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Gmat prep Question

by rakaisraka » Tue Aug 25, 2015 12:46 pm
Question - Before being simplified, the instructions for computing the income tax in country R were to add 2% of one's annual income to the average of 100 units of country R's currency and 1% of one's annual income. Which of the following represents the simplifed formula for computing the income tax , in country R'c 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

Im not able to understand the question. Please help. Thanks
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by GMATGuruNY » Tue Aug 25, 2015 12:48 pm
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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by rakaisraka » Tue Aug 25, 2015 1:01 pm
Thanks Mitch.
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by [email protected] » Tue Aug 25, 2015 5:17 pm
Hi rakaisraka,

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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by Brent@GMATPrepNow » Thu Nov 19, 2015 2:00 pm
Rich and Pitch have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
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