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 Post subject: GRE Data Analysis (Select One)
PostPosted: Thu Nov 25, 2010 5:30 am 
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The graph on the left shows the annual revenue growth rate of Company X. The graph on the right shows the tax rate as a percent of revenue for each year. If Company X's revenue in year ‘99 was $98.1 million, which one of the following is closest to how much more the company paid in taxes in year ‘01 than ‘00?

A. $4 million
B. $6 million
C. $13 million
D. $15 million
E. $20 million

The correct answer is (B). First, given 1999 revenue of $98.1 million, we can find the revenue in 2000 and 2001 because the increase from 1999 to 2000 was 4% and the increase from 2000 to 2001 was 5%:
1999: $98.1 million
2000: ($98.1)(1.04) = $102.024 million
2001: ($102.024)(1.05) = $107.1252 million.

Now, given each year's revenue amounts, calculate the taxes paid:
2000: ($102.024)(0.20) = $20.4048 million
2001: ($107.1252)(0.25) = $26.7813 million.

Now subtract the 2000 tax amount from the 2001 amount:
$26.7813 – $20.4048 = $6.3765 million.

The closest answer is choice (B), which is the correct answer.
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Is this question correct? The explanation stated: "First, given 1999 revenue of $98.1 million, we can find the revenue in 2000 and 2001 because the increase from 1999 to 2000 was 4% and the increase from 2000 to 2001 was 5%".

However, the graph shows that the increase from 2000 to 2001 was 1%.


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 Post subject: Re: math (test 3, question 19): data analysis, percentages.
PostPosted: Thu Nov 25, 2010 5:43 am 
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The graph shows that the revenue in 2001 grew by 1% more than it grew in 2000. Bu still in 2000 it grew 4% (comparing to 1999) and in 2001 it grew 5% (comparing to 2000).

Suppose the revenue in 1998 was Y.
In 1999 it grew 2%: revenue in 1999 was 1.02Y.
In 2000 it grew 4%: revenue in 2000 was 1.04 × (1.02Y).
In 2001 it grew 5%: revenue in 2001 was 1.05 × 1.04 × (1.02Y).


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 Post subject: Re: math (test 3, question 19): data analysis, percentages.
PostPosted: Sun Dec 12, 2010 5:25 am 
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Isn't the difference between the growth in 99' and the growth in 00' a difference of 2% instead of one of 4% as its suggested in the answer prompt? (because 99' is already at a level of 2% and 00' is at one of 4% so shouldn't the difference be 2%? Also should the diff. between 99' and 01' be 3%? instead of 5% as the answer prompt states?
Thanks.


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 Post subject: Re: math (test 3, question 19): data analysis, percentages.
PostPosted: Sun Dec 12, 2010 5:57 am 
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If it is not stated otherwise, the annual rate of growth shows how a quantity increased/decreased comparing to a PREVIOUS year, i.e. for 2000 it shows how a quantity in 2000 changed comparing to 1999, in 2001 - comparing to 2000, etc.

As you've mentioned, the difference between the growth RATE in 99' and the growth RATE in 00' is in fact 4% – 2% = 2%. But it doesn't give us anything in this question.
While the difference between the REVENUE in 99' and the REVENUE in 00' is 4% of the REVENUE in 99' (as the graph shows). This allows us to compare the revenues, not the growth rates.

If the REVENUE in 1999 was S, then in 2000 the REVENUE was 1.04 × S, in 2001 the REVENUE was 1.05 × 1.04 × S.

So the difference between the REVENUE in 99' and 01' is:
1.05 × 1.04 × SS = 1,092 × S, or 9.2% of the REVENUE in 99'.

The last paragraph should give you the full feeling of what the difference between the annual growth rate and growth rate compared to a certain year is.

If we rewrite the grow rate by year, COMPARING TO the revenue in 99' the numbers will be:
Image

If we rewrite the grow rate by year, COMPARING TO the revenue in 00' the numbers will be:
Image


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