A community theater has 450 seats. For a certain performance, 60 of these seats were reserved. Of the seats that...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A community theater has \(\mathrm{450}\) seats. For a certain performance, \(\mathrm{60}\) of these seats were reserved. Of the seats that were not reserved, \(\mathrm{20\%}\) were sold to students. How many seats were sold to students?
12
78
90
108
1. TRANSLATE the problem information
- Given information:
- Total seats: 450
- Reserved seats: 60
- 20% of non-reserved seats were sold to students
- What we need to find: Number of seats sold to students
2. INFER the solution strategy
- The key insight: We need 20% of the seats that were NOT reserved
- This means we first must find how many seats were not reserved
- Then take 20% of that number
3. SIMPLIFY to find non-reserved seats
- Non-reserved seats = Total seats - Reserved seats
- Non-reserved seats = \(450 - 60 = 390\) seats
4. TRANSLATE and calculate the percentage
- "20% of the non-reserved seats" means \(0.20 \times 390\)
- \(0.20 \times 390 = 78\) seats
Answer: B) 78
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread the problem and take 20% of the total seats instead of the non-reserved seats.
They calculate: \(20\% \text{ of } 450 = 0.20 \times 450 = 90\) seats
This may lead them to select Choice C (90)
Second Most Common Error:
Poor TRANSLATE reasoning: Students incorrectly think they need 20% of the reserved seats rather than the non-reserved seats.
They calculate: \(20\% \text{ of } 60 = 0.20 \times 60 = 12\) seats
This may lead them to select Choice A (12)
The Bottom Line:
The challenge in this problem is carefully parsing the language to understand exactly which quantity needs the percentage applied to it. The phrase "of the seats that were not reserved" is the critical piece that many students either miss or misinterpret.
12
78
90
108