Question:On a community cleanup team, 1/27 participants is a team leader. If there are x team leaders on the team,...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
On a community cleanup team, \(\frac{1}{27}\) participants is a team leader. If there are \(\mathrm{x}\) team leaders on the team, which expression gives the total number of participants on the team?
- \(\mathrm{x + 26}\)
- \(\mathrm{26x}\)
- \(\mathrm{28x}\)
- \(\mathrm{27x}\)
1. TRANSLATE the problem information
- Given information:
- 1 out of every 27 participants is a team leader
- There are \(\mathrm{x}\) team leaders total
- What this tells us: For every complete group of 27 people, exactly 1 person is a team leader
2. INFER the relationship structure
- Key insight: Each team leader represents one complete group of 27 participants
- This means we're not adding leaders to non-leaders - we're counting complete groups
- If there are \(\mathrm{x}\) team leaders, there are \(\mathrm{x}\) complete groups of 27 participants each
3. Calculate total participants
- Total participants = (number of groups) × (participants per group)
- Total participants = \(\mathrm{x \times 27 = 27x}\)
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "1 out of every 27" as meaning there are 26 non-leaders plus 1 leader, rather than understanding it describes the composition of each complete group of 27.
They think: "If there are \(\mathrm{x}\) leaders, then there must be \(\mathrm{26x}\) non-leaders, so total = \(\mathrm{x + 26x = 27x}\)... wait, that gives the right answer but feels wrong" or they get confused and think "\(\mathrm{x}\) leaders plus 26 equals total participants."
This may lead them to select Choice A (\(\mathrm{x + 26}\)).
Second Most Common Error:
Poor INFER reasoning: Students understand that there are non-leaders but incorrectly think each leader corresponds to 26 non-leaders separately, rather than being part of a group of 27 total.
They reason: "Each leader has 26 people under them, so \(\mathrm{x}\) leaders means \(\mathrm{26x}\) non-leaders total."
This may lead them to select Choice B (\(\mathrm{26x}\)).
The Bottom Line:
The key challenge is understanding that "1 out of every 27" describes the structure of complete groups, not a separate counting of leaders versus non-leaders. Students need to visualize complete teams of 27 people each, where 1 person in each team happens to be the leader.