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Before being simplified, the instructions for computing income tax in Country \(R\) were to add \(2\) percent of one's

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by VJesus12 » Thu Jul 22, 2021 3:33 am

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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. \(50 + \dfrac{I}{200}\)

B. \(50 + \dfrac{3I}{100}\)

C. \(50 + \dfrac{I}{40}\)

D. \(100 + \dfrac{I}{50}\)

E. \(100 + \dfrac{3I}{100}\)

Answer: C

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Re: Before being simplified, the instructions for computing income tax in Country \(R\) were to add \(2\) percent of one

by Brent@GMATPrepNow » Thu Jul 22, 2021 5:13 am
VJesus12 wrote: ↑
Thu Jul 22, 2021 3:33 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. \(50 + \dfrac{I}{200}\)

B. \(50 + \dfrac{3I}{100}\)

C. \(50 + \dfrac{I}{40}\)

D. \(100 + \dfrac{I}{50}\)

E. \(100 + \dfrac{3I}{100}\)

Answer: C

Source: GMAT Prep
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
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Before being simplified, the instructions for computing income tax in Country \(R\) were to add \(2\) percent of one

by swerve » Thu Jul 22, 2021 11:21 am
VJesus12 wrote: ↑
Thu Jul 22, 2021 3:33 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. \(50 + \dfrac{I}{200}\)

B. \(50 + \dfrac{3I}{100}\)

C. \(50 + \dfrac{I}{40}\)

D. \(100 + \dfrac{I}{50}\)

E. \(100 + \dfrac{3I}{100}\)

Answer: C

Source: GMAT Prep
Annual Income = i
\(2\%\) of annual income \(= 0.02i\)
Average of \(100 R\) and \(1\%\) of annual income \(= \dfrac{100+0.01i}{2}\)

\(\dfrac{100+0.01i}{2} + 0.02i\)
\((50+0.005i) + 0.02i\)
\(50 + 0.025i\)
\(50 + \dfrac{25i}{1000}\)
\(50 + \dfrac{5i}{200}\)
\(50 + \dfrac{i}{40}\)

Therefore, C
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