The table displays data on Brazilian agricultural products in 2009. Commodity Production, world share (%) Production, world rank Exports, world...

OWNING THE DATASET

Let's start by understanding what this table shows us about various commodities around the world:

The table presents data on multiple commodities (like beef, chickens, coffee) with two key metrics:

• Production share percentage: What percentage of global production comes from the top producer
• Export ranking: Where the top producer ranks in global exports of that commodity

Key insight: Notice how these two metrics aren't perfectly correlated - a country might be the #1 producer but not necessarily the #1 exporter (or vice versa). This relationship will be crucial for our analysis.

Before diving into calculations, let's observe the range of production shares (approximately \(15\% - 25\%\)) and export rankings (from 1 to higher numbers). Understanding these ranges helps us tackle the statements more strategically.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: No individual country produces more than one-fourth of the world's sugar.
What we're looking for:

• We need to check if the top producer of sugar has less than \(25\%\) of global production
• We only need to look at the sugar commodity row

In other words: Is the production share for sugar less than \(25\%\)?

Let's focus only on the sugar row in our table. This is a perfect example of where we can be extremely efficient by ignoring irrelevant data.

Looking at the sugar data, we see Brazil is the top producer with \(21\%\) of global production. Since \(21\% < 25\%\) (or one-fourth), the statement is Yes.

Teaching note: Notice how we didn't need to look at any other commodity? When a statement specifically mentions one item, we can often ignore all other data rows, saving significant time.

ANALYZING STATEMENTS 2 & 3 TOGETHER

Since Statements 2 and 3 are related, let's analyze them together to be more efficient.

Statement 2 Translation:
Original: If a country produces less than \(20\%\) of a commodity, then that country cannot be the leading exporter of that commodity.
What we're looking for:

• For commodities where production share \(< 20\%\)
• Check if any of these are #1 exporters

In other words: Is it true that low production (\(< 20\%\)) always means NOT being the #1 exporter?

Statement 3 Translation:
Original: For all commodities where a country is the leading exporter, that country produces more than \(20\%\) of the world's supply of that commodity.
What we're looking for:

• For commodities where export rank = 1
• Check if all have production share \(> 20\%\)

In other words: Do ALL #1 exporters have production shares above \(20\%\)?

Notice that these statements are testing the same relationship from opposite directions. This allows us to be very strategic in our approach.

Let's examine all the #1 exporters:

After sorting, we can immediately see that Beef, Chickens, Coffee, Orange juice, and Sugar all have export rank = 1.

Now, let's scan only these #1 exporters for their production percentages:

• Beef: \(16\%\) (below \(20\%\))
• Chickens: \(15\%\) (below \(20\%\))
• Coffee: [production %]
• Orange juice: [production %]
• Sugar: \(21\%\) (above \(20\%\))

We've found two commodities (Beef and Chickens) where:

1. Production share is less than \(20\%\) AND
2. Export rank is #1

These directly contradict both statements! Let's see how:

For Statement 2: Both Beef and Chickens have production share \(< 20\%\), yet they ARE the leading exporters. This provides counterexamples, making Statement 2 No.

For Statement 3: Both Beef and Chickens are leading exporters, yet they have production share \(\leq 20\%\), not \(> 20\%\). This provides counterexamples, making Statement 3 No.

Teaching note: When two statements test opposite sides of the same relationship, look for examples that can answer both at once. Also, we didn't need to check every commodity – once we found valid counterexamples, we could stop!

FINAL ANSWER COMPILATION

Evaluating our three statements:

• Statement 1: Yes (Sugar production is \(21\%\), which is less than \(25\%\))
• Statement 2: No (Beef and Chickens have \(< 20\%\) production but are #1 exporters)
• Statement 3: No (Beef and Chickens are #1 exporters but have \(\leq 20\%\) production)

Therefore, our answer is: A (Statement 1 alone is sufficient)

LEARNING SUMMARY

Skills We Used

• Strategic sorting: By sorting by export rank, we instantly identified all #1 exporters without manual checking
• Statement translation: Breaking down complex wording into clear criteria made verification much easier
• Visual scanning: After sorting, we could quickly scan for the values we needed
• Counterexample identification: We stopped checking once we found valid counterexamples

Strategic Insights

• Focus on the minimum data needed: For Statement 1, we only needed the sugar row
• Recognize statement relationships: Statements 2 and 3 tested the same relationship from different angles, letting us answer both with the same data points
• Use sorting as your first approach: Sorting instantly reveals patterns that would take much longer to find manually
• Stop when conclusive: For false statements, you only need one valid counterexample