Income tax calculation

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mallika hunsur: Master | Next Rank: 500 Posts; Posts: 107; Joined: Tue Oct 07, 2014 3:50 am

by mallika hunsur » Thu Apr 09, 2015 4:42 am

Hi,

Please can anyone explain this! I can't seem to understand what the question is asking!!

Regards,
Mallika

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Source: Beat The GMAT — Problem Solving | Thu Apr 09, 2015 4:42 am

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

by GMATGuruNY » Thu Apr 09, 2015 5:18 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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mallika hunsur: Master | Next Rank: 500 Posts; Posts: 107; Joined: Tue Oct 07, 2014 3:50 am

by mallika hunsur » Thu Apr 09, 2015 5:29 am

GMATGuruNY 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?

(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.

Thanks Mitch, I think the statement got me!! Couldn't understand what the Q was asking!!!

Thanks,
Mallika

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by [email protected] » Thu Apr 09, 2015 10:43 am

Hi Mallika,

I'm a big fan of TESTing VALUES in these types of situations (the approach that Mitch used). You can also approach this question algebraically.

In certain Quant questions, you might find it easier to "convert" data from one format to another. While the answers are in "fraction format", you can very easily do the work with decimals, if you find that format easier.

Here we'd need to translate the given question into decimals:

J = one's income (I'm using "J" because an "I" looks like a 1)

2% of one's income = .02(J)

Avg of 100 units and 1% of one's income = (100 + .01(J)) / 2

Tax = .02(J) + 50 + .005(J)
Tax = .025(J) + 50
Tax = J(1/40) + 50

Final Answer: C

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