Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person,...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person, what is the maximum number of people that could attend this event?
1. TRANSLATE the problem information
- Given information:
- Room size: 5,400 square feet
- Minimum space needed: at least 8 square feet per person
- Find: maximum number of people
2. INFER the mathematical relationship
- To find maximum capacity, we need to determine how many 8-square-foot spaces fit in 5,400 square feet
- This is a division problem: \(\mathrm{Total\ area \div Area\ per\ person = Number\ of\ people}\)
- Maximum people = \(\mathrm{5,400 \div 8}\)
3. SIMPLIFY the calculation
- \(\mathrm{5,400 \div 8 = 675}\)
Answer: B. 675
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students think "8 square feet per person" means they should multiply rather than divide.
They reason: "If each person needs 8 square feet, and there are 5,400 square feet, then 5,400 × 8 gives the total." This backwards thinking leads to 43,200.
This may lead them to select Choice D (43,200)
Second Most Common Error:
Poor TRANSLATE reasoning: Students misunderstand what "at least 8 square feet per person" means in the context of finding maximum capacity.
They might think this sets a minimum number of people rather than understanding it as a constraint that limits how many people can fit. This confusion leads to guessing or incorrect setup.
This leads to confusion and guessing among the remaining choices.
The Bottom Line:
The key insight is recognizing that "at least 8 square feet per person" creates a space constraint - you're finding how many 8-square-foot units fit into the total space, which requires division, not multiplication.