In Ms. Rodriguez's statistics class, Section A consists of 70 students and has a mean test score of 73 points....
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
In Ms. Rodriguez's statistics class, Section A consists of \(\mathrm{70}\) students and has a mean test score of \(\mathrm{73}\) points. Section B consists of \(\mathrm{30}\) students and has a mean test score of \(\mathrm{83}\) points. If both sections are combined into a single group, what is the mean test score, in points, of the combined group?
- 75
- 76
- 78
- 80
- 83
1. TRANSLATE the problem information
- Given information:
- Section A: 70 students, mean score = 73 points
- Section B: 30 students, mean score = 83 points
- Need to find: mean score of combined group
2. INFER the correct approach
- Key insight: You cannot simply average 73 and 83 to get the combined mean
- Why not? Because the sections have different numbers of students (70 vs 30)
- Strategy needed: Find the weighted average by calculating total points first
3. SIMPLIFY to find total points for each section
- Section A total points: \(70 \times 73 = 5{,}110\) points
- Section B total points: \(30 \times 83 = 2{,}490\) points
4. SIMPLIFY to find combined totals
- Total points for both sections: \(5{,}110 + 2{,}490 = 7{,}600\) points
- Total students: \(70 + 30 = 100\) students
5. SIMPLIFY to calculate final mean
- Combined mean = Total points ÷ Total students
- Combined mean = \(7{,}600 \div 100 = 76\) points
Answer: B) 76
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students think they can just average the two given means: \((73 + 83) \div 2 = 78\)
This completely ignores that Section A has more than twice as many students as Section B. The larger section should have more influence on the combined average, but this approach treats both sections equally.
This may lead them to select Choice C (78)
Second Most Common Error:
Poor SIMPLIFY execution: Students understand the weighted average approach but make arithmetic errors during the calculations
For example, miscalculating \(70 \times 73\) or making errors when adding the totals could lead to different final answers.
This may lead them to select other incorrect choices or causes them to get stuck and guess
The Bottom Line:
This problem tests whether students understand that combining groups with different sizes requires weighted averaging, not simple averaging. The key insight is recognizing that the section with more students (Section A) will pull the combined average closer to its mean (73) than to Section B's higher mean (83).