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
Before being simplified, the instructions for computing income tax in Country \(R\) were to add \(2\) percent of one's
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2 percent of one’s annual incomeVJesus12 wrote: ↑Thu Jul 22, 2021 3:33 amBefore 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
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
Annual Income = iVJesus12 wrote: ↑Thu Jul 22, 2021 3:33 amBefore 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
\(2\%\) 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