A Word Problem

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billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

by billzhao » Mon Feb 09, 2009 4:46 pm

Before bing simplified, the instructions for computing income tax in Country X were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I?
A. 50+I/200
B. 50+I*3/100
C. 50+I/40
D. 100+I/50
E. 100+I*3/100

my answer is E. Can someone help to explain?

Thanks!

Yiliang

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Source: Beat The GMAT — Problem Solving | Mon Feb 09, 2009 4:46 pm

DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member; Thanked: 23 times; GMAT Score:660

by DeepakR » Mon Feb 09, 2009 5:15 pm

I am getting the same. Is that correct ?
Is it 2I/100 + 100 + I/100 = (100 + (3I/100)) = E

- Deepak

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Mon Feb 09, 2009 5:38 pm

I'm getting C.
(100+.01I)/(2)+.02I=50+I/40
Remember that it says the arithmetic mean of 1 percent of the annual income and the 100 R Units. So it'd be .01I+100/2..

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billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

by billzhao » Mon Feb 09, 2009 8:25 pm

truplayer256, your answer is correct. i did not read the description carefully. Thanks!

Yiliang

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DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member; Thanked: 23 times; GMAT Score:660

by DeepakR » Tue Feb 10, 2009 5:43 pm

Before being simplified, the instructions for computing income tax in Country X were to add 2 percent of one's annual income [b]to the average (arithmetic mean) of 100 units of R's currency and 1 percent of one's annual income. [/b]

Actually its like adding A to B, where you have A is 2% annual income and
B= Avg arithmetic mean of (100 + 1%annual income)
Consider (eg. Avg arithmetic mean of x and y= (x+y)/2)
similarly, B= (100 + 1% annual income)/2

Now, we know Annual income = I hence,

B=(100 + (I/100))/2=50+(0.5I)/100

Now A + B = (2I/100) + 50 + (0.5I/100) = 50 + (2.5I/100)=
50 + (I/40)=Ans.) C

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