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Ten years ago the number of taxpayers in Greenspace County w

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Ten years ago the number of taxpayers in Greenspace County w

by BTGmoderatorAT » Thu Jan 04, 2018 5:31 am
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

What's the best approach to determine the answer? Can any experts help?
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by ErikaPrepScholar » Thu Jan 04, 2018 7:38 am
We can think about this algebraically. Let t represent taxpayers and v represent voters.

Ten years ago, there were slightly more taxpayers than voters:

t > v

Today, the number of taxpayers has doubled:

2t

But the number of voters has increased at a smaller rate - in other words, it is less than double:

less than 2v

We can extrapolate a few things from this:

1) there are still more taxpayers than voters. t > v, so 2t > 2v, so 2t > less than 2v.
2) there are less voters per taxpayer now than there were ten years ago. We originally had a ratio of v : t, or v taxpayers per t voters. Multiplying both sides by 2 gives us the equivalent ratio 2v : 2t. Now we have less than 2v : 2t, which is a lower ratio of voters to taxpayers.

A. The opposite of what we found in 1. Eliminate.
B. While there are less voters than taxpayers, we don't know that they are all taxpayers. If everyone in Greenspace County pays taxes, then, yes, all voters must be taxpayers. But this isn't necessarily true! There might be 100 people in the county, 98 of them pay taxes, and the 2 people who don't pay taxes vote. Eliminate.
C. This is the opposite of what we found in 2. Eliminate.
D. This is exactly what we found in 2! Correct.
E. This contracts what we found in 2: the ratio HAS changed. Eliminate.
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