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

It is currently 24 Sep 2018, 02:44

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

Of the 20 people who each purchased 2 tickets to a concert

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

Hide Tags

Intern
Intern
avatar
B
Joined: 08 Dec 2016
Posts: 8
Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 08:36
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:06) correct 38% (01:07) wrong based on 124 sessions

HideShow timer Statistics

Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1385
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 08:50
1
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?



20 people who each purchased 2 tickets, so there are total 40 tickets.

Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket.

(1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient.

(2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient.

Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Intern
Intern
avatar
B
Joined: 08 Dec 2016
Posts: 8
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 09:12
nguyendinhtuong wrote:
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?



20 people who each purchased 2 tickets, so there are total 40 tickets.

Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket.

(1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient.

(2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient.

Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient.



Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?"

So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used.
But obviously I'm misinterpreting something cuz C is the right answer
Intern
Intern
avatar
B
Joined: 08 Dec 2016
Posts: 8
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 09:14
Bunuel, whats your take on this?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49381
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 09:31
3
rahuldev31 wrote:
Bunuel, whats your take on this?


Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

Say:
x people used both tickets;
y people used one ticket;
z people used 0 tickets.

x + y + z = 20.

What percent of the tickets that were purchased by the 20 people were used by those people: (2x + y)/40 = ?

(1) Of the 20 people, 10 used only 1 ticket --> y = 10. Not sufficient.

(2) Of the 20 people, 4 used neither ticket --> z = 4. Not sufficient.

(1)+(2) y = 10 and z = 4 --> x = 6 --> (2x + y)/40 = 22/40 = 0.55. Sufficient.

Answer: C.
_________________

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
G
Joined: 04 Dec 2016
Posts: 56
Location: India
GPA: 3.8
WE: Operations (Other)
GMAT ToolKit User Reviews Badge
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 11:07
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?



S1: 10 used 1 ticket but we don't know how many tickets each of the other 10 used.....INSUFFICIENT

S2: 4 used neither ticket but we don't know how many tickets each of the other 16 used.....INSUFFICIENT


S1+S2: 10 buy 1 = `10*1 =10
4 buy 0 =0*4=0
therefore, 6 buy 2 = 6*2 =12.....SUFFICIENT...SO C
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1385
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 13 Feb 2017, 19:42
1
rahuldev31 wrote:
Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?"

So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used.
But obviously I'm misinterpreting something cuz C is the right answer


The question is like this:
20 people purchased total 40 tickets. What percent of these 40 tickets that were used by those 20 people.

In (2), we know the number of people who used neither, then yes we know the total number of people who used only 1 or both. However, the question is asking the percent of tickets, not the percent of people. Hence, we need to know the specific number of people who used only 1 ticket and the specific number who used both.

Hope this helps.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 650
Location: India
Schools: Rotman '20 (S)
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 14 Feb 2017, 02:32
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?



misread the question and thought that not all purchased 2 ticket rather some have purchased ...so landed to E

its C...
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3528
Location: United States (CA)
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 14 Feb 2017, 17:02
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


We can create the following formula:

Total people = # who only used only 1 ticket + # who used both tickets + # who used neither ticket

20 = # who only used only 1 ticket + # who used both tickets + # who used neither ticket

Since each of the 20 people bought 2 tickets, a total of 40 tickets were bought. Of course, not all tickets were used since some used only 1 ticket and some used neither ticket. We need to determine what percentage of the tickets that were purchased by the 20 people were used by those people.

Statement One Alone:

Of the 20 people, 10 used only 1 ticket.

We see that the # who only used only 1 ticket is 10. However, since we know nothing about the number of people who used neither ticket, we still cannot answer the question. Statement one alone is not sufficient.

Statement Two Alone:

Of the 20 people, 4 used neither ticket.

We see that the # who used neither ticket is 4. However, since we don’t know the number of people who used only 1 ticket, we still cannot answer the question. Statement two alone is not sufficient.

Statements One and Two Together:

Using the information from statements one and two, we see that:

20 = 10 + # who used both tickets +4

Thus, 20 - 14 = 6 people used both tickets.

Since a total of 40 tickets were purchased and only (6 x 2) + (10 x 1) = 22 were used, the percentage of tickets purchased by the 20 people that were used is 22/40 x 100 = 11/20 x 100 = 55 percent.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Manager
Manager
avatar
S
Joined: 17 Apr 2016
Posts: 96
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 14 Feb 2017, 20:06
rahuldev31 wrote:
nguyendinhtuong wrote:
rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?

(1) Of the 20 people, 10 used only 1 ticket.

(2) Of the 20 people, 4 used neither ticket.


Can this be solved using Overlapping sets instead of double matrix?



20 people who each purchased 2 tickets, so there are total 40 tickets.

Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket.

(1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient.

(2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient.

Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient.



Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?"

So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used.
But obviously I'm misinterpreting something cuz C is the right answer



Hi Rahul,


For finding percentage you require the count of tickets utilised and not the count of people. Option 2 gives us the count of people who have utilised the tickets. Out of 16, the breakup of number of people who utilized 2 tickets and the number of people who utilised 1 ticket is not provided.The total number of tickets used depends on this. Only after getting this value can we calculate the percantage of used tickets using formula(Total used tickets/40).
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8160
Premium Member
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

Show Tags

New post 11 Jul 2018, 21:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Of the 20 people who each purchased 2 tickets to a concert &nbs [#permalink] 11 Jul 2018, 21:57
Display posts from previous: Sort by

Of the 20 people who each purchased 2 tickets to a concert

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

Events & Promotions

PREV
NEXT


Copyright

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®.