Four friends–Amelie, Benedikt, Chiara, and Dominic–played four rounds of a card game together. In each round, each player scored a...

OWNING THE DATASET

Let's start by understanding what we're working with. This table shows game scores for multiple players across 4 rounds, with Chiara's Round 3 score missing.

Looking at the raw data, we can immediately identify several key insights:

Key Insights:

• Chiara scored highest in Round 1 (51) and Round 2 (55)
• Benedikt scored highest in Round 3 (61) and Round 4 (65)
• We're told Chiara scored highest in "exactly 2 rounds"
• This means Chiara CANNOT be highest in Round 3 (she already has her 2 highest rounds)

This last point is crucial - it immediately tells us that \(\mathrm{x} < 61\) (Benedikt's Round 3 score).

ANALYZING THE QUESTION

The question asks us to determine which statements are consistent with the information given. We know Chiara scored highest in exactly 2 rounds, and we've already identified those rounds (1 and 2).

Let's establish the boundaries for x (Chiara's Round 3 score):

• Upper bound: \(\mathrm{x} < 61\) (can't exceed Benedikt's Round 3 score)
• Lower bound: We don't have an explicit lower bound, but logically, scores would be positive numbers

Now let's examine each statement.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "Chiara's Round 3 score was 43."
What we're looking for:

• Is \(\mathrm{x} = 43\) consistent with all the information we have?
• Does this value satisfy our constraints?

In other words: Can Chiara's unknown score be 43?

Let's check if \(\mathrm{x} = 43\) works with what we know:

• Is 43 < 61? Yes, this satisfies our upper bound
• If \(\mathrm{x} = 43\), Chiara's total would be \(154 + 43 = 197\)
• Benedikt's total is 225
• But Chiara scored highest in Round 3

Therefore, a score of 43 is cannot be consistent with all the information we have.

Statement 1 is Not consistent

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "Chiara's Round 3 score was 58."
What we're looking for:

• Is \(\mathrm{x} = 58\) consistent with all the information we have?
• Does this value satisfy our constraints?

In other words: Can Chiara's unknown score be 58?

Let's check if \(\mathrm{x} = 58\) works with what we know:

• Is 58 < 61? Yes, this satisfies our upper bound
• If \(\mathrm{x} = 58\), Chiara's total would be \(154 + 58 = 212\)
• Benedikt's total is 225
• Chiara scored highest in Rounds 1 and 2, which matches our constraint of "exactly 2 rounds"

Therefore, a score of 58 is perfectly consistent with all the information we have.

Statement 2 is Consistent

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "Chiara won the game."
What we're looking for:

• Can Chiara have the highest total score?
• Is there any possible value of x that would give Chiara a higher total than Benedikt?

In other words: Is it possible for Chiara to win with any valid value for x?

Chiara's total score would be \(154 + \mathrm{x}\).
Benedikt's total score is 225.

For Chiara to win: \(154 + \mathrm{x} > 225\)
Solving for x: \(\mathrm{x} > 71\)

But we already established that \(\mathrm{x} < 61\) (since Benedikt had the highest score in Round 3).

Since x cannot simultaneously be > 71 and < 61, there is no value of x that would allow Chiara to win the game.

Statement 3 is Not Consistent

FINAL ANSWER COMPILATION

Evaluating the three statements:

• Statement 1: Not Consistent (Chiara's Round 3 score could be 43)
• Statement 2: Consistent (Chiara's Round 3 score could be 58)
• Statement 3: Not Consistent (Chiara cannot win the game with any valid value of x)

LEARNING SUMMARY

Skills We Used

• Quick Visual Scanning: We immediately identified who had the highest scores in each round
• Constraint Recognition: We recognized that "highest in exactly 2 rounds" creates a powerful boundary
• Inference Instead of Calculation: We didn't need to try every possible value for x
• Boundary Setting: We established that \(\mathrm{x} < 61\), which helped evaluate all statements

Strategic Insights

• When information states something happens "exactly N times," immediately identify where those occurrences are. This creates powerful constraints.
• For unknown values, establishing boundaries is often more efficient than calculating specific values.
• Always ask: "What can I know without computing?" before jumping into calculations.

Common Mistakes We Avoided

• We didn't waste time calculating Chiara's total score for every possible value of x.
• We didn't calculate unnecessary information for each player in each round.
• We recognized that Statement 3 could be evaluated using inequality logic rather than specific values.

Remember: In table analysis questions, the fastest approach often comes from recognizing what the constraints immediately tell you about the data, not from performing calculations on every value in the table.