Angelica and Basil are playing a game with the set of ordered pairs \(\mathrm{S = \{(1, 3), (2, 1), (3,...
GMAT Two Part Analysis : (TPA) Questions
Angelica and Basil are playing a game with the set of ordered pairs \(\mathrm{S = \{(1, 3), (2, 1), (3, 2), (4, 4)\}}\). In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set \(\mathrm{S}\). Basil takes the second turn and removes an ordered pair from among those remaining from set \(\mathrm{S}\). They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed. Assume that each player always selects the available ordered pair for which his or her preference number is greatest.
In the table, select a value for Angelica's final score and a value for Basil's final score that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization of the Game Setup
Let's create a table showing all ordered pairs with each player's preferences:
| Ordered Pair | Angelica's Preference | Basil's Preference |
| (1, 3) | 1 | 3 |
| (2, 1) | 2 | 1 |
| (3, 2) | 3 | 2 |
| (4, 4) | 4 | 4 |
Phase 2: Understanding the Question
The key rule: Each player always selects the available ordered pair for which their own preference number is greatest.
Let's trace through the game turn by turn:
Turn 1 - Angelica Goes First
Angelica looks at all pairs and sees her preferences: 1, 2, 3, and 4
- She chooses (4, 4) because 4 is her highest preference
- Angelica gets 4 points
Turn 2 - Basil's Turn
Remaining pairs: (1, 3), (2, 1), (3, 2)
Basil's preferences for these: 3, 1, and 2
- He chooses (1, 3) because 3 is his highest preference
- Basil gets 3 points
Turn 3 - Angelica's Turn
Remaining pairs: (2, 1), (3, 2)
Angelica's preferences for these: 2 and 3
- She chooses (3, 2) because 3 is her highest preference
- Angelica gets 3 more points
Turn 4 - Basil's Turn
Only (2, 1) remains
- Basil must take it
- Basil gets 1 more point
Phase 3: Finding the Answer
Final Score Calculation
Angelica's pairs and scores:
- (4, 4) → 4 points
- (3, 2) → 3 points
- Total: \(4 + 3 = 7\)
Basil's pairs and scores:
- (1, 3) → 3 points
- (2, 1) → 1 point
- Total: \(3 + 1 = 4\)
Phase 4: Solution
Final Answer:
- Angelica's final score: 7
- Basil's final score: 4