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A state legislator drafts an income tax proposal that imposes a tax of

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A state legislator drafts an income tax proposal that imposes a tax of [#permalink]

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New post 30 Mar 2018, 16:39
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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.
[Reveal] Spoiler: OA
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Re: A state legislator drafts an income tax proposal that imposes a tax of [#permalink]

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New post 31 Mar 2018, 05:59
Let us say, income of a resident is $300,000
Then, the amount he pays in income tax is -

20% of 100,000 + 25% of 50,000 + 5% of 50,000 + 5% of 50,000 + 40% of 50,000

=> 20,000 + 12500 + 2500 + 2500 + 20000
=> $57500 (Which is around 19.2% of the total income)

If the income is upto 100,000, he will pay only 20%.
If the income is upto 150,000, he will pay 32500, which is only 21.6%
If the income is upto 200,000, then also in that range.

But, if income is 350,000, then
20% of 100,000 + 25% of 50,000 + 5% of 50,000 + 5% of 50,000 + 40% of 100,000
=> 20,000 + 12500 + 2500 + 2500 + 40000
=> $77500 (Which is around 22.2% of the total income)

Now, options -
A) Median income is 65,000.
Now we dont know what the highest income is, it can even be a million dollars or a billion dollars, which can rise the average to 30%, or it can be 100,000 as well. Not sufficient.

B) This shows that no resident pays more than ~23% tax. Hence, answer is NO. Sufficient.

Option B.

Ayush1692 wrote:
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.
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Re: A state legislator drafts an income tax proposal that imposes a tax of [#permalink]

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Option 1:
Median = $65,000

This option doesn't tell anything useful -- the average tax can be more than 30% if the people above median earn a large amount (e.g. a billion $ each). Not sufficient.

Option 2:
Max income per resident = $350,000
The highest tax will be when everyone earns the max amount. So, if everyone earns $350,000. Tax:
20% of first $100,000 = $20k
25% of next $50,000 = $12.5k
30% of next $50,000 = $15k
35% of next $50,000 = $17.5k
40% of next $100,000 = $40k
Total = $105k
% Tax = $105k/350k = 30%.

So, the average tax rate cannot be "greater" than 30%. Sufficient.
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A state legislator drafts an income tax proposal that imposes a tax of [#permalink]

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New post 05 Apr 2018, 10:29
It is important to know than in this specific example, they are not asking us to solve it. They are asking us “Can you answer this question?”

A. The Median income tells us that everything above the median will be taxed at very close to 40% effective tax rate. Anything below the median will be taxed at 20%.

Taxable Income Tax Amount Tax Rate
Salary 1 $1.00 $0.20 20.00%
Salary 2 $60,000.00 $12,000.00 20.00%
Salary 3 $60,000.00 $12,000.00 20.00%
Salary 4 $60,000.00 $12,000.00 20.00%
Salary 5 $60,000.00 $12,000.00 20.00%
Salary 6 $60,000.00 $12,000.00 20.00%
Salary 7 $60,000.00 $12,000.00 20.00%
Salary 8 $60,000.00 $12,000.00 20.00%
Salary 9 $60,000.00 $12,000.00 20.00%
Salary 10 $60,000.00 $12,000.00 20.00%
Salary 11 $60,000.00 $12,000.00 20.00%
Salary 12 $60,000.00 $12,000.00 20.00%
Salary 13 $60,000.00 $12,000.00 20.00%
Salary 14 $60,000.00 $12,000.00 20.00%
Salary 15 $65,000.00 $13,000.00 20.00%
Salary 16 $350,000.00 $105,000.00 30.00%
Salary 17 $350,000.00 $105,000.00 30.00%
Salary 18 $350,000.00 $105,000.00 30.00%
Salary 19 $350,000.00 $105,000.00 30.00%
Salary 20 $350,000.00 $105,000.00 30.00%
Salary 21 $350,000.00 $105,000.00 30.00%
Salary 22 $350,000.00 $105,000.00 30.00%
Salary 23 $350,000.00 $105,000.00 30.00%
Salary 24 $350,000.00 $105,000.00 30.00%
Salary 25 $350,000.00 $105,000.00 30.00%
Salary 26 $350,000.00 $105,000.00 30.00%
Salary 27 $350,000.00 $105,000.00 30.00%
Salary 28 $350,000.00 $105,000.00 30.00%
Salary 29 $350,000.00 $105,000.00 30.00%
Salary 30 $350,000.00 $105,000.00 30.00%
Salary 31 $350,000.00 $105,000.00 30.00%

Average 25.16%

Since half the salaries are below $65,000 (20% tax rate) and half are max 40% then you`ll have the same amount of 20% tax rates as 40% tax rates so the overall average cannot be above 30% since 20+40 = 60 / 2 = 30%. So Sufficient.

B. This is very useful. You know the highest income of any resident is $350,000. If you assume everyone makes the highest, which is a possibility, then you can calculate what’s the highest tax rate the city will receive and your average cannot exceed this number. This is a Yes or No question. Therefore no math is necessary. So sufficient.

Please note, while it helps doing the math and confirming you can obtain a value, in this specific problem, for me, whether the answer is 20% or 40% is not relevant as long as we are certain that we can calculate an average rate with the information provided.

Answer: D either Statement is sufficient.
A state legislator drafts an income tax proposal that imposes a tax of   [#permalink] 05 Apr 2018, 10:29
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