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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, 02:39
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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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Difficulty: 600
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C
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Bunuel
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   06 Aug 2012, 02:40
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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   19 Dec 2013, 03:27
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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   06 Aug 2012, 11:43
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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   18 Dec 2013, 10:21
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, 01:01
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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   09 Sep 2014, 22:38
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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, 23:03
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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, 09:02
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, 03:18
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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When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   21 Sep 2015, 04:02
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pacifist85 wrote:
I really liked the solution by zerosleep.
Really easy. Nice and simple! Well done!



Yeah even i liked that approach too..
initially i did this question incorrectly

But what i figured out is this:

1000 + x = the entire sum that we need get.

1000= tax free
x= taxable amount

x*0.07 = 87.50
x= 87.25/0.07 ---- 8750/7-----1250

so the original price including excess is = 1000 + 1250 = 2250 ( Answer Choice C)
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When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   11 May 2016, 07:18
Usually I do it the following way. If we are told that 7% of the excess amount is 87.5 then we can find the value of one 1%, i.e. 87.5/7=12.5. From this we can derive the full value of the excess amount: 12.5*100=1250=excess amount. 1000+1250
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   11 May 2016, 07:27
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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



Although this problem seems challenging it is actually a simple word translation.

We know that when Leo imports a certain item he pays a 7% import tax on the portion of the total value IN EXCESS OF $1,000. “In excess of” is the key phrase here, and it means that Leo does not pay any tax on his items until he hits $1,000. The best way to complete this problem is to set up an equation.

First, let’s say that T = total value of the item, and, therefore, (T – 1000) is the portion that is taxable.

Next, we can create an equation to determine T:

87.5 = 0.07(T – 1,000)

87.5 = 0.07T – 70

157.5 = 0.07T

157.5/0.07 = T

15,750/7 = T

T = 2,250

Answer C.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   05 Jul 2016, 01:45
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



87.5$ was 7% of total money after exceeds 1000$, so 100% of this money will be 1250$
so 1250$ +1000$=2250$
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When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   05 Jul 2016, 02:36
87.5=0.07amount excess than 1000

amount excess = 1250
therefore total amt = 2250

C is correct

Total value=2250


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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   08 Jul 2017, 09:01
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Leo paid 7% for amt that is in excess of $1000
Let 'x' = excess amount. Then 7% of x = 87.50
=> x = 1250.
So, Total value = 1000 + 1250 = 2250. Hence (C)
Do not forget to add 1000, as that is the trap in such questions usually.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   30 Jan 2018, 20:38
Bunuel niks18 amanvermagmat chetan2u

Quote:
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


Can I approximate values in below manner?
I know 12 * 7 = 84

Given: Whatever is access of $1000 will be charged 7%, lets assume access of $1200 over $1000 so approx $84 will be charged. ($84 is closest to $87.50)
Only value that is closest to total of $2200 is (C)
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   30 Jan 2018, 20:58
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adkikani wrote:
Bunuel niks18 amanvermagmat chetan2u

Quote:
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


Can I approximate values in below manner?
I know 12 * 7 = 84

Given: Whatever is access of $1000 will be charged 7%, lets assume access of $1200 over $1000 so approx $84 will be charged. ($84 is closest to $87.50)
Only value that is closest to total of $2200 is (C)


Yes, you could do this way.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   06 Apr 2018, 19:30
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Solving questions with multiple methods is a key to learn and master a concept:

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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post   21 Jul 2018, 21:27
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tax paid =87.50
break up = 70+17.50
1000(no tax) + 1000(70) + 250(17.50)->[ (1/2(1000) = 500 i.e (70/2 = 35)), (1/2(500) = 250 i.e(35/2 =17.50))] = 2,250. Ans C.
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