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

 It is currently 23 May 2019, 08:09

### 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

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

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

13 Feb 2017, 08:36
10
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:33) correct 31% (01:33) wrong based on 214 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?
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

13 Feb 2017, 09:31
4
1
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.

_________________
##### General Discussion
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1353
Location: Viet Nam
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

13 Feb 2017, 08:50
2
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.
_________________
Intern
Joined: 08 Dec 2016
Posts: 8
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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

### Show Tags

13 Feb 2017, 09:14
Bunuel, whats your take on this?
Manager
Joined: 04 Dec 2016
Posts: 53
Location: India
GPA: 3.8
WE: Operations (Other)
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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
therefore, 6 buy 2 = 6*2 =12.....SUFFICIENT...SO C
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1353
Location: Viet Nam
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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.
_________________
Director
Joined: 14 Nov 2014
Posts: 622
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6206
Location: United States (CA)
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 17 Apr 2016
Posts: 84
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

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).
Intern
Joined: 21 May 2016
Posts: 28
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

02 Oct 2018, 01:50
On combining both the statements we get 4 used neither, 10 used only one and remaining 6 used both. Hence Sufficient.
_________________
If you like my post press +1 Kudos
Director
Joined: 02 Oct 2017
Posts: 729
Re: Of the 20 people who each purchased 2 tickets to a concert  [#permalink]

### Show Tags

03 Oct 2018, 20:01
rahuldev31

This ques can be solved using sets but since there are only three cases - 1 ticket , 2 ticket , Neither
The intersection part would not be there
So there could be two circles , one for 1 ticket other for 2 tickets without any overlapping and outside region of these two circles will be neither case.

In such case also C would be answer
As the sum of all three would be 20 = 1st circle + 2nd circle + Outside region
_________________
Give kudos if you like the post
Re: Of the 20 people who each purchased 2 tickets to a concert   [#permalink] 03 Oct 2018, 20:01
Display posts from previous: Sort by