
- Common in calculating GPA, course grades, or financial metrics.
Memory trick: Weights Matter for the True Average.