Ten years ago the number of taxpayers in Green County was slightly

Proportion of registered voters to taxpayers = R/T

10 years ago:
T was slightly greater than R.
So R/T was slightly less than 1.

Now:
T has become 2T
R has become say 1.5R (R has increased but at a lower rate so it has not become 2R)

1.5R/2T = (3/4)*(R/T) => This is smaller than R/T since R/T is multiplied by a number smaller than 1.

So R/T has reduced over the last 10 years.

Answer (D)

The Q is dealing with numbers and proportion..
# of taxpayers were T, slightly more than # of registered voters V. In last 10 years T has become 2T and V has also become xV where x <2.

lets see the statements-
A) The number of taxpayers is now smaller than the number of registered voters.
Noway, It will be Opposite

B) Everyone who is a registered voter is also a taxpayer.
Not necessary

C) The proportion of registered voters to taxpayers has increased over at the last ten years.
Proportion earlier was \(\frac{T}{V}.\).. and Now it is \(\frac{2T}{xV}\), where \(x<2\) and \(V<T\), so NO..

D) The proportion of registered voters to taxpayers has decreased over at the last ten years.
Proportion earlier was \(\frac{T}{V}.\)... and Now it is \(\frac{2T}{xV}\), where \(x<2\) and \(V<T\), so \(\frac{2}{x} *\frac{T}{V}\)......
so it is \(\frac{2}{x}\) times earlier proportion..
But \(\frac{2}{x} > 1\), so \(\frac{2}{x} * \frac{T}{V} > \frac{T}{V}\)..
Correct

E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years
we have already shown above that it is > than previous year

D
_________________

Just to make it easier :

Assume :
T= 10 ; V=5

then Tnew=20 (as double) and Vnew = say 9 (v<10 as increase rate is less than T)

Now as per D
The proportion of registered voters to taxpayers

(ten years ago) V/T --> (ten years later) Vnew/Tnew

5/10 --> 9/20
5/10 > 9/20

So, proportion has actually decreased over at the last ten years.

Imo D
The proportion decreased as number of taxpayer doubled and registered voters increased slightly .
Tax payer =100
Registered voter =90
After the increase Taxpayer =200
Registered voter =150
Initial proportion=90/100
Final proportion =150/200 so the proportion decreased .

Option B

Understand the choice

This option means that each registered voter is also a taxpayer.

Analyze in the context of the passage and the question stem

The passage only talks about the relation between the numbers of taxpayers and registered voters. It does not tell us anything about any overlap in the two categories. For example, we cannot determine from the information in the passage whether the same person is counted both in the taxpayer’s category and the registered voter’s category.

Hence, this option cannot be determined from the passage.


Choice D

This option says that if we look at the proportion of registered voters to taxpayers ten years ago and compare it to the same today, then we find that the proportion of registered voters to taxpayers has decreased.

Analyze in the context of the passage and the question stem

Ten years back the number of tax payers was already slightly higher than the number of registered voters

So, let us say in 2008--> taxpayers--> 100 (slightly higher than number of registered voters)

registered voters-->80

In 2018--> taxpayers--> 200 (doubled from 100)

(But number of registered voters grew at a lower rate, say at 50%)

Then number of registered voters in 2018 -->80+50% of 80= 80+40=120

Next, let us look at the proportion between the two in

2008--> registered voterstaxpayers= 80100= 45=4:5

2018-->registered voterstaxpayers =120200 = 35 = 3:5

We can take any percent growth other than 50% but lower than 100% and we will get a similar result.

We can clearly see that the proportion of registered voters to taxpayers has decreased over the last 10 years.

Hence, this choice is correct.
_________________

Inference :
Let assume No. of taxpayers No. of registered voters
Before 10 Yrs 100 110 it is given registered voters were slightly more
Last 10 yrs 200 210 (assume) <220 (registered voters has increased, but at a lower rate than has the number of taxpayers. so it can't be double)

Ratio (No. of registered voters)/( No. of taxpayers )
Before 10 yrs 110/100 = 1.1
Last 10 yrs 210/200 = 1.05 (this is the extreme case so definitely ratio wont be greater than 1.1)

So , here we can clearly see the ration has decreased.
Correct ans D

Two points, one that actually matters for the GMAT and one that doesn't.


