Before being simplified, the instructions for computing income tax in

Add
2% of Annual Income
TO
Average OF[100 units of currency AND 1% of annual Income]

Annual Income=x (using x for clarity because I looks like 1)

2% of Annual Income = 2x/100
1% of Annual Income = 1x/100= x/100
Average of [100 units of currency AND 1% of annual Income] = (100+(x/100))/2=((100)^2+x)/200

\(Tax=\frac{2x}{100}+\frac{100^2+x}{200}\)

\(Tax=\frac{4x+100^2+x}{200}\)

\(Tax=\frac{5x+100^2}{200}\)

\(Tax=\frac{5x}{200}+\frac{100^2}{200}\)

\(Tax=\frac{x}{40}+\frac{100*100}{200}\)

\(Tax=50+\frac{x}{40}\)

Ans: "C"

The language is a trap here, sometimes SC is tested in Quants

Wrong method:
(100/2)+(0.02I + 0.01 I) = 50+(3I/100)
Answer choice B

Right method:
0.02I + {(100+0.01 I)/2} = 50+I/40
Correct Answer Choice C

I- income
0.02I - 2% of I ; 0.01I - 1% of I ; 100 units - i count as 100.

so

0.02I + (100+0.01I)/2 --> (0.04I+100+0.01I)/2


(100+0.05I)/2

50 + 0.05I/2 -- (0.05I/2 --> 5I/200 --> I/40)

50+I/40

Hence Answer is C

Took me some time to translate the question, but here is how I did it:

Annual Income = i
2% of annual income = 0.02i
Average of 100 R and 1% of annual income = (100+0.01i)/2

(100+0.01i)/2 + 0.02i
(50+0.005i) + 0.02i
50 + 0.025i
50 + 25i/1000
50 + 5i/200
50 + 1i/40

Answer C

Hi pooja3017,

This question can be solved by TESTing VALUES.

I'm going to use the variable "J" instead of an "I" (since that might be mistaken for the number 1)...

We're told to add "2% of one's income" to "the average of 100 and 1% of one's income"

Let's TEST J = 100

So we're adding 2% of 100 to (100 + 1% of 100)/2....

2 + 101/2 =
2 + 50.5 =
52.5

So we're looking for an answer that equals 52.5 when J = 100. There's only one answer that matches...

Final Answer:
GMAT assassins aren't born, they're made,
Rich

The posts above demonstrate 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,
Brent

We are given that 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. We need to determine the formula for computing the tax for a person who earns “I” annual income.

The expression is as follows:

0.02I + (100 + 0.01I)/2

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

2I/100 + 100/2 + I/200

2I/100 + 50+ I/200

50 + 4I/200 + I/200

50 + 5I/200

50 + I/40

Answer: C

ScottTargetTestPrep Bunuel EMPOWERgmatRichC

In my test I did this: (100*R) + 0.01I. And I didn't know what to divide by to find the average. My question is, why do we just add 100 units of R plus 1 percent of income and then divide by 2? Shouldn't it be divided by 100 units + a number?

I think I am wrong at assuming that 100 units is a quantity not the total value of all the currency. How does the passage hint that 100 units is quantity * price instead of just quantity? Wouldn't it be more clear if it just said a total of 100 dollars? It makes reader think that "units" are actually the quantity of currency R.

Thank you

Hi Brego,

It might help to think about what exactly you are "averaging" and why. Here, we're averaging 2 things: "100 units of currency" and "1% of one's annual income", so you're probably thinking about either dividing by 2 or dividing by 101. Dividing by 101 wouldn't make much sense, since we're not asked to find the average of all of the individual items. The only other option would be to divide by 2, which would make sense, since we're trying to determine the calculation for the amount of income tax (and the prompt is clearly discussing the formula for that).

GMAT assassins aren't born, they're made,
Rich

The phrase “100 units of Country R's currency” actually means something like 100 dollars, except that it doesn’t have to be dollars; hence the saying “Country R's currency”. If Country R uses Euros, it would be 100 Euros, if Country R uses Pesos, it would be 100 Pesos etc. (100 * R) + 0.01l is not meaningful; in the question, R stands for nothing besides the country’s name. To simplify the question, let’s just say the country uses dollars and re-word the income tax, the way it is before simplification, as follows: 1) Find the average of 100 dollars and 1 percent of the individual's income 2) Add 2 percent of the individual's income to the result of the previous step. The result of step 1) is (100 + 0.01l)/2 and the result of step 2) is 0.02l + (100 + 0.01l)/2.

The phrase “100 units of Country R's currency” actually means something like 100 dollars, except that it doesn’t have to be dollars; hence the saying “Country R's currency”. If Country R uses Euros, it would be 100 Euros, if Country R uses Pesos, it would be 100 Pesos etc. (100 * R) + 0.01l is not meaningful; in the question, R stands for nothing besides the country’s name. To simplify the question, let’s just say the country uses dollars and re-word the income tax, the way it is before simplification, as follows: 1) Find the average of 100 dollars and 1 percent of the individual's income 2) Add 2 percent of the individual's income to the result of the previous step. The result of step 1) is (100 + 0.01l)/2 and the result of step 2) is 0.02l + (100 + 0.01l)/2.

Using Manhattan's approach to solve questions that do not involve absolute numbers - USE SMART NUMBERS!

Let Income (I) = 100
2% of I = 2
1% of I = 1

Formula F = 2 + [(100+1)/2]
=(4+101)/2
= 52.5

Okay, now come to the options. Always start with (C)
After substituting I = 100 in (C), we get 52.5 and hence C is our answer.

Hi Bunuel - how did you simplify 0.02∗I+100+0.01∗/2 to 50+0.04∗I+0.01∗I/2?

\(Tax=0.02*I+\frac{100+0.01*I}{2}\).

Now, \(0.02*I=\frac{0.04*I}{2}\) and\(\frac{100+0.01*I}{2}=50+\frac{0.01*I}{2}\).

So, \(Tax=0.02*I+\frac{100+0.01*I}{2}=\frac{0.04*I}{2}+50+\frac{0.01*I}{2}=50+\frac{0.04*I+0.01*I}{2}=50+\frac{0.05*I}{2}=50+\frac{I}{40}\).

2 percent of one's annual income: \(\frac{2}{100i}\)
average of 100 units of Country R's currency AND 1 percent of one's annual income: 100 + i/100 /2

\(\frac{2I}{100}\) + 50 + \(\frac{2i}{200}\)

50 + \(\frac{6i}{200}\) = 50 + \(\frac{i}{40}\)

Answer is C.

2% * I + [ (100 + 1%*I) / 2 ] =

(2/100)*I + [ (10,000 + I)/(100) / 2] =

(4/200)*I + (10,000 + I)/(200) =

----have Common DEN = 200 now so ADD ----

(4I + 10,000 + I) / (200) =

(5I/200) + (10,000/200) =

(I/40) + 50

-C-

The question can be understood/simplified in the following style

To get Total, Add A to B

where A = 2% of annual income
=0.02I
B= Average of 100 and 1% of annual income
= (100+0.01I)/2

Option C is the answer