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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]
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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]
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]
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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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When Leo imported a certain item, he paid a 7 percent import [#permalink]
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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
 

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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When Leo imported a certain item, he paid a 7 percent import [#permalink]
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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

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]
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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]
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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]
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]
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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]
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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]
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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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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]
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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

\({\text{?}}\,\,{\text{ = }}\,\,{\text{total}}\,\,{\text{value}}\,\, = \,\,\$ \,\,\left( {1000 + {\text{extra}}} \right)\)

\({\text{87}}{\text{.5}}\,\,{\text{ = }}\,\,\frac{7}{{100}}\left( {{\text{extra}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{extra}}\,\,{\text{ = }}\,\,\frac{{{\text{100}}}}{7} \cdot \frac{1}\\
{{10}}\left( {700 + 140 + 35} \right)\,\,\, = \,\,\,10 \cdot 125\)

\(? = \,1000 + 1250\,\,\,\left[ \$ \right]\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]
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

since 87.5 is 7% of some number suppose x (x=100%),
(87.5/7) * 100= 12.5 * 100 = 1250
calculated the division in this way 875/70 =12.5
total value = 1000+1250 = 2250­
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