The table gives information for 20 models of sports cars. Model Weight (lb) Engine size (L) Horsepower (HP) Price ($)...

OWNING THE DATASET

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

• Model names (like Granato, Olsen, PTZ, Biota, Chaffer, etc.)
• Horsepower ratings
• Engine sizes (in liters)
• Weight (in pounds)
• Price (in dollars)
• Power-to-weight ratios (HP/lb)
• Cost efficiency ($/HP)

Looking at this dataset, we immediately notice that we have both raw data (horsepower, engine size, weight, price) and derived data (HP/lb ratios, $/HP ratios). This means we can directly compare values without having to calculate them ourselves in many cases.

Key insight: When analyzing tables, we should first understand what calculations have already been done for us versus what we might need to compute ourselves.

ANALYZING THE STATEMENTS

Let's analyze each statement using the most efficient approach possible.

Statement 1 Analysis

Statement 1 Translation:
Original: "The model with the lowest horsepower has the smallest engine size."
What we're looking for:

• Identify all models with the lowest horsepower
• Check if the one with smallest engine size among them

In other words: Does the model with minimum HP also have minimum engine size?

Let's approach this efficiently by sorting:

1. First, let's sort by Horsepower (ascending) to find the models with the lowest HP: We immediately see that Granato, Olsen, and PTZ all tie for lowest horsepower at 300 HP.
2. Now, let's sort by Engine Size (ascending) to find which of these three has the smallest engine: We find that Olsen has a 3L engine, Granato has a 3.5L engine, PTZ has a 3.8L engine
3. Since Olsen has both the lowest horsepower (tied with others) AND the smallest engine size, Statement 1 is TRUE.

Teaching callout: Notice how sorting immediately grouped all the lowest horsepower models together, saving us from scanning the entire table multiple times. We didn't need to calculate anything - just sort and observe!

Statement 2 Analysis

Statement 2 Translation:
Original: "The model with the lowest weight has the highest horsepower-to-weight ratio."
What we're looking for:

• Identify the lightest model
• Compare its HP/lb ratio to all other models
• Verify if it has the highest ratio

In other words: Does the lightest car also deliver the most power per pound?

Let's use sorting and strategic sampling to solve this efficiently:

1. Sort by Weight (ascending) to immediately identify the lightest model: Biota is the lightest at 3208 pounds with 430 HP
2. Calculate Biota's HP/lb ratio: \(430 \mathrm{HP} ÷ 3208 \mathrm{lb} = 0.134 \mathrm{HP/lb}\)
3. Now, instead of calculating ratios for all models, let's use strategic sampling: Sort by Horsepower (descending) to identify high-HP models. Let's check Chaffer, which has 540 HP and weighs 3920 lb. Chaffer's ratio: \(540 \mathrm{HP} ÷ 3920 \mathrm{lb} = 0.138 \mathrm{HP/lb}\)
4. Since \(0.138 > 0.134\), we've found a model with a higher HP/lb ratio than Biota. We can stop here - Statement 2 is FALSE.

Teaching callout: We avoided calculating ratios for all models by strategically sampling. Once we found a counterexample, we could immediately stop. This is much faster than the brute force approach of calculating all ratios.

Statement 3 Analysis

Statement 3 Translation:
Original: "The model with the lowest price-per-horsepower ratio is also the model with the lowest price."
What we're looking for:

• Identify model with lowest $/HP ratio
• Identify model with lowest overall price
• Check if they're the same model

In other words: Is the most "horsepower value for money" car also the cheapest car overall?

Let's solve this with efficient sorting:

1. Sort by $/HP (ascending) to find the model with the lowest ratio: T-400 has the lowest $/HP ratio at 67.93
2. Sort by Price (ascending) to find the cheapest model: Tesco has the lowest price at $24,120
3. Since these are different models (T-400 vs Tesco), Statement 3 is FALSE.

Teaching callout: By using sorting, we transformed what could have been a calculation-heavy problem into a simple observation task. We didn't need to perform any calculations - just two quick sorts to get our answer.

ANSWER COMPILATION

After analyzing all three statements:

• Statement 1: TRUE
• Statement 2: FALSE
• Statement 3: FALSE

Therefore, our answer is T/F/F.

LEARNING SUMMARY

Skills We Used

• Sorting as first action: We consistently used sorting to transform calculation problems into observation problems.
• Strategic sampling: For Statement 2, we only calculated HP/lb ratios for promising candidates instead of all models.
• Early stopping: Once we found a counterexample in Statement 2, we immediately stopped.

Strategic Insights

• The "Sort First" principle: Always consider sorting as your first action when working with tables. It often reveals patterns that would take much longer to find manually.
• Extreme value recognition: Sorting immediately reveals minimum/maximum values, making them easy to identify.
• Pattern grouping: Sorting clusters similar values together, helping us quickly identify all models with the same characteristic.

Common Mistakes We Avoided

• Manually scanning the table multiple times for minimum values
• Calculating HP/lb ratios for all models unnecessarily
• Performing duplicate lookups between different columns

Remember, in Table Analysis questions, our goal is to transform searching and calculating into observing and confirming. The formula for success is:

TRADITIONAL: Scan → Find → Calculate → Repeat → Decide
OPTIMIZED: Sort → Observe → (Minimal calculation if needed) → Decide

By mastering the "Sort First" principle, you'll solve these problems with greater speed and confidence!