Begoña lives in a country with a progressive tax system. All

Question

Begoña lives in a country with a progressive tax system. All income is taxed at a base rate of 20%. In addition, any income above $40,000 is subject to an extra 25% tax. Furthermore, if a person’s income is at least $100,000, an additional 2% tax is applied to all income. Which of the following cannot be Begoña’s effective tax rate?

A. 32%
B. 34%
C. 36%
D. 38%
E. 42%

A. 32%
B. 34%
C. 36%
D. 38%
E. 42%

Devikaudcaps · Answer

how do we solve this?

Cooley · Answer

wording of the question is what you are looking for. Once income hits 100k, 2 percent of tax is hit on all income. When you approach 100k effective tax is 35 percent, once you hit 100k, 2 percent tax effects entire income, so effective rate jumps to 37%, then slowly approaches (but never hits) 47 percent (20+25+2). So only gap is anywhere ≥ 35 and < 37.

kevincan · Answer

Great second post ! Welcome to Gmatclub!

Vinayakkalra10 · Answer

Great Solution! which category do these set of q's belong to?

kevincan · Answer

Percents and also Functions

Gun99 · Answer

Detailed Explanation incase anyone is still not clear -

1. Break Down the Tax Rules

Let x be Begoña's total income. The problem describes three distinct rules:
 
  Base Rate:  20% on all income. 
  Surtax 1:  An extra 25% on any income  above  $40,000. 
  Surtax 2:  An additional 2% on  all  income if total income is  at least  $100,000.  
 
2. Analyze the Critical Threshold at $100,000
The most interesting part of this tax system is what happens right as income approaches and hits  $100,000 . Because the 2% tax applies to  all  income retrospectively once you hit $100,000, it causes a sudden jump (a discontinuity) in the effective tax rate.

Scenario A: Income is just under $100,000 (e.g., x -> Just less than $100,000)
If she earns exactly $100,000, but we look at the limit from below (no 2% rule yet):
 
  Tax on first $40,000:  20% * 40,000 = $8,000 
  Tax on next $60,000:  (20% + 25%) * 60,000 = 45% * 60,000 = $27,000 
  Total Tax:  $8,000 + $27,000 = $35,000  
Effective Tax Rate = $35,000 / $100,000 = 35%
As income approaches $100,000 from below, the effective tax rate approaches  35% .

Scenario B: Income hits exactly $100,000
The moment her income reaches $100,000, the 2% additional tax triggers on  all  income:
 
  Previous Tax:  $35,000 
  Additional 2% on all income:  $2% * $100,000 = $2,000 
  Total Tax:  $35,000 + $2,000 = $37,000  
Effective Tax Rate = $37,000 / $100,000 = 37%
 
3. Identify the Impossible Range
Because of this sudden 2% jump on the entire pool of money:
 
 For any income  less than $100,000 , the maximum possible effective tax rate is strictly less than  35% . 
 For any income  equal to or greater than $100,000 , the minimum possible effective tax rate starts at  37%  (and slowly climbs toward 47% as income approaches infinity).  
Therefore, it is completely impossible to have an effective tax rate  between 35% and 37%

So Answer is Option C.

kevincan · Answer

Beautifully explained !

Kinshook · Answer

Begoña lives in a country with a progressive tax system. All income is taxed at a base rate of 20%. In addition, any income above $40,000 is subject to an extra 25% tax. Furthermore, if a person’s income is at least $100,000, an additional 2% tax is applied to all income.

Which of the following cannot be Begoña’s effective tax rate?

Tax slabs: -
Below $40,000 = 20%
$40,000 - $100,000 = 20% + 25% = 45%
Above $100,000 = additional 2% tax to all income

Let the income be $x

Case 1: x < $40,000
Effective tax rate = 20%

Case 2: $40,000 < x < $100,000
Tax = $40,000*20% + 45%*(x-40,000) = $8,000 + 45%x - $18,000 = 45%x - $10,000
At $100,000 - > Tax = $35,000; Effective tax rate = 35%

Case 3: x > $100,000
Tax = $40,000*20% + 45%*(x-40,000) + 2%*x = 47%x - $10,000
At $100,001 - > Tax = $37,000; Effective tax rate = 37%

There is no effective tax rate possible between 35% and 37%

IMO C

Begoña lives in a country with a progressive tax system. All

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Begoña lives in a country with a progressive tax system. All

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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