The table displays nutrition data per 240 mL serving for selected cooked or uncooked vegetables: percent water, energy in kilocalories...

Owning the Dataset

Let's start by understanding what we're working with. We have a table showing nutritional information for 15 vegetables, with some cooked and others uncooked.

Key insights at first glance:

• 10 cooked vegetables vs. 5 uncooked vegetables
• The table tracks protein, carbohydrates, and fiber content
• Cooking status is a critical differentiator that will likely be relevant for our analysis
• We should expect nutritional values to differ based on cooking status

This type of comparative data is perfect for sorting approaches, which will help us quickly identify patterns and relationships without tedious manual calculations.

Analyzing Statement 1

Statement 1 Translation:
Original: "The median protein content for uncooked vegetables is one-third the median protein content for cooked vegetables."
What we're looking for:

• Find median protein for uncooked vegetables
• Find median protein for cooked vegetables
• Check if uncooked median = \(\frac{1}{3} \times \mathrm{cooked\,median}\)

In other words: We need to compare two median values with a specific ratio relationship.

Let's approach this strategically using sorting:

1. First, let's sort by cooking status. This immediately separates our 15 vegetables into two groups: 5 uncooked and 10 cooked.
2. Now, while maintaining our cooking status sort, let's sort by protein content as a secondary criterion. This automatically arranges each group in protein order.
3. For the uncooked vegetables (5 items): - With 5 values, the median is the 3rd value = 1g
4. For the cooked vegetables (10 items): - With 10 values, the median is the average of the 5th and 6th values = 3g
5. Now we can check our ratio: Is \(1\mathrm{g} = \frac{1}{3} \times 3\mathrm{g}\)?
   \(1\mathrm{g} = \frac{1}{3} \times 3\mathrm{g} = 1\mathrm{g}\) ✓

Statement 1 is YES.

Teaching note: Notice how sorting instantly organized our data into meaningful groups. Instead of writing down all 15 protein values and manually separating them, sorting did the heavy lifting for us!

Analyzing Statement 2

Statement 2 Translation:
Original: "The carbohydrate content of cooked corn is more than three times the median carbohydrate content of all other vegetables in the table."
What we're looking for:

• Identify carbohydrate content of cooked corn
• Find median carbohydrate content of the remaining 14 vegetables
• Check if cooked corn's carbs > 3 × median carbs of others

In other words: We're comparing one specific value against a multiple of the median of all other values.

Let's solve this efficiently:

1. First, let's identify cooked corn's carbohydrate value = 32g
2. Now, let's sort the entire table by carbohydrate content. This places cooked corn near the top (since it has a high carb content) and helps us quickly identify the median of the remaining vegetables.
3. With cooked corn removed, we have 14 remaining vegetables: - The median for 14 items is the average of the 7th and 8th values = 8g
4. Now we can check: Is \(32\mathrm{g} > 3 \times 8\mathrm{g}\)?
   \(32\mathrm{g} > 3 \times 8\mathrm{g} = 24\mathrm{g}\) ✓

Statement 2 is YES.

Teaching note: We didn't need to manually list and sort all carbohydrate values. By sorting the table directly, we could visually identify the median without writing anything down!

Analyzing Statement 3

Statement 3 Translation:
Original: "All vegetables with less than 3.0 grams of fiber have no more than 10 grams of carbohydrates."
What we're looking for:

• Identify all vegetables with fiber \(< 3.0\mathrm{g}\)
• Check if ALL of these have carbohydrates \(\leq 10\mathrm{g}\)
• If even one has carbs \(> 10\mathrm{g}\), the statement is false

In other words: We need to confirm that low fiber always corresponds with low carbs.

Here's our approach:

1. Let's sort the table by fiber content in ascending order. This immediately groups all vegetables with fiber \(< 3.0\mathrm{g}\) at the top.
2. Without changing our sort, we can scan the carbohydrate column for these low-fiber vegetables to see if any exceed 10g.
3. Visual confirmation: None of the vegetables with fiber \(< 3.0\mathrm{g}\) have carbohydrates exceeding 10g.

Statement 3 is YES.

Teaching note: This statement requires checking a relationship between two variables. Our sorting approach made this relationship visually apparent without having to manually track each vegetable and its values.

Final Answer Compilation

Looking at our results:

• Statement 1: YES
• Statement 2: YES
• Statement 3: YES

The correct answer is: ALL THREE STATEMENTS ARE YES.

Learning Summary

Skills We Used

• Strategic Sorting: We used sorting as our primary analytical tool, which dramatically simplified each question
• Visual Pattern Recognition: After sorting, we used visual scanning rather than calculations
• Median Identification: We quickly identified medians for both even and odd-numbered sets
• Multi-Variable Analysis: We efficiently analyzed relationships between different nutritional components

Strategic Insights

1. Sort First, Calculate Later: Always begin by sorting the data in a way that makes patterns emerge
2. Use Double-Sorting When Needed: For Statement 1, we sorted by cooking status first, then protein
3. Let the Table Do the Work: Instead of extracting data into lists, we manipulated the table itself
4. Categorical Filters First: When data has categories (like cooking status), use this as your primary filter

Common Mistakes We Avoided

• Manual Extraction: We didn't waste time copying values into separate lists
• Unnecessary Calculations: We focused only on the specific values needed for each statement
• Inefficient Sorting: We chose the most relevant columns to sort by for each specific statement
• Redundant Work: We didn't recalculate values that were already visible after sorting

Remember, on the GMAT, table analysis questions reward strategic sorting and visual pattern recognition. The table tools are there for a reason - use them to your advantage and let the data organization do the heavy lifting for you!