Princeton Review
A state legislator drafts an income tax proposal that imposes a tax of 20% on the first $100,000 of an individual's income, increases the tax to 25% on the next $50,000 in income, and increases the tax by an additional 5% on each additional $50,000 in income, to a maximum tax of 40% on the portion of income over $250,000. Under the proposal, would the state collect an average (arithmetic mean) of more than 30% of the income of the residents of County X?
1) The median income for a resident of County X is $65,000.
2) No resident of County X earns an income of more than $350,000.
OA B
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A state legislator drafts an income tax proposal that
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Statement 1 is insufficient, because maybe everyone earns $65,000, and the answer to the question is 'no', or maybe someone earns $1 trillion, and the percent of income collected is close to 40%.
If someone earns $350,000, they pay:
20% on their first $100k
25% on their next $50k
30% on their next $50k
35% on their next $50k
40% on their last $100k
The first and last percentages in the list above are taken from the same amount of money, so will average to 30% (the average of 20% and 40%), and the middle three are also taken from the same amounts, so average to 30% (the average of 25%, 30% and 35%). So someone earning $350k is paying exactly 30%, and if $350k is the maximum income in the community, the state can't possibly collect more than 30% from any individual earner, let alone from the total income of all residents. So the answer is B.
If someone earns $350,000, they pay:
20% on their first $100k
25% on their next $50k
30% on their next $50k
35% on their next $50k
40% on their last $100k
The first and last percentages in the list above are taken from the same amount of money, so will average to 30% (the average of 20% and 40%), and the middle three are also taken from the same amounts, so average to 30% (the average of 25%, 30% and 35%). So someone earning $350k is paying exactly 30%, and if $350k is the maximum income in the community, the state can't possibly collect more than 30% from any individual earner, let alone from the total income of all residents. So the answer is B.
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