Number of High School Students Who Completed Summer InternshipsHigh schoolYear20082009201020112012Foothill8780757670Valley4454657682Total1311341401521...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Number of High School Students Who Completed Summer Internships
| High school | Year | ||||
|---|---|---|---|---|---|
| 2008 | 2009 | 2010 | 2011 | 2012 | |
| Foothill | 87 | 80 | 75 | 76 | 70 |
| Valley | 44 | 54 | 65 | 76 | 82 |
| Total | 131 | 134 | 140 | 152 | 152 |
The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?
1. TRANSLATE the question requirements
- Given information:
- Table showing internship data for two high schools across five years
- Need to focus on 2010 data only
- Question asks for fraction of 2010 students who were from Valley High School
- What this tells us: We need to find Valley students as a fraction of ALL students who completed internships in 2010
2. TRANSLATE the relevant data from the table
- From the 2010 column:
- Foothill: 75 students
- Valley: 65 students
- Total: 140 students
3. INFER the correct fraction setup
- Key insight: "Fraction of students who were from Valley" means:
- Numerator: Valley students (65)
- Denominator: ALL students who completed internships (140)
- This gives us: \(\frac{65}{140}\)
Answer: B. \(\frac{65}{140}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what the question is asking for and set up the wrong fraction comparison.
Instead of comparing Valley students to ALL students \(\frac{65}{140}\), they compare Valley students to Foothill students \(\frac{65}{75}\). This happens because they see two schools and assume they need to compare them directly rather than finding Valley as a part of the whole group.
This may lead them to select Choice D \(\frac{65}{75}\)
Second Most Common Error:
Poor TRANSLATE reasoning: Students correctly identify they need a fraction with 140 in the denominator but put the wrong school in the numerator.
They might read "Valley High School" but accidentally use Foothill's number (75) instead of Valley's number (65), giving them \(\frac{75}{140}\).
This may lead them to select Choice C \(\frac{75}{140}\)
The Bottom Line:
This problem tests whether students can correctly identify what "fraction of the group" means - it's always the specific part divided by the total whole, not comparing one part to another part.