For a particular custom basketball game, a player receives a personal warning upon accumulating at least 3 fouls within any...
GMAT Two Part Analysis : (TPA) Questions
For a particular custom basketball game, a player receives a personal warning upon accumulating at least 3 fouls within any 12 minute quarter and complete ejection from the court upon accumulating 5 such fouls at any time during the 48 minute game. For any single 48 minute game, missing between 2 minutes and 4 minutes of playtime counts as one-third of an absence, missing between 4 minutes and 10 minutes of playtime counts as half an absence, and missing more than 10 minutes counts as a full absence. However, a basketball player may postpone playtime to make up for up to 3 minutes of unexcused absence at another time.
The table contains descriptions of the unexcused absences of 5 players of a particular custom basketball game. Assume that in each case the basketball player had no other unexcused absences and made up no other time. In the table, select a description of a basketball player who qualified for a personal warning but not a complete ejection, and select a description of a basketball player who qualified for a complete ejection. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Understanding the Rules
We have two key thresholds:
- Personal warning: \(\geq 3\) fouls within ANY 12-minute quarter
- Complete ejection: \(\geq 5\) fouls total during the 48-minute game
Visual Representation
Let's create a table showing each player's fouls:
| Player | Q1 | Q2 | Q3 | Q4 | Total | Warning? | Ejection? |
| 1 | 1 | 0 | 2 | 1 | 4 | ? | ? |
| 2 | 0 | 0 | 2 | 2 | 4 | ? | ? |
| 3 | 0 | 0 | 0 | 4 | 4 | ? | ? |
| 4 | 2 | 1 | 1 | 0 | 4 | ? | ? |
| 5 | 1 | 1 | 1 | 2 | 5 | ? | ? |
Phase 2: Understanding the Question
We need to find:
- Statement 1: A player with personal warning (\(\geq 3\) fouls in any quarter) but NOT complete ejection (\(< 5\) total fouls)
- Statement 2: A player with complete ejection (\(\geq 5\) total fouls)
Phase 3: Finding the Answer
Checking Each Player
Player 1:
- Quarter fouls: 1, 0, 2, 1 (max = 2, no warning ✗)
- Total: 4 (no ejection ✗)
Player 2:
- Quarter fouls: 0, 0, 2, 2 (max = 2, no warning ✗)
- Total: 4 (no ejection ✗)
Player 3:
- Quarter fouls: 0, 0, 0, 4 (\(4 \geq 3\), WARNING! ✓)
- Total: 4 (no ejection ✗)
- This player has warning but no ejection!
Player 4:
- Quarter fouls: 2, 1, 1, 0 (max = 2, no warning ✗)
- Total: 4 (no ejection ✗)
Player 5:
- Quarter fouls: 1, 1, 1, 2 (max = 2, no warning ✗)
- Total: 5 (EJECTION! ✓)
- This player has complete ejection!
Updated Visual
| Player | Q1 | Q2 | Q3 | Q4 | Total | Warning? | Ejection? |
| 1 | 1 | 0 | 2 | 1 | 4 | No | No |
| 2 | 0 | 0 | 2 | 2 | 4 | No | No |
| 3 | 0 | 0 | 0 | 4 | 4 | Yes | No |
| 4 | 2 | 1 | 1 | 0 | 4 | No | No |
| 5 | 1 | 1 | 1 | 2 | 5 | No | Yes |
Phase 4: Solution
Statement 1 (Personal warning): Player 3 - "Fouled none in the first quarter, none in the second quarter, none in the third quarter, and four times in the fourth quarter"
Statement 2 (Complete ejection): Player 5 - "Fouled once in the first quarter, once in the second quarter, once in the third quarter, and twice in the fourth quarter"
These selections satisfy our requirements perfectly:
- Player 3 has a warning (4 fouls in Q4) but no ejection (\(4 < 5\))
- Player 5 has complete ejection (\(5 \geq 5\) total fouls)