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The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.
If the statements above are true, which of the following must also be true?
| Passage Statement | Visualization and Linkage |
|---|---|
| The percentage of households with an annual income of more than \(\$40,000\) is higher in Merton County than in any other county. | Establishes: Merton County leads in households earning \(>\$40K\) Example:
Key insight: Merton dominates the broad middle-to-upper income category |
| However, the percentage of households with an annual income of \(\$60,000\) or more is higher in Sommer County. | Establishes: Sommer County leads in households earning \(≥\$60K\) Example:
Key insight: Despite having fewer \(>\$40K\) households overall, Sommer has more high earners |
| Overall Implication | Income Distribution Paradox Revealed: Merton County has more households in the \(\$40K+\) range but fewer in the \(\$60K+\) range than Sommer County. This means Merton must have a higher concentration of households in the \(\$40K-\$60K\) income bracket, while Sommer has fewer middle-income earners but more high earners. Pattern: Different income distribution shapes - Merton is "middle-heavy," Sommer is "top-heavy" |
Inference: Merton County must have a higher percentage of households with annual incomes between \(\$40,000\) and \(\$60,000\) than Sommer County.
Supporting Logic: Since Merton County has a higher percentage of households earning more than \(\$40,000\) than Sommer County, but Sommer County has a higher percentage earning \(\$60,000\) or more, the only way both facts can be true simultaneously is if Merton County has significantly more households in the \(\$40,000-\$60,000\) range. This middle-income segment must be large enough in Merton to offset Sommer's advantage in the \(\$60,000+\) category.
Clarification Note: While we can definitively conclude about the \(\$40K-\$60K\) income bracket distribution, we cannot determine anything about households earning less than \(\$40,000\) in either county, as the passage provides no information about lower income ranges.
This goes too far beyond what we can determine. We know Sommer County leads in the \(\$60,000+\) category, but we have no information about the specific \(\$80,000+\) subcategory. Sommer could have more households at \(\$60,000-\$80,000\) while Merton has more at \(\$80,000+\), or vice versa. The passage doesn't give us enough detail to make this determination.
We can't conclude this ranking. While we know Sommer County has the highest percentage of households earning \(\$60,000+\), and Merton County has fewer than Sommer in this category, we don't know how Merton compares to all other counties in the \(\$60,000+\) range. Merton could rank anywhere from second to last among all counties for this income bracket.
This must be true based on the given information. Since Merton County has the highest percentage of households earning more than \(\$40,000\) but Sommer County has the highest percentage earning \(\$60,000\) or more, there must be households in Merton County that fall between these two income thresholds. The math demands that some Merton County households earn between \(\$40,000\) and \(\$60,000\) to account for this pattern.
This confuses percentages with absolute numbers. Even if Merton County has a higher percentage of households earning more than \(\$40,000\), we don't know the total number of households in each county. Sommer County could have a much larger population, making its absolute number of high-income households greater despite having a lower percentage.
We cannot determine average income from this information. Merton County could have many households earning \(\$45,000-\$55,000\), while Sommer could have fewer total high earners but those earners make much more money. The distribution patterns don't tell us enough about averages to make this conclusion.