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

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Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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08 Jul 2015, 10:52
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78% (01:37) correct 22% (01:43) wrong based on 1875 sessions

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Ten years ago the number of taxpayers in Greenspace County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers.

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

(A) The number of taxpayers is now smaller than the number of registered voters.

(B) Everyone who is a registered voter is also a taxpayer.

(C) The proportion of registered voters to taxpayers has increased over the last ten years.

(D) The proportion of registered voters to taxpayers has decreased over the last ten years.

(E) The proportion of registered voters to taxpayers has remained unchanged over the last ten years.

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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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02 Mar 2016, 21:43
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WillGetIt wrote:
Ten years ago the number of taxpayers in Greenspace County was slightly greater than the number o registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers.
Which of the following must be true in Greenspace County if the statements above are true?

A. The number of taxpayers is now smaller than the number of registered voters.

B. Everyone who is a registered voter is also a taxpayer.

C. The proportion of registered voters to taxpayers has increased over the last ten years.

D. The proportion of registered voters to taxpayers has decreased over the last ten years.

E. The proportion of registered voters to taxpayers has remained unchanged over the last ten years

Advice to attempt this question: This is easy problem as long as you write equation before answering

[i]"Please hit kudos if you like this post"

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.

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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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Updated on: 04 Jun 2016, 23:46
2
12
Official Guide for GMAT Verbal Review 2016
Practice Question
Question No.:16
Page: 125
Difficulty:

Ten years ago the number of taxpayers in Green County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers. Which of the following must be true in Greenspace County if the statements above are true?

A) The number of taxpayers is now smaller than the number of registered voters.
B) Everyone who is a registered voter is also a taxpayer.
C) The proportion of registered voters to taxpayers has increased over at the last ten years.
D) The proportion of registered voters to taxpayers has decreased over at the last ten years.
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years.

Originally posted by nycgirl212 on 31 May 2016, 14:33.
Last edited by nycgirl212 on 04 Jun 2016, 23:46, edited 1 time in total.
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Posts: 7437
Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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31 May 2016, 19:37
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nycgirl212 wrote:
Official Guide for GMAT Verbal Review 2016
Practice Question
Question No.:16
Page: 125
Difficulty:

Ten years ago the number of taxpayers in Green County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers. Which of the following must be true in Greenspace County if the statements above are true?

A) The number of taxpayers is now smaller than the number of registered voters.
B) Everyone who is a registered voter is also a taxpayer.
C) The proportion of registered voters to taxpayers has increased over at the last ten years.
D) The proportion of registered voters to taxpayers has decreased over at the last ten years.
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years.

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
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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01 Jun 2016, 00:34
nycgirl212 wrote:
Official Guide for GMAT Verbal Review 2016
Practice Question
Question No.:16
Page: 125
Difficulty:

Ten years ago the number of taxpayers in Green County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers. Which of the following must be true in Greenspace County if the statements above are true?

A) The number of taxpayers is now smaller than the number of registered voters.
B) Everyone who is a registered voter is also a taxpayer.
C) The proportion of registered voters to taxpayers has increased over at the last ten years.
D) The proportion of registered voters to taxpayers has decreased over at the last ten years.
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years.

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
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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14 Dec 2016, 20:16
nycgirl212 wrote:
Ten years ago the number of taxpayers in Green County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers. Which of the following must be true in Greenspace County if the statements above are true?

Type - Inference
Boil it down - Ten years ago number of taxpayers(T) slightly > than number of registered voters(V)
-number of taxpayers(T) = 2x but number of voters(V) increased at a lower rate .

T>> V

V/T has decreased over last 10 years as rate of increase of T has exceeded V and T was slightly more to begin with

A) The number of taxpayers is now smaller than the number of registered voters. Incorrect
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. Incorrect -
D) The proportion of registered voters to taxpayers has decreased over at the last ten years. Correct
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years . Incorrect

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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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18 Dec 2016, 22:42
1
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.
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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10 Jul 2017, 23:26
oh man, working with proportion concept may really devastate your mental visualization.
I do go for D after reading the passage, but it takes me 3 min to figure it out how D fits in the real formula.
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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11 Jul 2017, 10:22
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 .
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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11 Jul 2017, 16:39
arvind910619 wrote:
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 .

