When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
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Mohammad Aasim
I have read the response to the query of Rachel L Little. But still i don't get to digest the logic behind the provided explanation. I know that it is straight forward but still appears to be a little twisted.
I fail to grasp the point that how the 7% tax turns out to be the part of the amount over and above the $10000?
Hi Phil!
Good question! Actually, long division IS what you would do there. But it's pretty quick "long" division, since you're only dividing by a single-digit number. You're right that the GMAT wouldn't require lengthy, time-consuming calculations, but this kind of long division could be necessary. I hope that helps :)
I'm a little confused as to the reasoning behind finding the answer. Math is not my strong point, so please bear with me - but why did you choose/know that 100% would be the excess above the $1000 tax free portion? In other words, how did you know that 100% would give you the amount that was taxed 7% ?
Happy to help! The tax only applies to the part of the cost of the item above $1000. In other words, the first $1000 of the cost is not taxed, while the amount after $1000 is taxed. This means that the 7% tax (= $87.50) is 7% of the part of the price that was taxed or, to say it another way 87.50 is 7% of the taxed part of the item:
87.5 / taxed part = 0.07
So, when we solve for the unknown in this equation, we end up with the total taxed part of the item, the cost in excess of $1000. At that point, to determine the total price of the item, we must add that first $1000 of the price to the taxed portion of $1250.
Does that make sense, Rachel? I hope this clears up your doubts! If not, please let us know :)
3 Explanations