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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, 01:39
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A
B
C
D
E

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Question Stats:

82% (02:06) correct 18% (01:01) wrong based on 316 sessions
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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Question: 11
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Difficulty: 600
[Reveal] Spoiler: OA

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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 06 Aug 2012, 01:40
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 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] New post 06 Aug 2012, 10:43
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 10 Aug 2012, 02:27
Expert's post
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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 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.
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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 19 Dec 2013, 00:01
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.

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}.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: When Leo imported a certain item, he paid a 7 percent import [#permalink] New post 19 Dec 2013, 02:27
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)
Re: When Leo imported a certain item, he paid a 7 percent import   [#permalink] 19 Dec 2013, 02:27
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