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In the year following an eight-cent increase in the federal [#permalink]
23 Feb 2006, 07:24
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In the year following an eight-cent increase in the federal tax on a pack of cigarettes,
sales of cigarettes fell ten percent. In contrast, in the year prior to the tax increase, sales
had fallen one percent. The volume of cigarette sales is therefore strongly related to the
after-tax price of a pack of cigarettes.
The argument above requires which of following assumptions?
A. During the year following the tax increase, the pretax price of a pack of cigarettes
did not increase by as much as it had during the year prior to the tax increase.
B. The one percent fall in cigarette sales in the year prior to tax increase was due to a
smaller tax increase.
C. The pretax price of a pack of cigarettes gradually decreased throughout the year
before and the year after the tax increase.
D. For the year following the tax increase, the pretax price of a pack of cigarettes
was not eight or more cents lower than it had been the previous year.
E. As the after-tax price of a pack of cigarettes rises, the pretax price also rises.
I think it is D.
Lets create equations for before and after years
Before year >> x + y = z
After yesr >> a +b = c
x and a are pre tax figures, y and b are taxes and z and c are after tax figures.
We are interested in c-z = (a-x) + (b-y)
We know that b-y = 8 cents
So if c-z has to be positive, a-x > -8 or a > x-8
That means the a can not be 8 or more cents lower than x
I think B is the answer. Because the author concludes that the volume of sales of cigarettes is related to the after tax price.For which he shows the evidence that the 10 % decrease in sales is due to 8 cent increase in tax and in previous year the sales had just decreased to 1 %. which means that he has assumed that the 1% decrease was due to the low increase in tax.
We must be sure that the pretax prices of the cigarettes remain the same, or are just slightly higher than those of the previous year, to have evidence that the reduced smoking is due to higher after-tax prices, and thus due to the tax increase.