The table gives information for 20 models of sports cars. ModelWeight (lb)Engine size (L)Horsepower (HP)Price ($)S/HP ratioBiota32086.243045170105.05B...

OWNING THE DATASET

Let's start by understanding what we're working with. This table contains information about various car models with several key specifications:

• Model name: Names of different car models (Chaffer, Phantom, Titan, Tesco, etc.)
• Horsepower (HP): Engine power measurement
• Weight (lb): Vehicle weight in pounds
• Price ($): Vehicle cost in dollars
• Engine Size (L): Engine displacement in liters

Looking at one complete example: The Chaffer model has 540 horsepower, weighs 3,900 lb, costs $61,200, and has a 6.2L engine.

Key insight: With 20 models and multiple specifications, sorting will be essential for quickly finding patterns and relationships rather than scanning everything manually.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "There are no models that have more than 500 horsepower."
What we're looking for:

• Whether ANY model exceeds 500 horsepower
• Just one counterexample would disprove this statement

In other words: We need to check if all models have \(\leq 500 \mathrm{HP}\).

Let's sort the data by horsepower in descending order to immediately see the highest values at the top.

After sorting, we can see that the Chaffer model has 540 horsepower, which exceeds 500.

Teaching callout: Notice how sorting instantly revealed our answer! Rather than scanning through all 20 models one by one, sorting brought the key information to the top. This is especially powerful when looking for maximum or minimum values or when checking "no X exceeds Y" statements.

Statement 1 is No.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "All of the models that weigh more than 4,000 lb have more than 400 horsepower."
What we're looking for:

• First, which models weigh more than 4,000 lb
• Then, whether ALL of these models have more than 400 horsepower

In other words: Every single heavy car (\(> 4,000 \mathrm{lb}\)) must have high power (\(> 400 \mathrm{HP}\)).

Let's sort the data by weight in descending order to immediately group all the heaviest models at the top.

After sorting, we can see the three models that exceed 4,000 lb:

• Gia: 4,200 lb with 450 HP
• Phantom: 4,150 lb with 420 HP
• Titan: 4,050 lb with 368 HP

The Titan model weighs more than 4,000 lb but has only 368 horsepower, which is less than 400.

Teaching callout: By sorting, we quickly identified all relevant models and found a counterexample without needing to check every car in the dataset. For "all X have Y" statements, finding just one exception immediately disproves the claim.

Statement 2 is No.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "The least expensive model produces the least horsepower per liter of engine size."
What we're looking for:

• First, which model has the lowest price
• Then, calculate its HP/L ratio
• Finally, compare this ratio against other models to see if it's the lowest

In other words: Does the cheapest car have the lowest power-to-engine-size ratio?

First, let's sort by price (ascending) to find the least expensive model.

After sorting, we can see that Tesco is the least expensive at $24,120.

Now, let's calculate Tesco's horsepower per liter:
Tesco: \(310 \mathrm{HP} ÷ 5.7\mathrm{L} = 54.39 \mathrm{HP/L}\)

Instead of calculating this ratio for all 20 models, let's be strategic. Models most likely to have a lower HP/L ratio would be those with:

1. Lower horsepower than Tesco (\(\leq 310 \mathrm{HP}\))
2. Larger engine size than Tesco (\(\geq 5.7\mathrm{L}\))

Let's sort by engine size (descending) and check models with large engines:

• Any model with a large engine (\(> 5.7\mathrm{L}\)) and low HP (\(< 310\)) would be a prime candidate

Let's also sort by horsepower (ascending) and check models with low power:

• Any model with low HP and decent engine size could have a lower ratio

After checking these high-potential candidates, we find that no model has a lower HP/L ratio than Tesco's \(54.39\).

Teaching callout: Notice how we used strategic sampling instead of exhaustively calculating all 20 ratios. By understanding which cars were most likely to have lower ratios, we focused our attention only where it mattered.

Statement 3 is Yes.

FINAL ANSWER COMPILATION

After analyzing each statement:

• Statement 1: No (Chaffer has 540 HP, exceeding 500)
• Statement 2: No (Titan weighs >4,000 lb but has only 368 HP, less than 400)
• Statement 3: Yes (Tesco has the lowest HP/L ratio at 54.39)

Therefore, the correct answer is: No No Yes

LEARNING SUMMARY

Skills We Used

• Efficient Data Organization: Sorting the data differently for each statement
• Strategic Sampling: Checking only the most promising candidates for Statement 3
• Pattern Recognition: Identifying which models needed verification vs. which could be skipped

Strategic Insights

1. Sort First, Calculate Last: Sorting instantly revealed the answers for Statements 1 and 2
2. One Counterexample Is Enough: For Statements 1 and 2, finding just one exception immediately gave us the answer
3. Focus on Extreme Values: For Statement 3, we identified the cheapest model and then only checked models likely to have lower ratios

Common Mistakes We Avoided

1. Manual Scanning: We avoided checking all 20 models one by one
2. Excessive Calculations: For Statement 3, we didn't calculate HP/L for all models
3. Random Checking: We used sorting to create organized approaches for each statement

Remember that in table analysis questions, sorting is your most powerful tool. It transforms a chaotic dataset into an organized one where patterns become immediately visible, saving you significant time and mental effort.