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Country X taxes each of its citizens an amount equal to 12

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Country X taxes each of its citizens an amount equal to 12 [#permalink] New post 15 Mar 2012, 00:03
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

79% (02:41) correct 21% (00:55) wrong based on 57 sessions
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

A. $40,000
B. $56,000
C. $64,000
D. $66,667
E. $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.
[Reveal] Spoiler: OA

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MGMAT 2--> 640
MGMAT 3 ---> 610 :-(


Last edited by Bunuel on 15 Mar 2012, 00:59, edited 1 time in total.
Edited the question.
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Re: Country X [#permalink] New post 15 Mar 2012, 00:58
Expert's post
enigma123 wrote:
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

(A) $40,000
(B) $56,000
(C) $64,000
(D) $66,667
(E) $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.


Equation is correct, so math must be a problem.

0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.

Answer: B.

Hope it helps.
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Re: Country X taxes each of its citizens an amount equal to 12 [#permalink] New post 03 May 2012, 10:39
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enigma123 wrote:
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

A. $40,000
B. $56,000
C. $64,000
D. $66,667
E. $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.




Guys a simple way to crack problems like this

so for first 40000$ the tax rate is 12% so 40000*12/100=4800 so the total tax payable is 8000 so if we deduct 4800 from 8000 we get 3200 which is 20% of the remaining so with this we can set the equation like this

20% 3200
100% x

By cross multiplication we get .2x=3200*1 =>x=3200/.2 => 32000/2(multiplying numerator and denominator with 10 to get rid .2 in denominator ) so we get 16000$ so total income before tax was 40000$+16000$=56000$


Ans option is B

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Re: Country X taxes each of its citizens an amount equal to 12 [#permalink] New post 16 Nov 2013, 14:57
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Re: Country X [#permalink] New post 20 Nov 2013, 04:21
Bunuel wrote:
enigma123 wrote:
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

(A) $40,000
(B) $56,000
(C) $64,000
(D) $66,667
(E) $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.



Equation is correct, so math must be a problem.

0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.

Answer: B.

Hope it helps.


I Bunuel, I usually solve like this:

0.12 * 40,000 + 0.2 * x

x is the income above 40,000

0.12 * 40,000 = 4800 ==> 8000 - 4800 = 3200

so 0.2x=3200, x = 16,000

thus total income = 40,000+16,000=56,000

Could there be trouble in other problems? Or can I use my approach as well? I see that if I do it like you I get the total income right away, but for me it's easier to do it the other way (it's just clearer to me).

Thanks!
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Re: Country X [#permalink] New post 20 Nov 2013, 04:23
Expert's post
unceldolan wrote:
Bunuel wrote:
enigma123 wrote:
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

(A) $40,000
(B) $56,000
(C) $64,000
(D) $66,667
(E) $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.



Equation is correct, so math must be a problem.

0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.

Answer: B.

Hope it helps.


I Bunuel, I usually solve like this:

0.12 * 40,000 + 0.2 * x

x is the income above 40,000

0.12 * 40,000 = 4800 ==> 8000 - 4800 = 3200

so 0.2x=3200, x = 16,000

thus total income = 40,000+16,000=56,000

Could there be trouble in other problems? Or can I use my approach as well? I see that if I do it like you I get the total income right away, but for me it's easier to do it the other way (it's just clearer to me).

Thanks!


I see nothing wrong with your approach.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Country X taxes each of its citizens an amount equal to 12 [#permalink] New post 28 Dec 2013, 10:28
enigma123 wrote:
Country X taxes each of its citizens an amount equal to 12 percent of the fi…rst $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?

A. $40,000
B. $56,000
C. $64,000
D. $66,667
E. $80,000

Guys - this is how I am trying to solve this algebraically, but its not giving me right answer. Any idea why?

Let the total income = x

Taxes = 0.12 (40000) + 0.2(x-40000) = 8000

Solve for x.



40000/100 = 400 --> 400*12 = 4800


8000 - 4800 = 3200 ---> (20/100)x = 3200 ---> x = 16000.. 16000 is the excess salary over 40000.. So 40000 + 160000 = 56000
Re: Country X taxes each of its citizens an amount equal to 12   [#permalink] 28 Dec 2013, 10:28
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