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

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

Therefore income before taxes = 10000 + 3000 = 13000

Option (B)

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)

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

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:

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

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.