PS Help...

[ramonsa]

8. 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

Thanks

[vineetbatra]

non taxable income is 3000

so 12000 - 3000 = 9000 is the income after taxation.

tax rate is 10% so 9000 is 90%

total taxable income is 9000*100/90 I.e 10000
total income is 10000+3000=13000

[Brent@GMATPrepNow]

8. 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

Thanks

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