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

 It is currently 21 Oct 2019, 12:01

### 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

### Show Tags

31 Dec 2013, 07:21
3
14
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:33) correct 30% (01:41) wrong based on 707 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

For a recent play performance, the ticket prices were $25 per adult and$15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?

(1) Revenue from ticket sales for this performance totaled $10,500. (2) The average (arithmetic mean) price per ticket sold was$21.

Data Sufficiency
Question: 14
Category: Algebra Simultaneous equations
Page: 154
Difficulty: 650

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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58396

### Show Tags

01 Jan 2014, 22:31
1

After reading the given problem we get this problem:
x +y = 500
25x +15y = (The sum of money spent for tickets)=> This is what we need to solve the problem.

(1) is sufficient. It tells us about revenue which is the sum of all prices of tickets.
(2) is also sufficient. If we have average price and the number of all tickets then we can find the total sum.
Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
Re: For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 02 Jan 2014, 00:57 1 For a recent play performance, the ticket prices were$25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults? (1) Revenue from ticket sales for this performance totaled$10,500.
(2) The average (arithmetic mean) price per ticket sold was $21. Sol: Let A = Total no. of Adult tickets C: Total no. of Child Tickets Given A+C=500, we need to find A ? Price of Adult Ticket:$25
Price of Child Ticket : $15 From St 1, we have 25*A+15*C = 10500 We also know A+C= 500 We have 2 variables and 2 equations and therefore we can solve for A. We can leave it that. So B C and E ruled out From St 2 we have Average price is$ 21. Refer attachment

Attachment:

WA.PNG [ 12.23 KiB | Viewed 7511 times ]

Now $21 is 6$ more than Child Ticket price and $4 Less than Adult ticket price. So by Weighted Average principle. Total difference between Adult and Child Ticket price is$ 10

Number of Adult Tickets will be: 6/10 *500 = 300 -----> A

Just for clarity purpose we can calculate St 1 as well

5A+3C= 2100-------Eq 1
A+C=500-----> 3A+3C= 1500-------> Eq 2

Subtracting 2 from1, we get 2A=600 or A =300.

Ans D
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27

### Show Tags

05 Jan 2014, 11:54
SOLUTION

For a recent play performance, the ticket prices were $25 per adult and$15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?

(1) Revenue from ticket sales for this performance totaled $10,500 --> $$25a+15c=10,500$$ --> $$25a+15(500-a)=10,500$$. We can solve for a. Sufficient. (2) The average (arithmetic mean) price per ticket sold was$21 --> $$\frac{25a+15c}{500}=21$$ --> $$25a+15c=10,500$$. The same info as above. Sufficient.

_________________
Manager
Joined: 11 Aug 2018
Posts: 110
Re: For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 27 Sep 2018, 04:18 nutshell wrote: Since the question asks for the number of tickets sold for adults, let us assume x to be the number of tickets sold to adults. Average price/ticket = (no. of adult tickets) * (Price/adult ticket) + (no. of child tickets) * (Price/child ticket) Av. price = 25 * A + 15 * C Since A + C = 500; C = 500 - A Av. price = 25A + 15(500 - A) = 25A + 7500 - 15A = 10A + 7500; So, if we know the av.price/ticket, we can A; 1) Av.price = 10500/500 = 21; Sufficient 2) Av.price is given as 21; Sufficient. Hence (D). This is more clean D x: the tickets sold were for adults 1) 25x + (500-x)*15 = 10500 => sufficient 2) The average (arithmetic mean) price per ticket sold was$21.
=> Revenue from ticket sales 500x21 = 10500
=> sufficient because it' has the same condition with 1)
_________________
If you like this post, be kind and help me with Kudos!

Cheers!
VP
Joined: 14 Feb 2017
Posts: 1204
Location: Australia
Concentration: Technology, Strategy
Schools: LBS '22
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
WE: Management Consulting (Consulting)
For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 10 Dec 2018, 20:29 Got this wrong in a GMATFocus test, but I realise I just made silly mistakes. 25A + 15C = Total$ However, we are told the # tickets sold, so lets include this now
25A + 15(500-A) = Total$1. Total$ = 10,500
25A + 15(500-A) = 10,500.

Sufficient to solve for A

2. [25A + 15(500-A)]/500 = 21
25A + 15(500-A) = 21*500
25A + 15(500-A) = 10,500 (Sufficient to solve for A

D
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Re: For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 27 Apr 2019, 07:47 Top Contributor Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition For a recent play performance, the ticket prices were$25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults? (1) Revenue from ticket sales for this performance totaled$10,500.
(2) The average (arithmetic mean) price per ticket sold was $21. Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled$10,500
In other words, 25A + 15C = 10,500
When we add our given equation, C + A = 500, we can see that we have a system of 2 different linear equations with 2 variables.
Since we COULD solve this system for A, we COULD answer the target question with certainty.
So statement 1 is SUFFICIENT

Statement 2: The average (arithmetic mean) price per ticket sold was $21. We'll use this fact: average of n numbers = (sum of the n numbers)/n Rearrange to get sum of the n numbers = (average of n numbers)(n) If 500 tickets were sold and the average ticket price was$21, then the sum of all tickets sold = (21)(500) = $10,500 IMPORTANT: Statement 2 is just another way of telling us that the total revenue from ticket sales was$10,500 (this is exactly what statement 1 told us)
Since statement 1 was SUFFICIENT, statement 2 must also be SUFFICIENT

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com