Formula Percentage

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Formula Percentage

by singhmaharaj » Sun Apr 06, 2014 5:48 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 + 3 I/100

(c) 50 + I/40

(d) 100 + I/50

(e) 100 + 3 I/100
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by [email protected] » Sun Apr 06, 2014 12:14 pm
Hi singmaharaj,

This question can be approached by either TESTing VALUES or by doing algebra. Here's the algebra approach:

This prompt requires translating text into algebra...(note: I'm using the letter "A" instead of the letter "I" from the prompt)

A = annual income

2% of annual income + the average of 100 unites and 1% of annual income....

Income Tax = .02A + (100 + .01A)/2

Now we can simplify

.02A + 50 + .005A

50 + .025A

50 + A/40

Final Answer: C

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by GMATGuruNY » Sun Apr 06, 2014 2:12 pm
Before being simplified, the instructions for computing income tax in Country Rwere to add 2 percent of one's annual income to the average(arithmetic mean)of 100units 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

OA C
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 yields 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 singhmaharaj » Mon Apr 07, 2014 2:09 am
I guess it was problem with my understand of average of 100 units and 1 percent of annual income.

I wrote the formula as 0.02*I + 100 + 0.01*I ..I could not understand how do I average the 100 units. Missed to understand that it is the average of (100 + 0.01*I)/2

Thanks a ton guys.