Researcher: We conducted an experiment where we asked people to each build the same simple model. We enlisted 200 volunteers...
GMAT Two Part Analysis : (TPA) Questions
Researcher: We conducted an experiment where we asked people to each build the same simple model. We enlisted 200 volunteers and randomly divided them into 4 groups (Groups 1-4) of 50 members each. Each volunteer was assigned to exactly one of the groups. Each member of Group 1 was given as much time as that member needed to build the model. Each member of Group 2 was given a limited amount of time in which to build the model. Each member of Group 3 was asked to build the model while wearing a blindfold, and was given as much time as needed. Each member of Group 4 was asked to build the model while wearing a blindfold, and was given a limited amount of time. The researchers found that 98% of Group 1, 46% of Group 2, 90% of Group 3, and 20% of Group 4 were able to successfully build the model.
Select for Number blindfolded the total number of volunteers who succeeded in building the model while wearing a blindfold, and select for Number timed the total number of volunteers who succeeded in building the model while given a limited amount of time, according to the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visual Organization
Let's create a table to organize all the information:
| Group | Time Given | Blindfold | Success Rate | # Successful |
| 1 | Unlimited | No | 98% | ? |
| 2 | Limited | No | 46% | ? |
| 3 | Unlimited | Yes | 90% | ? |
| 4 | Limited | Yes | 20% | ? |
Key facts:
- 200 total volunteers
- 4 groups of 50 volunteers each
- Each volunteer in exactly one group
Phase 2: Understanding the Question
We need to find:
- Number blindfolded: Total volunteers who succeeded while wearing a blindfold (Groups 3 and 4)
- Number timed: Total volunteers who succeeded with limited time (Groups 2 and 4)
Notice that Group 4 contributes to BOTH counts since they were both blindfolded AND timed.
Phase 3: Finding the Answer
Calculate successful builders in each group:
- Group 1: \(50 \times 0.98 = 49\) people
- Group 2: \(50 \times 0.46 = 23\) people
- Group 3: \(50 \times 0.90 = 45\) people
- Group 4: \(50 \times 0.20 = 10\) people
Let's update our table:
| Group | Time Given | Blindfold | Success Rate | # Successful |
| 1 | Unlimited | No | 98% | 49 |
| 2 | Limited | No | 46% | 23 |
| 3 | Unlimited | Yes | 90% | 45 |
| 4 | Limited | Yes | 20% | 10 |
Calculate totals for each category:
Number blindfolded (Groups 3 and 4):
- Group 3: 45 successful
- Group 4: 10 successful
- Total: \(45 + 10 = 55\)
Number timed (Groups 2 and 4):
- Group 2: 23 successful
- Group 4: 10 successful
- Total: \(23 + 10 = 33\)
Phase 4: Solution
Our answers are:
- Number blindfolded: 55
- Number timed: 33
These values satisfy all requirements and account for Group 4 being counted in both categories.