THE POINT THAT MATTERS FOR THE GMAT:

When SPECIFIC TERMS are used in a passage, DO NOT BRING IN ANY INFORMATION FROM OUTSIDE THE PASSAGE.
Basically, treat these terms—such as "taxpayer", in this problem—exactly as you would treat unfamiliar new words whose definitions are provided in the passage. Just go with what's in the passage, and do not incorporate ANYTHING AT ALL from any other source.

Here, actually, "taxpayer" isn't specifically defined at all—so, just treat it like a strange word whose meaning you don't know at all.
The functionality of this problem is unchanged if "taxpayer" is replaced by "elephant", "EENO-985347", "γιλιτερςαυ", or literally other string of characters. Proceed accordingly.



____


THE POINT THAT DOESN'T MATTER FOR THE GMAT:

In the U.S., common convention is to use the word "taxpayer" specifically to refer to individuals who pay personal income tax—NOT any other type of tax. So, paying sales taxes, vehicle registration fees, property taxes, or whatever other tax assessments doesn't make you a "taxpayer" as that word is most commonly used in the United States.
Notably, persons who collect low-income tax credits from the Federal government—in other words, who 'pay' a negative amount of personal income tax for that year—are NOT considered 'taxpayers' in most discussions that use the word 'taxpayer'.

The origins of this convention lie in the thousands and thousands of documents and instruction manuals published by the IRS (= the U.S. Federal tax agency) and by state tax agencies, which all refer to persons filing forms with those agencies as 'taxpayers'.
I've never seen an instruction manual for, e.g., sales tax—hence the discrepancy in how the word is or isn't used.

MOST IMPORTANTLY, if you are thinking about any of this stuff when you see the word 'taxpayer' in a GMAT passage, you're doing it wrong.

t= tax payer =10
r = voters = 9
this is let say 10 yrs ago

T=20
R=15
Now

=> T/R>t/r

Dis ans

Happy to help here:
Argument Analysis: Ten years ago in Maricopa county, fewer than 50 percent of seniors graduated from the high schools.
To counter this situation the county introduced a solution in form of the virtual tutor in the schools with poorest graduation rates.
Current Situation: Graduation rates have now improved to over 60 percent.
Conclusion: Personalised learning technology has contributed towards boosting graduation rates in Maricopa County.
What does the author takes for granted?
Author certainly takes for granted that there isn't any other reason for the increase in the graduation rates other than the personalised learning technology.
One this certainly doesn't seem logical for an assumption for this particular question. When the argument states that what does the author takes for granted, it basically wants to know the assumption that the author makes for the argument.
Assumption is something without which the argument can't stand, and needs to strengthen the conclusion. Here the answer option doesn't talk anything about the reason of the increase of the graduation rates.
Secondly, it isn't necessary for the percentage to correspond with the number. It is possible that number of students may decrease but the percentage may increase.
Hence this option goes out.
Well, it would be too extreme to say that MOST students proffered technology over live instructor. We have not been provided with any such information. Graduation rates have improved after the technology was implemented, but may be no one used the technology and the reason for the improved rates is something else.
This seems feasible as it talks about the reason of increase/decrease of graduation rates. Let's negate this "The criterion for the graduation in Maricopa county HAS been significantly stringent ten years back than it is now" If that's the case, that the criteria of graduation has been relaxed, then it significantly weakens the conclusion.

It shows that the cause of the situation isn't the one that conclusion supports, but is something else.
Hence the actual statement strengthens the conclusion, by eliminating the alternate cause of the result.
Let's keep C
We don't know this. Whether most schools have shown the improvement. All we know is the cumulative rates of the county has increased to more than 60 percent. May be the schools which were already performing well have been even better over time. Goes Out.
Similar reasoning as in D to eliminate E.
C is the best option.

