GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Sep 2018, 17:45

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 05 Feb 2014, 02:31
1
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (00:54) correct 24% (01:15) wrong based on 604 sessions

HideShow timer Statistics

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


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 05 Feb 2014, 02:31
4
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 245
Location: India
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 05 Feb 2014, 08:27
1
Ans B

Total=14 (items with higher price than the radio)+19(items with lower price than radio)+1(radio itself)=34
Manager
Manager
User avatar
Joined: 11 Jan 2014
Posts: 92
Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 07 Feb 2014, 13:36
2
I got (B) too. However, is it correct to use this approach?

20+15-1 (to avoid double-counting) = 34.
Manager
Manager
User avatar
B
Joined: 14 Jan 2013
Posts: 148
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 07 Feb 2014, 21:42
I am not clear how to solve this problem.... Can any one detail out... thanks
_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 08 Feb 2014, 04:14
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 175
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 18 May 2015, 03:33
1
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
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 962
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 03 Jul 2017, 12:07
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?

Given: Price of Radio is 15th Heighest and 20th Lowest

Which means form top if you count price will be 15th and if you count from bottom the count will be 20th.

So, from top it is 15th and there are 19 more items below the list (As this is 20th from bottom)

Hence, 15 + 19 = 34

So, in all there were 34 items sold at the garage.

Hence, Answer is B
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3509
Location: United States (CA)
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 29 Mar 2018, 17:38
1
Bunuel wrote:

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


Since the radio is the 15th highest and 20th lowest we see that 14 items have price higher than the radio and 19 items have price lower than the radio, so the total number of items at the sale is 14 + 19 + 1 = 34. (Note that the +1 item is the radio itself.)

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2856
Location: Canada
Re: At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 31 Mar 2018, 06:50
1
Top Contributor
Bunuel wrote:
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



The price of the radio was the 15th highest price
So, there were 14 items that were more expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
........... radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

The price of the radio was the 20th lowest price
So, there were 19 items than were less expensive than the radio.
In other words, if we listed all of the prices in ascending order, we'd get something like:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio,......

So, when we combine both pieces of information, we have 19 items that were less expensive than the radio, and we have 14 items that were more expensive than the radio:
X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X

So, the total number of items sold = 19 + 14 + 1 (the radio itself)
= 34
= B

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

GMAT Tutor
User avatar
B
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 168
At a garage sale, all of the prices of the items sold were d  [#permalink]

Show Tags

New post 04 Sep 2018, 09:31
Bunuel wrote:
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

A simple drawing does the trick!

? = 20+14 = 34.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Attachments

04Set18_11t.gif
04Set18_11t.gif [ 2.78 KiB | Viewed 169 times ]


_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

At a garage sale, all of the prices of the items sold were d &nbs [#permalink] 04 Sep 2018, 09:31
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.