Income Tax

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DevB: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sun Apr 06, 2014 10:50 am; Thanked: 1 times; Followed by:1 members

Income Tax

by DevB » Sat Jul 26, 2014 7:54 am

Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country 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?

1. 50 + I/200
2. 50 + 3I/100
3. 50 + I/40
4. 100 + I/50
5. 100 + 3I/100

Above question is from GMAT Prep. Please help in answering...!!

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Source: Beat The GMAT — Problem Solving | Sat Jul 26, 2014 7:54 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Sat Jul 26, 2014 9:18 am

DevB wrote:Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country 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?

1. 50 + I/200
2. 50 + 3I/100
3. 50 + I/40
4. 100 + I/50
5. 100 + 3I/100

Above question is from GMAT Prep. Please help in answering...!!

The instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income

Let, Income = I

2% of annual Income = (2/100)I
Average of 100 Units of R's Currency and 1% of annual income = [100 + (1/100)I]/2

Following the instruction above:
To calculate the Tax "The required Addition" = (2/100)I + [100 + (1/100)I]/2
Income Tax = I/50 + (50 + I/200)
Income Tax = I/40 + 50

Answer: Option C

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 am; Location: NY; Thanked: 28 times; Followed by:11 members

by abhasjha » Sat Jul 26, 2014 9:55 am

Assume I = 100 .... (as numbers given in percentage )
2 % of I = 2
Mean = (100+1)/2= 50.5
ACCORDING TO QUESTION
2+ 50.5 = 52.5

Check now ....
(a) 50+ (I/200)= 50 +(100/200)= 50+.5= 50.5 . This is not equal to 52.5 RULE OUT CHOICES WHICH IS NOT EQUAL TO 52.5

Only (c) equals 52.5 . Hence answer C

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Jul 26, 2014 10:20 am

Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country 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+3I/100
(C) 50+I/40
(D) 100+I/50
(E) 100+3I/100

Let I = 200 units of currency.
The tax is the SUM of two values: 2% of the income AND the average of 100 units of currency and 1% of the income.
2% of the income = .02(200) = 4.
The average of 100 units of currency and 1% of the income = (100 + .01(200)) / 2 = 102/2 = 51.
Tax = 4+51 = 55. This is our target.

Now plug I=200 into the answers to see which yield our target of 55.

Only answer choice C works:
50 + I/40 = 50 + 200/40 = 55.

The correct answer is C.

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