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The table gives information for 20 models of sports cars.
| Model | Weight (lb) | Engine size (L) | Horsepower (HP) | Price ($) | S/HP ratio |
|---|---|---|---|---|---|
| Biota | 3208 | 6.2 | 430 | 45170 | 105.05 |
| Boris | 3232 | 3.7 | 332 | 40450 | 121.84 |
| Chaffer | 3920 | 5.4 | 540 | 41930 | 77.65 |
| Corbin | 3972 | 5.7 | 368 | 34000 | 92.39 |
| D2 | 3704 | 4 | 420 | 48900 | 116.43 |
| Dasher | 3860 | 6.2 | 426 | 33195 | 77.92 |
| Gazelle | 3524 | 3.5 | 306 | 34050 | 111.27 |
| Gia | 4083 | 6.1 | 425 | 34000 | 80 |
| Granato | 3356 | 4.6 | 300 | 26695 | 88.98 |
| Hawk | 3947 | 5.7 | 376 | 40000 | 106.38 |
| Olsen | 3582 | 3 | 300 | 40800 | 136 |
| Phantom | 4027 | 6.1 | 425 | 40000 | 94.12 |
| PTZ | 3913 | 6.2 | 400 | 33195 | 82.99 |
| Stallion | 3603 | 5 | 412 | 33500 | 81.31 |
| T-400 | 3725 | 6 | 400 | 27170 | 67.93 |
| Tesco | 3466 | 5.7 | 310 | 24120 | 77.81 |
| Titan | 4006 | 4.6 | 368 | 33000 | 89.67 |
| Victor | 3909 | 5 | 500 | 99100 | 198.2 |
| Windsor | 3578 | 3.5 | 306 | 36550 | 119.44 |
| XR3 | 3534 | 4.6 | 315 | 29695 | 94.27 |
For each of the following statements, select Yes if the statement is true based on the information given. Otherwise select No.
There are no models that have more than 500 horsepower.
All of the models that weigh more than 4,000 lb (pounds) have more than 400 horsepower.
The least expensive model produces the least horsepower per liter of engine size.
Let's start by understanding what we're working with. This table contains information about various car models with several key specifications:
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.
Statement 1 Translation:
Original: "There are no models that have more than 500 horsepower."
What we're looking for:
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.
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:
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:
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.
Statement 3 Translation:
Original: "The least expensive model produces the least horsepower per liter of engine size."
What we're looking for:
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:
Let's sort by engine size (descending) and check models with large engines:
Let's also sort by horsepower (ascending) and check models with low power:
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.
After analyzing each statement:
Therefore, the correct answer is: No No Yes
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.
There are no models that have more than 500 horsepower.
All of the models that weigh more than 4,000 lb (pounds) have more than 400 horsepower.
The least expensive model produces the least horsepower per liter of engine size.