When Leo imported a certain item, he paid a 7 percent import : GMAT Problem Solving (PS)
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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, 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 Practice Questions Question: 11 Page: 153 Difficulty: 600 [Reveal] Spoiler: OA _________________ Math Expert Joined: 02 Sep 2009 Posts: 36540 Followers: 7071 Kudos [?]: 93005 [0], given: 10541 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 06 Aug 2012, 01:40 Expert's post 5 This post was BOOKMARKED 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, 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]

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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. Math Expert Joined: 02 Sep 2009 Posts: 36540 Followers: 7071 Kudos [?]: 93005 [0], given: 10541 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 10 Aug 2012, 02:27 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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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. Math Expert Joined: 02 Sep 2009 Posts: 36540 Followers: 7071 Kudos [?]: 93005 [1] , given: 10541 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 19 Dec 2013, 00:01 1 This post received KUDOS 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 $$0.07(x-1,000)=87.5$$ --> $$x-1,000=1,250$$ --> $$x=2,250$$.

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]

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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) Manager Joined: 07 Apr 2014 Posts: 147 Followers: 1 Kudos [?]: 23 [0], given: 81 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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.. Manager Status: I am not a product of my circumstances. I am a product of my decisions Joined: 20 Jan 2013 Posts: 132 Location: India Concentration: Operations, General Management GPA: 3.92 WE: Operations (Energy and Utilities) Followers: 4 Kudos [?]: 92 [0], given: 68 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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=$87.50 7/100 = 87.50/X ==> 1250.. 1250+1000 = 2250. though i got an answer correct . how we could consider 87.50 for only 1250 rather than 2250? .. I got tried on blind guess but i got the answer.. Consider it like this: 7% of x = 87.50 (7/100) X = 87.50 7X = 8750 X= 1250$

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. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1928 [0], given: 193 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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 _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 06 Nov 2014 Posts: 13 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 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? Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 443 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 2 Kudos [?]: 109 [0], given: 169 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 08 Jan 2015, 12:22 I really liked the solution by zerosleep. Really easy. Nice and simple! Well done! Manager Joined: 10 Dec 2012 Posts: 52 Followers: 0 Kudos [?]: 8 [0], given: 39 When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 21 Sep 2015, 03:02 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) Current Student Joined: 12 Aug 2015 Posts: 307 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) Followers: 5 Kudos [?]: 282 [0], given: 1474 When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 11 May 2016, 06:18 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 _________________ KUDO me plenty Director Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 506 Location: United States (CA) Followers: 19 Kudos [?]: 181 [1] , given: 2 Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 11 May 2016, 06:27 1 This post received KUDOS 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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05 Jul 2016, 00:45
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$Manager Joined: 20 Jan 2016 Posts: 97 GMAT 1: 600 Q47 V26 Followers: 2 Kudos [?]: 3 [0], given: 5 When Leo imported a certain item, he paid a 7 percent import [#permalink] ### Show Tags 05 Jul 2016, 01:36 87.5=0.07amount excess than 1000 amount excess = 1250 therefore total amt = 2250 C is correct Total value=2250 Sent from my iPhone using GMAT Club Forum mobile app Intern Joined: 08 Sep 2015 Posts: 36 Followers: 0 Kudos [?]: 8 [0], given: 16 OG 16 Question #9 [#permalink] ### Show Tags 23 Sep 2016, 23:25 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
OG 16 Question #9   [#permalink] 23 Sep 2016, 23:25

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