After paying a 10 percent tax on all income over $3,000, a

Question

After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?

A. $13,300
B. $13,000
C. $12,900
D. $10,000
E. $9,000

ravitejar · Accepted Answer

simple way to solve the problem

as for first 3000$ there is no tax, so the amount given after deducting 10% tax is 12000$(9000+3000) that means it also incl 3000$ so after deducting that 3000 from 1200 leaves 9000 which is 90% of the taxable income so the equation looks like this

for 90% 9000
for 100 % 10000

therefore the total taxable income is 10000$ and income before deducting tax is 10000$+3000$=13000$

Answer option is b

Hope it short and clear

if satisfied give me +1 kudos.

Bunuel · Answer

Say x is the income before taxes (as you've denoted), then equation should be:

3,000+(x-3,000)*0.9=12,000 ;

x=13,000 .

Answer: B.

Hope it's clear.

GyanOne · Answer

Let x be the income over 3000
Then (x-x/10) + 3000 = 12000
=> x = 10000

Therefore income before taxes = 10000 + 3000 = 13000

Option (B)

KarishmaB · Answer

Using options works wonderfully well too because of the good round numbers. You know that net income was 12000 so gross must be more. Hence (D) and (E) are definitely out.

Also, first 3000 is non-taxable so say the gross income is 13,000 (easiest of the options). Taxable income becomes 10000, 10% of which is 1000 (the amount of tax).
This gives us net income of 12000, as expected. So answer is 13,000.

Answer (B)

JeffTargetTestPrep · Answer

We can let the initial income = n and thus:

12,000 = n - 0.1(n - 3,000)

12,000 = n - 0.1n + 300

11,700 = 0.9n

117,000 = 9n

n = 117,000/9 = 13,000

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

We're told that AFTER paying a 10% tax on all income OVER $3,000, a person had a net income of $12,000. We're asked for the income BEFORE taxes. This question can be solved by TESTing THE ANSWERS.

Since the income after taxes was $12,000, the income BEFORE taxes MUST be greater than $12,000. Among the first 3 answer choices, let's TEST Answer B first...

Answer B: $13,000

IF.... total income was $13,000 
10% tax was paid on ($13,000-$3,000) = (.1)($10,000) = $1,000 
Thus, income AFTER tax was $13,000 - $1,000 = $12,000 
This is an exact match for what we were told, so this MUST be the answer!

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

STRATEGY : Upon reading any GMAT Problem Solving question, we should always ask,   Can I use the answer choices to my advantage?   
In this case, we can easily test the answer choices. In fact, I can already see that I can immediately eliminate 2 answer choices, which means I'll be able to identify the correct answer my testing  only 1  answer choice. 
From here, I'd typically give myself up to 20 seconds to identify a faster approach, but I can already see that testing the answer choices will be super fast (and less prone to silly mistakes)

Since the income before taxes must be GREATER THAN the income after the taxes are paid, we can automatically eliminate answer choices D and E, since they’re both less than the after-tax income of $12,000.

I’ll now test answer choice B for two reasons: 
i) The calculations are much easier with $13,000 than they are with $13,300 and $12,900.
ii) Since B is the middle value, I know that if testing the pretax income of $13,000 results in an after-tax income that’s  less than  $12,000, then I can eliminate choices A and B, since we’d need the pre-tax income to be  greater than  $13,000. Conversely, if testing $13,000 results in an after-tax income that’s  greater than  $12,000, then I can eliminate choices B and C, since we’d need the pre-tax income to be  less than  $13,000.

Let’s test answer choice  C - $13,000 
The taxable income (the amount greater than $3000) =  $13,000  - $3000 = $10,000
A 10% tax on $10,000 = $1,000, which means the after-tax income = $13,000 - $1000 = $12,000....Perfect!

Answer: B

demawtf · Answer

After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?

X= income before taxes

x-(x-3000)10%=12000
x-10%x+300=12000
x(1-10%)=11700
x=11700/(1-10%)=11700/0,9=11700*100/90-->13000

pierjoejoe · Answer

a quick dumb sidenote i want to make sure.

i aced this problem, but something is always bugging me out on the way they are logically solved.

the "tax" function is TAX = 10% * (all the income above 3000) = 10% * (INCOME-3000)

and it is fine, because if the income is 4000$ then you'll pay 10% on (4000-3000) = 1000.

but shouldn't this function be a "step" function? 
for example:

TAX = 0 for INCOME<3000
TAX = 10%*(INCOME-3000) for INCOME>3000

tusharmurkute22 · Answer

A simple way to solve this

Tax is on income above 3000, thus (12000 - 3000) = 9000 is taxed

let x be before tax income

9000 = 0.9x%

x = 10000

Thus net icome = 10,000 + 3,000 = 13,0000

NextstopISB · Answer

Nice explanation well done

Jaival · Answer

Yes this is what I was able to translate from the problem too.
Might be a bit lengthy but is accurate and leaves no doubt at the end

Shivam2027 · Answer

the language had got me but yep

After paying a 10 percent tax on all income over $3,000, a

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