Loading...
The table displays data on Brazilian agricultural products in 2009.
| Commodity | Production, world share (%) | Production, world rank | Exports, world share (%) | Exports, world rank |
|---|---|---|---|---|
| Beef | 16 | 2 | 22 | 1 |
| Chickens | 15 | 3 | 38 | 1 |
| Coffee | 40 | 1 | 32 | 1 |
| Corn | 8 | 4 | 10 | 2 |
| Cotton | 5 | 5 | 10 | 4 |
| Orange juice | 56 | 1 | 82 | 1 |
| Pork | 4 | 4 | 12 | 4 |
| Soybeans | 27 | 2 | 40 | 2 |
| Sugar | 21 | 1 | 44 | 1 |
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise select No.
No individual country produces more than one-fourth of the world's sugar.
If Brazil produces less than 20% of the world's supply of any commodity listed in the table, Brazil is not the world's top exporter of that commodity.
Of the commodities in the table for which Brazil ranks first in world exports, Brazil produces more than 20% of the world's supply.
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:
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.
Statement 1 Translation:
Original: No individual country produces more than one-fourth of the world's sugar.
What we're looking for:
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.
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:
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:
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:
We've found two commodities (Beef and Chickens) where:
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!
Evaluating our three statements:
Therefore, our answer is: A (Statement 1 alone is sufficient)
No individual country produces more than one-fourth of the world's sugar.
If Brazil produces less than 20% of the world's supply of any commodity listed in the table, Brazil is not the world's top exporter of that commodity.
Of the commodities in the table for which Brazil ranks first in world exports, Brazil produces more than 20% of the world's supply.