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importing an item

by Lattefah84 » Sun Dec 27, 2009 11:09 am
When Leo imported a certan item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was 87.50, what was the total value of the item?


(A) 1600
(B) 1850
(C) 2250
(D) 2400
(E) 2750

Solution: 0,07*(x-1000) =87.50,
x - 1000= 1250
x= 2250

this equality doesn't seam right to me... Can someone explain how do I get this equality, please?
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by linkinpark » Mon Dec 28, 2009 7:33 am
in simple words, he will be levied a duty of 7% on goods if the total value of goods exceeds 1000$ and that duty will be applied on [actual amount - 1000] i.e. first 1000$ worth of goods are duty free.

from the given question we're told that he paid duty of 87.50

lets say x is total amouht of the goods, so on [x-1000] he paid 87.50 at 7%

generating equation for it

7/100 * [x-1000] = 87.50 [here 7% = 7/100]
x-1000 = 87.50 * 100/7 [ cross multiply both sides by 7/100]

solve this to get x-1000 = 1250 and total 2250.

hope its clear now
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by thephoenix » Mon Dec 28, 2009 9:10 am
in other words suppose x is excess amnt(that is abve $1000) on which he pays 7% tax
---->7/100(x)=87.5--->x=8750/7=1250

hence the excess amnt is 1250 and therfore the tot amnt is 1250+1000=2250
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by Lattefah84 » Mon Dec 28, 2009 12:01 pm
thephoenix wrote:in other words suppose x is excess amnt(that is abve $1000) on which he pays 7% tax
---->7/100(x)=87.5--->x=8750/7=1250

hence the excess amnt is 1250 and therfore the tot amnt is 1250+1000=2250
so he does pay the tay on the whole amount, not just on part of it? The confusing part for me is that he pays the whole amount and the formula is 0.07*(x-1000) so it looks like he pays a tax only for the part which is above $1000
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by vittalgmat » Mon Dec 28, 2009 2:27 pm
Simple!!.
7% of x = 87.50
ie (7/100)*x = 87.50.
Solve this to get 1250.
Now the import tax is not levied for the first $1000, we need to add 1000 to the above result.
So answer is 2250.
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by Stuart@KaplanGMAT » Mon Dec 28, 2009 5:30 pm
Lattefah84 wrote:When Leo imported a certan item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was 87.50, what was the total value of the item?


(A) 1600
(B) 1850
(C) 2250
(D) 2400
(E) 2750
Also a perfect question for backsolving.

Let's start with some common sense; if he owed duty on $1000, he'd owe $700. Therefore, the owes duty on more than $1000, so the price must be more than $2000; eliminate A and B.

With 3 choices left, let's start with the middle answer, D.

If the total value is $2400, then he owes duty on $2400 - $1000 = $1400.

7% of $1400 = 7/100 * 1400 = 7 * 14 = 98.

We want the duty to be 87.50, not 98; therefore, D is too big an amount. Accordingly, we eliminate D and E.

A, B, D, E all gone... choose C!
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