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At a garage sale, all of the prices of the items sold were d

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At a garage sale, all of the prices of the items sold were d [#permalink] New post 05 Feb 2014, 01:31
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Difficulty:

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Question Stats:

68% (01:54) correct 32% (01:28) wrong based on 233 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

Problem Solving
Question: 80
Category: Arithmetic Operations with integers
Page: 72
Difficulty: 600


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Expert Post
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Kudos [?]: 49813 [0], given: 7497

Re: At a garage sale, all of the prices of the items sold were d [#permalink] New post 05 Feb 2014, 01:31
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SOLUTION

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

Answer: B.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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: At a garage sale, all of the prices of the items sold were d [#permalink] New post 05 Feb 2014, 07:27
Ans B

Total=14 (items with higher price than the radio)+19(items with lower price than radio)+1(radio itself)=34
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Re: At a garage sale, all of the prices of the items sold were d [#permalink] New post 07 Feb 2014, 12:36
2
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I got (B) too. However, is it correct to use this approach?

20+15-1 (to avoid double-counting) = 34.
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Kudos [?]: 114 [0], given: 29

Re: At a garage sale, all of the prices of the items sold were d [#permalink] New post 07 Feb 2014, 20:42
I am not clear how to solve this problem.... Can any one detail out... thanks
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Kudos [?]: 49813 [0], given: 7497

Re: At a garage sale, all of the prices of the items sold were d [#permalink] New post 08 Feb 2014, 03:14
Expert's post
SOLUTION

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

(A) 33
(B) 34
(C) 35
(D) 36
(E) 37

As the price of an item was BOTH 15th highest price and the 20th lowest price then # of items is: 15 + 20 - 1 = 34.

Why do we have -1 there? In 15 + 20 the item is counted TWICE: in 15 (as it's 15th highest priced item) as well as in 20 (as it's 20th lowest priced item), hence we should subtract 1 to get rid of double counting.

Answer: B.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
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Kudos [?]: 23 [0], given: 147

Re: At a garage sale, all of the prices of the items sold were d [#permalink] New post 18 May 2015, 02:33
There are 14 objects that have a higher price as the radio, as well as 19 objects that have a lower price than the radio.

14 + 19 + 1 (the radio itself) = 34 different objects
Re: At a garage sale, all of the prices of the items sold were d   [#permalink] 18 May 2015, 02:33
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