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Intern  Joined: 29 Sep 2009
Posts: 22
Before being simplified, the instructions for computing income tax in  [#permalink]

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3
67 00:00

Difficulty:   75% (hard)

Question Stats: 58% (02:16) correct 42% (02:24) wrong based on 514 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Before being simplified, the instructions for computing income tax in  [#permalink]

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21
20
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

Tax is the sum of the following:
2 percent of one's annual income - $$0.02I$$;
The average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income - $$\frac{100+0.01I}{2}$$.

$$Tax=0.02*I+\frac{100+0.01*I}{2}=50+\frac{0.04*I+0.01*I}{2}=50+\frac{0.05*I}{2}=50+\frac{I}{40}$$.

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Re: Hard GMAT PREP PS problem  [#permalink]

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4
lionheart187 wrote:
Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of ones'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/300
C) 50 + I/40
D) 100 + I/50
E) 100 + 3I/100

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"
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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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3
1
The language is a trap here, sometimes SC is tested in Quants Wrong method:
(100/2)+(0.02I + 0.01 I) = 50+(3I/100)

Right method:
0.02I + {(100+0.01 I)/2} = 50+I/40
Manager  Joined: 07 Apr 2014
Posts: 98
Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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1
1
nesta wrote:
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 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

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

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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5
pooja3017 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

2 percent of one’s annual income
If income = i, then 2% of income = (2/100)i = 0.02i

average of 100 units of country R’s currency and 1 percent of one’s annual income
1 percent of one’s annual income = (0.01)i
So, average of 100 units of country R’s currency and 1 percent of one’s annual income = (100 + 0.01i)/2 = 50 + 0.005i

So, TOTAL TAX = 0.02i + (50 + 0.005i)
= 0.025i + 50
= (25/1000)i + 50
= (1/40)i + 50
= i/40 + 50
= C

Cheers,
Brent
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GMAT 1: 640 Q39 V38 GMAT 2: 700 Q47 V38 Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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1
pooja3017 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

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

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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5
1
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...

GMAT assassins aren't born, they're made,
Rich
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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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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 - http://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - http://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - http://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent
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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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nesta 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

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

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Joined: 09 Mar 2017
Posts: 33
Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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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).

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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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Brego wrote:
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

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.
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# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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Brego wrote:
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

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.
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# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

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Joined: 21 Mar 2018
Posts: 6
Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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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

After substituting I = 100 in (C), we get 52.5 and hence C is our answer. Re: Before being simplified, the instructions for computing income tax in   [#permalink] 24 Nov 2019, 04:08
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