An insurance company offers a series of three information sessions. 1,250 people attended the first information session. 72% of the...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
An insurance company offers a series of three information sessions. \(\mathrm{1,250}\) people attended the first information session. \(\mathrm{72\%}\) of the people who attended the first information session attended the second information session, and \(\mathrm{36\%}\) of the people who attended the first and second information sessions attended the third information session. How many people attended all three information sessions?
1. TRANSLATE the problem information
- Given information:
- First session: 1,250 people attended
- Second session: 72% of first session attendees also attended
- Third session: 36% of people who attended both first AND second sessions also attended
- Find: Number who attended all three sessions
2. INFER the sequential structure
- This is a sequential percentage problem where each step builds on the previous result
- The key insight: "36% of people who attended first and second" means we first need to find how many attended both first and second sessions
3. SIMPLIFY to find second session attendance
- People who attended first and second sessions: 72% of 1,250
- \(0.72 \times 1,250 = 900\) people (use calculator)
4. SIMPLIFY to find all three session attendance
- People who attended all three sessions: 36% of the 900 from step 3
- \(0.36 \times 900 = 324\) people (use calculator)
Answer: 324
Why Students Usually Falter on This Problem
Most Common Error Path:
Poor INFER reasoning: Students misunderstand the sequential structure and apply 36% to the original 1,250 instead of to the 900 who attended both first and second sessions.
Their thinking: "36% of the original 1,250 people attended the third session" leading to \(0.36 \times 1,250 = 450\). This shows they missed that the 36% only applies to those who had already attended the first two sessions.
This leads to confusion when their answer doesn't match any realistic expectation for the problem.
Second Most Common Error:
Weak TRANSLATE skills: Students correctly identify the sequential nature but make calculation errors, such as converting percentages incorrectly (using 72 instead of 0.72) or making arithmetic mistakes in the multiplication steps.
This causes them to get numbers that don't make logical sense in context, leading to second-guessing and potential guessing.
The Bottom Line:
This problem tests whether students can recognize when percentages apply sequentially to subsets rather than always to the original total. The language "of the people who attended the first and second" is the key phrase that signals this sequential relationship.