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# Before being simplified, the instructions for computing income tax in

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

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23 Mar 2010, 15:25
3
25
00:00

Difficulty:

75% (hard)

Question Stats:

62% (01:24) correct 38% (01:34) wrong based on 428 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
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Joined: 02 Sep 2009
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Before being simplified, the instructions for computing income tax in  [#permalink]

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23 Mar 2010, 16:16
13
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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

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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03 Jun 2011, 03:11
3
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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26 Aug 2012, 09:47
1
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
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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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06 Sep 2014, 23:56
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

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

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19 Nov 2015, 14:09
3
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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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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19 Nov 2015, 15:46
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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Re: Before being simplified, the instructions for computing income tax in  [#permalink]

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19 Nov 2015, 17:23
4
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...

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

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19 Nov 2015, 21:09
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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26 Apr 2018, 14:47
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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Re: Before being simplified, the instructions for computing income tax in &nbs [#permalink] 26 Apr 2018, 14:47
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