yeah, I follow the same method, but i make a mistake
let registered voters 10 and tax payers 11 => then new registered voter is 20 and taxpayers are 22 => big mistake right.
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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11 Jul 2017, 23:20
Error Analysis:

No. of taxpayers=110
No. of voters=100

Proportion of Voters to Tax payers= (100/110)=0.9

After 10 years
No. of Tax Payers=1000
No .of voters =800

Proportion of Voters to Tax Payers= (800/1000)=0.8

Therefore the Proportion has decreased. Option D.
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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11 Aug 2017, 21:18
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

CounterSniper wrote:
nycgirl212 wrote:
Official Guide for GMAT Verbal Review 2016
Practice Question
Question No.:16
Page: 125
Difficulty:

Ten years ago the number of taxpayers in Green County was slightly greater than the number of registered voters. The number of taxpayers has doubled over the last ten years, while the number of registered voters has increased, but at a lower rate than has the number of taxpayers. Which of the following must be true in Greenspace County if the statements above are true?

A) The number of taxpayers is now smaller than the number of registered voters.
B) Everyone who is a registered voter is also a taxpayer.
C) The proportion of registered voters to taxpayers has increased over at the last ten years.
D) The proportion of registered voters to taxpayers has decreased over at the last ten years.
E) The proportion of registered voters to taxpayers has remained unchanged over at the last ten years.

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
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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25 Sep 2017, 01:57
1
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
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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03 Feb 2018, 21:15
chetan2u

Quote:
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 $$Vso it is \(\frac{2}{x}$$ times earlier proportion..
But $$\frac{2}{x} > 1$$, so $$\frac{2}{x} * \frac{T}{V} > \frac{T}{V}$$..
Correct

On few rare occasions, my approach matched with experts.
However I took x as 1.5 since I knew that the no of registered voters has increase but not as
much as that of tax payers. Will this work good too?
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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31 May 2018, 02:37
Let "T" be number of taxpayers in Greenspace County
Let "V" be number of registered voters

Given that ten years ago T > V
Over ten years "T" has doubled to 2T
& "V" has increased but at a lower rate than "T", i.e. lets assume 1.5V

Using smart number can communicate the message quickly:-
Let T + V = 100 [Given that ten years ago T > V, let T = 60 and V = 40]
Proportion of V to T is 2 to 3 [40 to 60]

Over ten years "T" has doubled to 2T - i.e. 60 became 120
& "V" has increased but at a lower rate than "T", i.e. lets assume 1.5V - i.e. 40 became 60
Revised Proportion 1.5V to 2T is 1 to 2 [60 to 120]

Clearly "The proportion of registered voters to taxpayers has decreased over the last ten years, i.e. from 2/3 to 1/2". Therefore Option D is correct answer.
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Re: Ten years ago the number of taxpayers in Green County was slightly  [#permalink]

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30 Dec 2018, 21:09
Question Type -> Inference

Given -> 10 years ago -> number of taxpayers > registered voters
After 10 years -> the number of taxpayers doubled and the number of registered voters increased

I took the mathematical approach here
Initially -> I assumed number of taxpayers to be 10 > registered voters can be 5
After ten years-> number of taxpayers became 20 > registered voters can be anywhere between 5 and 19.

Following that
(A) The number of taxpayers is now smaller than the number of registered voters. -> Incorrect as per the data
(B) Everyone who is a registered voter is also a taxpayer. -> Not necessary, it can be a subset or not.
(C) The proportion of registered voters to taxpayers has increased over the last ten years.
(D) The proportion of registered voters to taxpayers has decreased over the last ten years.
(E) The proportion of registered voters to taxpayers has remained unchanged over the last ten years. -> Not true, it has changed.

Bottom 2 choices will be C and D
In C
-> the proportion can be 6/20 or or it can be 10/20(in this case it will be same as the initial ratio of 5/10) but after 10/20 it will be the opposite of the stated claim.

In D
-> the proportion will have more cases of it being greater than the initial ratio, 11/20, 12/20.Thereby relating with the statement

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Re: Ten years ago the number of taxpayers in Green County was slightly   [#permalink] 30 Dec 2018, 21:09
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