Question

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.

Answer 1

Answer:

D

Explanation:

It is better if we understand this problem with numbers. Let´s suppose the number of taxpayers is 100.000 and the number of registered voters is 90.000. The proportion of registered voters to taxpayers was 90.000/100.00=0.9. Over the last ten years, the number of taxpayers has double: 100.000*2=200.000, and the number of registered voters has increased, but at a lower rate, let´s suppose that at a rate of 1.5: 90.000*1,5=135.000. Now, the proportion  of registered voters to taxpayers is 135.000/200.000= 0,68

The number of taxpayers remains bigger than the number of registered voters. And the proportion of registered voters to taxpayers has decreased over the ten years. It is possible that everyone who is registered voter is also a taxpayer because the registered voters are less than the taxpayers but we don´t know for sure. What we know is that not all the taxpayers are registered voters because there are more taxpayers than registered voters.