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The table shows the Six members of a certain chess club, each of whom will play against exactly one other member in a game of chess today. For the person named in the column heading, the column entries indicate which member of the club that person would prefer to have as his or her opponent for today. The number 1 indicates the first choice (most- preferred opponent), 2 the second, and so on. The members of the club have as a goal that Priyanka and Sneha should each have her first choice of opponent.
| Aditi | Dhruv | Priyanka | Raj | Sneha | Vijay | |
|---|---|---|---|---|---|---|
| Aditi | - | 3 | 5 | 5 | 5 | 1 |
| Dhruv | 1 | - | 2 | 2 | 1 | 5 |
| Priyanka | 3 | 2 | - | 1 | 2 | 3 |
| Raj | 5 | 4 | 1 | - | 3 | 4 |
| Sneha | 2 | 1 | 3 | 3 | - | 2 |
| Vijay | 4 | 5 | 4 | 4 | 4 | - |
For each of the following members of the chess club, select Could achieve the stated goal if denying that member's first and second choice of opponent for today could result in Priyanka and Sneha each having her first choice. Otherwise, select Could NOT achieve the stated goal.
Aditi
Dhruv
Raj
Let's start by understanding our chess pairing preferences table with the goal of "owning the dataset" completely.
This table shows six chess players (Priyanka, Raj, Sneha, Dhruv, Aditi, and Vijay) and their ranked preferences for playing partners. Each player has ranked the other five players from 1 (most preferred) to 5 (least preferred).
Key insights from our dataset:
These observations will be crucial for our efficient solving approach, especially when we need to check constraints against specific pairings.
Original: "If the following conditions must be satisfied:
Can these conditions be satisfied?"
What we're looking for:
In other words: We need to determine if the preference constraints prevent any of our required pairings from happening.
Rather than checking every possibility, let's use a powerful pattern recognition insight:
Key Insight: When 6 players must form 3 pairs, fixing 2 pairs automatically determines the 3rd pair!
If Priyanka must play with Raj, and Sneha must play with Dhruv, then by simple elimination, Aditi MUST play with Vijay. This transforms our approach completely - we just need to check if any constraints directly prevent these specific pairings.
Let's analyze each constraint directly against our required pairings:
Statement Translation:
Original: "Dhruv cannot play with either his first or second choices"
What we're looking for:
According to our data, Dhruv's preferences show:
Direct Contradiction Found: Sneha is one of Dhruv's 1st choices, but the constraint says he cannot play with his 1st choices. This directly prevents the required Dhruv-Sneha pairing.
Statement Translation:
Original: "Raj cannot play with his first choice"
What we're looking for:
According to our data:
Direct Contradiction Found: Priyanka is Raj's 1st choice, but the constraint says he cannot play with his 1st choice. This directly prevents the required Raj-Priyanka pairing.
Statement Translation:
Original: "No player can play with their first choice"
What we're looking for:
According to our data:
Direct Contradiction Found: Vijay is Aditi's 1st choice, but the constraint says no player can play with their 1st choice. This prevents the Aditi-Vijay pairing that would be forced by the other requirements.
We've identified three direct contradictions:
Any one of these contradictions alone would make it impossible to satisfy all conditions. Since we have three separate contradictions, we can confidently conclude that Could NOT achieve the stated goal.
Remember: In GMAT Table Analysis questions, the key is often recognizing a structural insight that makes the solution nearly instant. Always check constraints directly against requirements rather than exploring all possibilities.
Aditi
Dhruv
Raj