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When Leo imported a certain item, he paid a 7 percent import

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When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 06 Aug 2012, 01:39
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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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

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Question: 11
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Difficulty: 600
[Reveal] Spoiler: OA

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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 06 Aug 2012, 01:40
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SOLUTION

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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve:
If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B.
If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 06 Aug 2012, 09:04
(x-1000)*0.07=87.5
x=2250
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 06 Aug 2012, 10:43
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Used back substitution.

using A we get $42 of interest. So we want something close to double the price to get the right answer. C was the next candidate.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 10 Aug 2012, 02:27
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SOLUTION

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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve:
If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B.
If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 18 Dec 2013, 09:21
Bunuel wrote:
SOLUTION

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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve:
If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B.
If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.


Do you have tips or a guide on how to most efficiently divide with non-integers in the denominator? I have seen two PS questions where they want us to divide some integer value with a non-integer (0.8 and now 0.07), and I do not really know how to properly approach the division.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 19 Dec 2013, 00:01
Expert's post
aeglorre wrote:
Bunuel wrote:
SOLUTION

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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Let the value of the item be \($x\), then \(0.07(x-1,000)=87.5\) --> \(x-1,000=1,250\) --> \(x=2,250\).

Answer: C.

Else, you could backsolve:
If the value of the item is $2,000 the tax is \((2,000-1,000)*0.07=70\), so the value must be more than $2,000. Eliminate A and B.
If the value of the item is $2,400 the tax is \((2,400-1,000)*0.07=98\), so the value must be less than $2,400. Eliminate D and E.

Only answer choice C is left.


Do you have tips or a guide on how to most efficiently divide with non-integers in the denominator? I have seen two PS questions where they want us to divide some integer value with a non-integer (0.8 and now 0.07), and I do not really know how to properly approach the division.


Work with integers:
\(0.07(x-1,000)=87.5\);

\(7(x-1,000)=8750\);

\(x-1,000=\frac{8750}{7}\).
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 19 Dec 2013, 02:27
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Since we know Leo pays 7% of the amount that is in excess of $1000
We can assume 'x' to be the excess amount. Then 7 percent of x = 87.50 => x = 1250.
Hence total value = 1000 + 1250 = 2250. Hence (C)
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 09 Sep 2014, 21:38
Bunuel wrote:
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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Practice Questions
Question: 11
Page: 153
Difficulty: 600


Hi bunuel,

please let me know whether my reasoning is correct..


7 percent import tax on the portion of the total value of the item. Tax paid=$87.50

7/100 = 87.50/X ==> 1250..
1250+1000 = 2250.

though i got an answer correct . how we could consider 87.50 for only 1250 rather than 2250? .. I got tried on blind guess but i got the answer..
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 09 Sep 2014, 22:03
luckyme17187 wrote:
Bunuel wrote:
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?

(A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

Practice Questions
Question: 11
Page: 153
Difficulty: 600


Hi bunuel,

please let me know whether my reasoning is correct..


7 percent import tax on the portion of the total value of the item. Tax paid=$87.50

7/100 = 87.50/X ==> 1250..
1250+1000 = 2250.

though i got an answer correct . how we could consider 87.50 for only 1250 rather than 2250? .. I got tried on blind guess but i got the answer..



Consider it like this:
7% of x = 87.50
(7/100) X = 87.50
7X = 8750
X= 1250 $

Now tax is payed on an amount in excess of 1000$. So the total value of the item = 1250 + 1000 = 2250 Ans (B)
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 14 Nov 2014, 08:02
Ballparking, instead of $87,5, $84 is easily divisible by 7.
If 7% of the sum is=$84 -->
That means 1% is=$84/7 -> $12, which means 100% is $1200

$1200+$1000= $2200 --> little more than that so best choice $2250, other ones are way to far apart.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 20 Nov 2014, 02:18
87.5 is the tax paid @ 7%

So the excess amount \(= 87.5 * \frac{7}{100} = 1250\)

Amount = 1000+1250 = 2250

Answer = C
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 20 Nov 2014, 02:32
PareshGmat wrote:
87.5 is the tax paid @ 7%

So the excess amount \(= 87.5 * \frac{7}{100} = 1250\)

Amount = 1000+1250 = 2250

Answer = C


What's the easiest way to calculate 87.5*7/100 without a calculator?
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 08 Jan 2015, 12:22
I really liked the solution by zerosleep.
Really easy. Nice and simple! Well done!
Re: When Leo imported a certain item, he paid a 7 percent import   [#permalink] 08 Jan 2015, 12:22
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