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The town of Zenith has a population of 50,000. The average income of a

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The town of Zenith has a population of 50,000. The average income of a person who lives in Zenith is $3,700 per year. Which of the following statements can be inferred from the table and the information about Zenith given above?

I. Every person in Zenith paid $37 in tax.
II. Tax is a linear function of income.
III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
[Reveal] Spoiler: OA

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Re: The town of Zenith has a population of 50,000. The average income of a [#permalink]

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New post 24 Oct 2017, 06:20
Bunuel wrote:
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The town of Zenith has a population of 50,000. The average income of a person who lives in Zenith is $3,700 per year. Which of the following statements can be inferred from the table and the information about Zenith given above?

I. Every person in Zenith paid $37 in tax.
II. Tax is a linear function of income.
III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III


hi..

lets look at the three sentences

I. Every person in Zenith paid $37 in tax.
NO. how can we say the LEAST income is how much..
if someone has an income of $100, he pays 1% of it that is $1


II. Tax is a linear function of income.
Clearly NO... the % increase is NOT linear

We can answer here as III has to be true because choices mention as ATLEAST 1 to be true ..
answer C


III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.
total population is 50000 and average income is 3700..
so TOTAL = 50000*3700 = 185000000..
Now minimum TAX is 1%, so ATLEAST 1% of 185000000 = 1850000
TRUE


C
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Re: The town of Zenith has a population of 50,000. The average income of a [#permalink]

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New post 24 Oct 2017, 20:30
Hello chetan2u.. i have few doubts .. can you please clarify ?

Why tax is not linear function ? As percentage of tax will be dependent on income... also for III there will be people below 3700 who will lower the atleast value since 3700 is only the average ?


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The town of Zenith has a population of 50,000. The average income of a [#permalink]

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Bunuel wrote:
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The town of Zenith has a population of 50,000. The average income of a person who lives in Zenith is $3,700 per year. Which of the following statements can be inferred from the table and the information about Zenith given above?

I. Every person in Zenith paid $37 in tax.
II. Tax is a linear function of income.
III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

woodywheel , this might help.
Evaluating:

I. Every person in Zenith paid $37 in tax.
NO. An average income of $3700 (in which an AVERAGE person indeed pays $37) tells you nothing about the income values that were summed to get the income average, and hence taxes that would be paid.

One person, for example, could pay $74, another $37, and a third, $0.
\(\frac{(74 + 37 + 0)}{3}\) = $37

II. Tax is a linear function of income.
NO. Linear functions have a constant rate of change, are a straight line on a graph.

Here, the rate of change is NOT constant. It is marginally progressive: the more you make, the higher percentage you pay. (Now, if only it actually operated that way.)

The slope of each bracket, if x = income and y = taxes, is not identical. Look at the beginning bracket numbers.

$4000 = $40 tax = 1 percent
$6000 = $80 tax = 1.33 percent
$8000 = $149 tax = 1.75 percent
$10,000 = $220 tax = 2.2 percent
Change rate: +0.33, +0.43, +0.45. Rate of change not constant. Steeper slope at $10,000 than at $6,000.

If everyone paid a flat tax of 80%, that would be a linear function. Where y = (.80)(income). Plug in x = income, you will get a linear result for y as a function of x.

At this point you do not have to evaluate III. A, B, D, and E contain option I, or II, or both. Both are false.

Answer C

III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.
YES.
Average income = $3700
\((A*n) = S\)

$3700 per person * 50,000 persons = $185,000,000

Everyone pays at least 1 percent.
$185,000,000 *.01 = $1,850,000

Some people could pay zero (if $0 in income), some people could pay a lot. The point: the SUM of incomes has been determined, then divided by 50,000 to get AVERAGE income of $3,700.

It doesn't matter if some pay zero tax and one honest person pays $500,000. Total and average income have been determined. No matter what, at least 1% of (average income * # of people) will be paid.

IF average income had not been determined, then having a few pay zero, and even fewer paying a high amount, would be an issue. You wouldn't know how to weight the average. This average has already been weighted by income, at least on the absolute minimum side.

Answer C

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Re: The town of Zenith has a population of 50,000. The average income of a [#permalink]

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New post 29 Oct 2017, 06:45
Bunuel wrote:
Image
The town of Zenith has a population of 50,000. The average income of a person who lives in Zenith is $3,700 per year. Which of the following statements can be inferred from the table and the information about Zenith given above?

I. Every person in Zenith paid $37 in tax.
II. Tax is a linear function of income.
III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III


Let’s analyze each Roman numeral.

I. Every person in Zenith paid $37 in tax.

This might not be true since the average income of $3,700 does not mean everyone earns that amount. Some might earn that amount, some might earn more, and some might earn less. If someone earns an amount other than $3,700, his or her income tax would not be $37.

II. Tax is a linear function of income.

This is not true, either, since the percentages for the income tax brackets are not the same. When graphed, each income bracket is linear since its percentage number is the slope of the line. However, since each income bracket has a different percentage, the whole graph is piecewise linear, but not one straight line when all the income brackets are put together.

III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

This is true because if everyone earns $3,700, then each person will pay $37 in income tax. Since there are 50,000 people, the total income taxes paid will be 50,000 x $37 = $1,850,000. Of course, as mentioned in Roman numeral I, some might earn more than $3,700 and some might earn less. If someone earns less than $3,700, he or she still pays 1% of his or her income tax. However, anyone who earns more than $4,000, say $5,000, will be paying an income tax of more than 1%. In other words, the total income taxes paid will only increase when there are people earning an income in higher brackets. Thus, the total income taxes paid by all residents are at least $1,850,000.

Answer: C
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Re: The town of Zenith has a population of 50,000. The average income of a [#permalink]

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New post 06 Dec 2017, 10:50
I felt it was like a CR + DS question :) Admittedly it took a while:

The town of Zenith has a population of 50,000. The average income of a person who lives in Zenith is $3,700 per year. Which of the following statements can be inferred from the table and the information about Zenith given above?

I. Every person in Zenith paid $37 in tax.
II. Tax is a linear function of income.
III. The total amount of taxes paid by the people of Zenith was at least $1,850,000.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

1) 37$ in tax. This the 'at least amount' basis $3700 avg income. But this doesn't apply to the higher slabs (they pay more tax). So NS

2) II--> no it is not linear. Evident. There is not much of a pattern among the taxation slabs

3) III --> YES. ppl in the 25000 bracket paid at least 1070 + 1820 in tax (say if income was 26000). That into 50,000 ppl is 144500000 --> so even if the 50K people were evenly distributed they would have paid 1850000 easily.

so III only.

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Re: The town of Zenith has a population of 50,000. The average income of a   [#permalink] 06 Dec 2017, 10:50
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