The table shows the scores earned by 6 students on a recent quiz.Student AStudent BStudent CStudent DStudent EStudent F85927888?91If the...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The table shows the scores earned by 6 students on a recent quiz.
| Student A | Student B | Student C | Student D | Student E | Student F |
|---|---|---|---|---|---|
| 85 | 92 | 78 | 88 | ? | 91 |
If the mean score for these 6 students is \(86\), what is the score earned by Student E?
1. TRANSLATE the problem information
- Given information:
- 6 students took a quiz
- 5 known scores: 85, 92, 78, 88, 91
- 1 unknown score (Student E)
- Mean of all 6 scores is 86
- What this tells us: We can use the mean formula to find the missing score
2. INFER the approach
- Since \(\mathrm{Mean = Sum ÷ Count}\), we can find the total sum needed
- Strategy: Find total sum required → subtract known scores → get unknown score
- This reverse-engineering approach is the most efficient path
3. SIMPLIFY to find the required total sum
- If mean = 86 and count = 6 students:
- Total sum = \(\mathrm{86 × 6 = 516}\)
4. SIMPLIFY by calculating the sum of known scores
- Sum of known scores = \(\mathrm{85 + 92 + 78 + 88 + 91 = 434}\)
5. SIMPLIFY to find Student E's score
- Student E's score = \(\mathrm{516 - 434 = 82}\)
Answer: B) 82
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skills: Students may try to find the mean of just the 5 known scores, thinking they need to somehow use this partial mean to find the missing score.
They calculate: \(\mathrm{(85 + 92 + 78 + 88 + 91) ÷ 5 = 434 ÷ 5 = 86.8}\), then get confused about how to proceed from there. This leads to confusion and guessing.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up the problem but make arithmetic errors when adding the known scores or performing the final subtraction.
For example, they might miscalculate the sum as 424 instead of 434, leading to Student E's score = \(\mathrm{516 - 424 = 92}\). Since 92 isn't among the answer choices, this causes them to get stuck and guess.
The Bottom Line:
The key insight is recognizing that you can work backwards from the given mean. Instead of trying to build up to the mean, use the mean to determine what the total must be, then find the missing piece.