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

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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. Manager Joined: 12 Jan 2013 Posts: 107 Own Kudos [?]: 206 [0] Given Kudos: 47 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 $$0.07(x-1,000)=87.5$$ --> $$x-1,000=1,250$$ --> $$x=2,250$$.

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: $$0.07(x-1,000)=87.5$$; $$7(x-1,000)=8750$$; $$x-1,000=\frac{8750}{7}$$. Manager Joined: 07 Apr 2014 Posts: 66 Own Kudos [?]: 112 [1] Given Kudos: 81 When Leo imported a certain item, he paid a 7 percent import [#permalink] 1 Bookmarks 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..­ Manager Joined: 20 Jan 2013 Status:I am not a product of my circumstances. I am a product of my decisions Posts: 95 Own Kudos [?]: 276 [5] Given Kudos: 71 Location: India Concentration: Operations, General Management GPA: 3.92 WE:Operations (Energy and Utilities) When Leo imported a certain item, he paid a 7 percent import [#permalink] 4 Kudos 1 Bookmarks 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)­ Target Test Prep Representative Joined: 14 Oct 2015 Status:Founder & CEO Affiliations: Target Test Prep Posts: 18873 Own Kudos [?]: 22262 [4] Given Kudos: 285 Location: United States (CA) Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] 2 Kudos 2 Bookmarks Expert Reply 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

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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. IIM School Moderator Joined: 04 Sep 2016 Posts: 1260 Own Kudos [?]: 1249 [0] Given Kudos: 1207 Location: India WE:Engineering (Other) 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) Math Expert Joined: 02 Sep 2009 Posts: 93334 Own Kudos [?]: 624712 [1] Given Kudos: 81899 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] 1 Kudos Expert Reply 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. Intern Joined: 01 May 2017 Posts: 28 Own Kudos [?]: 46 [2] Given Kudos: 40 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] 2 Kudos Solving questions with multiple methods is a key to learn and master a concept: Intern Joined: 13 Jan 2016 Posts: 5 Own Kudos [?]: 2 [1] Given Kudos: 152 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] 1 Kudos 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. Tutor Joined: 12 Oct 2010 Status:GMATH founder Posts: 892 Own Kudos [?]: 1382 [0] Given Kudos: 56 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] Expert Reply 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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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink]
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