Anthony, who lives in Zoolandia, pays 20% income tax on his earnings

Question

Anthony, who lives in Zoolandia, pays 20% income tax on his earnings up to Z$30'000, 30% from Z$30'000 to Z$50'000 and 40% above Z$50'000. How much did he earn last year if he paid a 36% effective tax rate?

A) Z$210'000

B) Z$200'000

C) Z$190'000

D) Z$180'000

E) Z$160'000

-----
Find more questions on https://www.gmatwiz.co - Tutor in your pocket
Daily questions in your inbox - Track your progress - Set up study reminders

F: https://www.facebook.com/GMATwiz-443620 ... page_panel
T: https://www.twitter.com/GMATwiz
E: [email protected]

amanvermagmat · Accepted Answer

On his first $30,000 he pays income tax = 20% of 30000 = $6000
On his next $20,000 (30000 to 50000) he pays income tax = 30% of 20000 = $6000
So on first $50,000 he pays total $12000 income tax

Let his total income be $ x. 
Then on remaining income of $(x-50000) - he pays income tax = 40% of (x-50000) = 0.4x - 20000

Total income tax paid = 12000 + 0.4x - 20000 = 0.4x - 8000
This is given as 36% of net income

So 0.4x - 8000 = 36% of x = 0.36x
Solving, we get 0.04x = 8000 or x = $ 200,000

Hence  B answer

Abhishek009 · Answer

Used by checking the options -

I. 20% income tax on his earnings up to Z$30'000 = 6000
II. 30% from Z$30'000 to Z$50'000 ( ie 30% of 20000) = 6000
III. 40% above Z$1,50'000 = 60000

Total Tax = 72,000
Total Income = 20,0000

Thus, effective Tax Rate is 36%

Hence, answer must be (B) 36  %

anshul1989 · Answer

Hi experts,
Can you please help me with this question. Is there is any way to solve this question quickly. I used the plugin method. though, i got the right answer but it took me approx 3 min.

danbrown9445 · Answer

Total tax = tax 1 + tax 2 + tax 3
Total tax rate is 36% (Given as "effective tax rate")
Let total income be x

So:-

0.36(x) = 0.2(30k) + 0.3(50k-30k) + 0.4(x-50k)
0.36x = 6k + 6k + 0.4x - 20k
0.36x = 0.40x - 8k
-0.04x = -8000
4x = 800000
x = 200000

anirchat · Answer

Is it a fair way to select the middle value of 190,000 and then use option elimination or do you think the other options are too closely located and we may end up making a mistake ?

Actually that's what happened, lol !

Sometime algebra is better .. At least gives you a right answer

0.36*x = 12,000 + 0.4*(x-50,000)
x= 200,000.

0.36*x = 12,000 + 0.4*(x-50,000) x= 200,000.

KarishmaB · Answer

Average of 20%, 30% and 40% is 36%. We know that 20% was paid on 30k and 30% on 20k so their average will be 24% (using the scale method). Average of 24% and 40% is 36% so distance of 36 from 24 : distance of 36 from 40 is 3:1. This means that weights given to 24% and 40% are in the ratio 1:3. Since he paid overall 24% on 50k, he paid 40% on 150k. Overall amount is 50k + 150k = 200k Answer (B) I have discussed weighted averages with 3 quantities here: https://youtu.be/Ye8IEJ_lz6E

luisdicampo · Answer

Deconstructing the Question

Income tax brackets:

20% up to  30,000  
30% from  30,000 to 50,000  
40% above  50,000

The effective tax rate is  36% .

Step-by-step

Tax on first bracket:

0.20 	imes 30000 = 6000

Tax on second bracket:

0.30 	imes 20000 = 6000

Total tax up to 50,000:

12000

Let total income be  X .

Tax above 50,000:

0.40(X-50000)

Total tax:

12000 + 0.40(X-50000)

Effective rate:

\frac{12000 + 0.40(X-50000)}{X} = 0.36

Solve:

12000 + 0.40X - 20000 = 0.36X

0.40X - 8000 = 0.36X

0.04X = 8000

X = 200000

Answer: 200000

Anthony, who lives in Zoolandia, pays 20% income tax on his earnings

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Anthony, who lives in Zoolandia, pays 20% income tax on his earnings

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards