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State X has a sales tax rate of k percent on all purchases

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by BTGmoderatorDC » Mon Dec 16, 2019 8:46 pm
State X has a sales tax rate of k percent on all purchases and State Y has a sales tax rate of n percent on all purchases. What is the value of k − n ?

(1) The sales tax on a $15 purchase is 30 cents more in State X than in State Y.
(2) The sales tax rate in State X is 1.4 times the sales tax rate in State Y.



OA A

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Source: — Data Sufficiency |
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by Gene@KaplanGMAT » Tue Dec 17, 2019 5:23 pm
Statement (1)
With a $15 purchase, your tax in State X would be (k/100) * 15 ----> 15k/100 ----> 3k/20
With a $15 purchase, your tax in State Y would be (n/100) * 15 -----> 15n/100 ----> 3n/20
The difference between those totals is 30 cents.
So (3k/20) - (3n/20) = 30 Multiply both sides by 20....
3k - 3n = 600 Divide both sides by 3....
k - n = 200 BINGO! WE have what the question is looking for with the value of "k-n". SUFFICIENT

[One of the interesting things here is that you can often find the value of an EXPRESSION even if you don't know the values of the individual variables housed within it. We don't know "k" or "n" individually, but we have enough for "k-n".

Statement (2)
k = 1.4n But there's no way to manipulate this to get the value of "k-n". INSUFFICIENT

Answer (A).
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