A) The number of taxpayers is now smaller than the number of registered voters. --(contradicts the argument-- out !!)
B) Everyone who is a registered voter is also a taxpayer. (no where mentioned and what is mentioned is- number of taxpayers in Green County was slightly greater than the number of registered voters---out !!)
C) The proportion of registered voters to taxpayers has increased over at the last ten years. ( 2nd line of the argument says --registered voters has increased ,but at a lower rate than has the number of taxpayers --so out !! )
D) The proportion of registered voters to taxpayers has decreased over at the last ten years. ( has to be true --as registered voters has increased ,but at a lower rate than has the number of taxpayers)
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years (-- )

so D

Curious to know how one may be a registered voter if one is not a taxpayer. I suppose you could avoid paying taxes and still be a registered voter (but for how long?). Is this the logic behind this question?

I selected B because it does mention number of taxpayers > number of registered voters
You must pay taxes, but you are not required to be a registered voter

Would like to know what others think

Can someone please explain why A is wrong here?

when Nume < deno

Here, both Numerator and denominator in the fraction were Increased. So the value or the result will be decreased.
Example:
Taxpayers > registered voters
tax doubled > reg increased
Taxpayers > reg voters initially:5>2............
Taxpayers > reg voters updated:10>3
Numerator in options are reg Voters
Denominator in options are Taxpayers
compare option C and D :2/5=.4................3/10=.3
the value was decreased.
option D is the answer

Passage Analysis

Ten years ago, the number of taxpayers in Green County

We are talking about the number of taxpayers in Green County 10 years ago.

was slightly greater than the number of registered voters.


This number of tax payers was slightly greater than the number of registered voters

The number of taxpayers has doubled over the last ten years,

Over the last 10 years the number of tax payers has increased and is now double the number ten years back.

while the number of registered voters has increased,

The number of registered voters has also increased

but at a lower rate than has the number of taxpayers.

But this increase in the number of registered voters has taken place at a lower rate as compared to the rate at which the number of taxpayers has increased.

Gist of the passage


We are talking about the number of taxpayers and the number of registered voters in Green County
We are looking at what these numbers were ten years back and what they are now
We are looking at these numbers in comparative terms
Ten years back the number of taxpayers (say T) was just slightly (that means by a small margin) greater than the number of registered voters (say V)
Hence, ten years back T > V

Over this period of ten years, both T and V have grown in numbers
T has doubled and is now --> 2T
V has also grown but not at the same rate as T
V has grown at a lower rate than T


Question stem Analysis


Which of the following must be true in Greenspace County if the statements above are true?

Each of the options presents a possible conclusion that can be drawn from the information given in the passage. We must identify which option has complete support from the information given in the passage.
_________________

I realize that Choice D is the best answer.

However, for Choice B, doesn't everyone pay taxes in some form (e.g., even if someone is exempt from income taxes, they are paying a sales tax when they buy something)? Don't you have to assume that there is one person who doesn't pay income taxes, nor do they buy anything for B to not be true?

Thank you!

Option (A) is not necessarily true based on the information given. We do not know the current number of taxpayers or registered voters.

Option (B) cannot be inferred from the given information. We only know that the number of taxpayers was slightly greater than the number of registered voters ten years ago, but we do not know if this relationship still holds true.

Option (C) is not necessarily true based on the information given. We know that the number of registered voters has increased at a lower rate than taxpayers, but we do not know the exact proportions or ratios of either group.

Option (D) is the correct answer. If the number of taxpayers has doubled while the number of registered voters has increased at a lower rate, then the proportion of registered voters to taxpayers must have decreased over the last ten years.

Option (E) is not necessarily true based on the information given. We do not know the exact proportions or ratios of either group to determine if the proportion has remained unchanged.

Therefore, the correct answer is (D).