Source: Official Guide for the GMAT 13th Ed. Problem Solving; #11 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #11

5

When Leo imported a certain item, he

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?

3 Explanations

3

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?

Aug 10, 2017 • Comment

Jonathan , Magoosh Tutor

Hi Mohammad,

The question tells us that 7% is the tax on the part over 1,000:

"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."

So, he pays 7% of the value that is in excess of 1,000.

7% of that excess is 87.50. Let "x" be the excess.
.07x = 87.50
So x = 1,250.

1,250 is the value over 1,000. So the total value is 1,000 + 1,250.

Sep 4, 2017 • Reply

2

Shakib Huq

Hi all,

The algebraic solution is quite simple as well which is as follows:

Let Total Value be X
7/100(X-1000)=87.5
7(X-1000)=8750
X-1000=1250
X=2250 which is Answer Choice (C)

Cheers!

Feb 20, 2016 • Comment

3

Gravatar Mike McGarry, Magoosh Tutor

Dec 26, 2013 • Comment

Phil McDonald

How did you quickly figure out 12.50 was 1% of the unknown? I resorted to long division which I know I need to avoid..

Nov 20, 2014 • Reply

Jonathan , Magoosh Tutor

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 :)

Nov 26, 2014 • Reply

Rachel L Little

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% ?

Mar 31, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Rachel :)

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 :)

Apr 15, 2016 • Reply

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