Dietician: Because of their chemical makeup, some oils are better suited for cooking at high heat than others. This is...

Owning the Dataset

Let's start by understanding our cooking oils dataset. We have information about various cooking oils including:

• Name: Different cooking oil types (coconut, corn, grape-seed, etc.)
• Temp (°C): The maximum temperature each oil can reach before smoking
• Type: Whether the oil is Unrefined (U) or Refined (R)
• Price ($): The cost of the container
• Amount (ml): The volume of oil in the container

Key insight: The "Temp (°C)" column immediately divides oils into two categories - high-heat oils (\(190°\mathrm{C}\) or above) and low-heat oils (below \(190°\mathrm{C}\)). This temperature threshold will be crucial for our analysis.

Rather than manually going through each row, let's sort by temperature first to create a more scannable dataset. This immediately highlights:

• High-heat oils (\(190°\mathrm{C}+\)): Coconut, Corn, Grape-seed, Light olive, Peanut, and Sunflower
• Low-heat oils (below \(190°\mathrm{C}\)): The remaining oils like Extra virgin olive, Flaxseed, etc.

This strategic sorting gives us a powerful advantage for analyzing all three statements efficiently.

Analyzing Statement 1

Statement 1 Translation:

Original: "Exactly one of the high-heat cooking oils is unrefined."
What we're looking for:

• Identify all high-heat oils (\(\mathrm{temp} \geq 190°\mathrm{C}\))
• Count how many of these are unrefined (Type = "U")
• Check if the count equals exactly one

In other words: Is it true that only one high-heat oil is unrefined?

Now that we've already sorted by temperature, we can easily see our high-heat oils. Let's check which of these are unrefined:

1. Scan the "Type" column for our high-heat oils:

• Coconut: Type = "U" ✓ (Unrefined)
• Corn: Type = "R" (Refined)
• Grape-seed: Type = "R" (Refined)
• Light olive: Type = "R" (Refined)
• Peanut: Type = "R" (Refined)
• Sunflower: Type = "R" (Refined)

We can see that among our high-heat oils, only Coconut oil is unrefined. That's exactly one unrefined high-heat oil.

Teaching callout: Notice how sorting first made this verification almost instant. We didn't need to manually list every oil and its properties - instead, we could visually scan our already-organized data.

Statement 1 is True.

Analyzing Statement 2

Statement 2 Translation:

Original: "The price per milliliter of grape-seed oil is lower than that of each of the other high-heat cooking oils."
What we're looking for:

• Calculate the price per ml of grape-seed oil
• Compare this to the price per ml of each other high-heat oil
• Check if grape-seed has the lowest price per ml among high-heat oils

In other words: Is grape-seed oil the cheapest high-heat oil when we look at price per ml?

Let's start by calculating the price per ml for grape-seed oil:
Grape-seed: \(\$10.5 \div 500\mathrm{ml} = \$0.021/\mathrm{ml}\)

Now, instead of calculating the exact value for each remaining oil, let's check if any high-heat oil has a lower price per ml:

Coconut: \(\$8\) for \(250\mathrm{ml}\)
Quick estimate: \(\$8 \div 250\mathrm{ml} = \$0.032/\mathrm{ml}\) (clearly higher than grape-seed)

Key efficiency insight: We only need to find ONE oil with a lower price/ml to prove the statement false. Let's check another:

Corn: \(\$6.5\) for \(1000\mathrm{ml}\)
Quick estimate: \(\$6.5 \div 1000\mathrm{ml} = \$0.0065/\mathrm{ml}\) (lower than grape-seed!)

We found that corn oil has a lower price per ml (\(\$0.0065/\mathrm{ml}\)) than grape-seed oil (\(\$0.021/\mathrm{ml}\)). We can stop here!

Teaching callout: Notice how we didn't need to calculate the price per ml for all six high-heat oils. Once we found corn oil had a lower price per ml, we could immediately determine the statement was false.

Statement 2 is False.

Analyzing Statement 3

Statement 3 Translation:

Original: "Among cooking oils, the price of the oil increases as the amount of oil in the container increases."
What we're looking for:

• Examine if there's a direct relationship between container size and price
• Check if larger containers consistently have higher prices
• Look for any counterexamples that break this pattern

In other words: Do bigger containers always cost more?

For this statement, let's sort by "Amount (ml)" in ascending order to see if prices consistently increase as container size increases:

After sorting, we can scan the "Price ($)" column to check if the values consistently increase as we move down the list:

• Small containers (\(250\mathrm{ml}\) range): Some have prices as high as \(\$20\) (safflower)
• Large containers (\(1000\mathrm{ml}\)): Some have prices as low as \(\$6.5\) (corn)

We can immediately spot multiple counterexamples where larger containers have lower prices than smaller ones. There's no consistent relationship between container size and price.

Teaching callout: Sorting by amount made pattern violations immediately visible. We didn't need to manually group oils by container size or calculate anything - the lack of correlation jumped out visually.

Statement 3 is False.

Final Answer Compilation

Let's compile our findings:

• Statement 1: True (Exactly one high-heat oil is unrefined)
• Statement 2: False (Corn oil has a lower price per ml than grape-seed oil)
• Statement 3: False (No consistent relationship between container size and price)

The correct answer is A (Only Statement 1 is true).

Learning Summary

Skills We Used

• Strategic Sorting: We sorted the data first by temperature to identify high-heat oils, and later by amount to check for patterns - this saved significant time over manual checking
• Visual Scanning: After sorting, we used visual scanning to quickly identify patterns and exceptions
• Calculation Efficiency: We calculated only what we needed and stopped as soon as we found a counterexample

Strategic Insights

1. Sort before analyzing: Starting with sorting created immediate insights that benefited multiple statements
2. Calculate strategically: For Statement 2, we only needed to find one oil with a lower price/ml to disprove the statement
3. Information carries forward: Our work identifying high-heat oils for Statement 1 gave us the exact subset needed for Statement 2
4. Lookout for early stopping points: In Statement 2, once we found corn oil had a lower price/ml, we could immediately determine the statement was false

Common Mistakes We Avoided

1. Calculating price per ml for all oils when we only needed to find one counterexample
2. Manually creating groups of oils by container size when sorting made pattern violations immediately visible
3. Approaching statements in strict sequence rather than in an order that builds on previous work

Remember: In table analysis questions, sorting is your superpower! Almost always sort the data first, then use visual scanning to spot patterns and exceptions. This approach transforms minutes of work into seconds while maintaining perfect accuracy.