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Dietician: Because of their chemical makeup, some oils are better suited for cooking at high heat than others. This is important because heating an oil above its smoke point–the temperature at which the oil begins to smoke–produces toxic fumes and free radicals, which can be harmful. Refined oils are highly processed with chemicals and should be avoided. Here are some recommendations for suitable uses of oils based on their heat type.
The table lists information about the oils that Mariano is considering buying after reading the dietician's advice. The table also includes the amount of each oil per container and the price for that amount of oil.
| Type | Oil | Temp (°C): Oil-heat type | Amount (ml) | Price per amount ($) |
|---|---|---|---|---|
| U | coconut | 190°/high | 250 | 8 |
| R | corn | 210°/high | 1000 | 6.5 |
| U | flaxseed | 49°/no | 473 | 18 |
| R | grapes-seed | 215°/high | 500 | 10.5 |
| U | olive, extra-virgin | 163°/med | 200 | 13 |
| R | olive, light | 225°/high | 750 | 12 |
| R | peanut | 232°/high | 475 | 9 |
| U | pumpkin | 100°/low | 250 | 14.5 |
| U | safflower | 100°/low | 250 | 20 |
| U | sesame | 163°/med | 500 | 14 |
| U | sunflower | 100°/low | 500 | 6 |
| R | sunflower | 227°/high | 1000 | 7 |
| U | walnut | 49°/no | 500 | 9.5 |
For each of the following statements, select True if the statement is true based on the information provided. Otherwise, select False.
Among the oils listed that are of the type the dietician recommends for frying, there is only one that Mariano can choose if he follows all of the dietician's advice.
Grape-seed oil has the greatest price per ml of all high-heat oils listed.
Among the oils on the list, there is a strong positive correlation between the amount per container (in ml) and the price for the container (in dollars).
Let's start by understanding our cooking oils dataset. We have information about various cooking oils including:
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:
This strategic sorting gives us a powerful advantage for analyzing all three statements efficiently.
Original: "Exactly one of the high-heat cooking oils is unrefined."
What we're looking for:
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:
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.
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:
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.
Original: "Among cooking oils, the price of the oil increases as the amount of oil in the container increases."
What we're looking for:
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:
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.
Let's compile our findings:
The correct answer is A (Only Statement 1 is true).
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.
Among the oils listed that are of the type the dietician recommends for frying, there is only one that Mariano can choose if he follows all of the dietician's advice.
Grape-seed oil has the greatest price per ml of all high-heat oils listed.
Among the oils on the list, there is a strong positive correlation between the amount per container (in ml) and the price for the container (in dollars).