Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) 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

## The third question fro GMATprep

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Algebraically:BigFisch wrote:Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) 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

2%(I) + (100 + 1%(I))/2

(2/100)I + 100/2 + ((1/100)I)/2

(2/100)I + (1/200)I + 50

(4/200)I + (1/200)I + 50

50 + (5/200)I

50 + (1/40)I

50 + I/40

choose (C)!!

For a quick guess, we know that the average formula is sum/# of terms. Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.

We also know that the other part is 2%(i) + something else, so eliminate (a). Worse case, you have a 50/50 shot.

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I had a lot of trouble understanding the wording of the question. How do you get from "the average (arithmetic mean) of 100 units of Country R’s currency" to a division by 2?Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.

appreciate!

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You need to read the entire sentence:leovonp wrote:Sorry Stuart, one thing is unclear to me...

I had a lot of trouble understanding the wording of the question. How do you get from "the average (arithmetic mean) of 100 units of Country R’s currency" to a division by 2?Since the number of terms in that part of the formula is 2, we know that the answer should include 100/2 = 50, so eliminate (d) and (e) quickly.

appreciate!

It's not the average of 100 units of currency; it's the average of 100 units of currency AND 1% of annual income.average (arithmetic mean) of 100 units of Country R’s currencyand1 percent of one’s annual income

So, the two terms are:

(1) 100 units of currency; and

(2) 1% of annual income.

And since average = (sum of terms)/(# of terms), we know that the denominator is "2".

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I don't believe GMATPRep could trick me with such a word-problem!! oh boy!!

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We also could plug in.BigFisch wrote:Hello everyone, i really appreciate that if anyone could tell me how to solve this question. Thank you so much guys.

(Question 3) Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of oneï¿½s annual income to the average (arithmetic mean) of 100 units of Country Rï¿½s currency and 1 percent of oneï¿½s annual income. Which of the following represents the simplified formula for computing the income tax, in Country Rï¿½s 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 = 400.

1% of income = 4.

Average of 100 + 1% of income = (100+4)/2 = 52.

2% of income = 8.

Total tax = 52+8 = 60. This is our target.

Now we plug I=400 into the answers to see which yields our target of 60.

Only answer choice C works:

50 + I/10 = 50 + 400/40 = 60.

The correct answer is C.

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