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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]

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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 Practice Questions Question: 11 Page: 153 Difficulty: 600 _________________ ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 50058 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 06 Aug 2012, 02:40 2 5 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.
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Re: When Leo imported a certain item, he paid a 7 percent import  [#permalink]

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06 Aug 2012, 11:43
2
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: 157 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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 $$0.07(x-1,000)=87.5$$ --> $$x-1,000=1,250$$ --> $$x=2,250$$.

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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19 Dec 2013, 01:01
1
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: 15 Aug 2013 Posts: 56 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 19 Dec 2013, 03:27 3 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]

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09 Sep 2014, 22:38
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]

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09 Sep 2014, 23:03
2
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]

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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]

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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

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

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21 Sep 2015, 04:02
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]

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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]

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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. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 20 Oct 2015 Posts: 37 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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]

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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]

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08 Jul 2017, 09:01
1
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. Study Buddy Forum Moderator Joined: 04 Sep 2016 Posts: 1209 Location: India WE: Engineering (Other) Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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) _________________ It's the journey that brings us happiness not the destination. Math Expert Joined: 02 Sep 2009 Posts: 50058 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 30 Jan 2018, 20:58 1 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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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]

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21 Jul 2018, 21:27
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.
Re: When Leo imported a certain item, he paid a 7 percent import &nbs [#permalink] 21 Jul 2018, 21:27

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

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