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

 It is currently 15 Jan 2019, 18:15

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar

Author Message
TAGS:

### Hide Tags

Intern
Joined: 30 Jun 2008
Posts: 4

### Show Tags

21 Aug 2008, 20:36
prashi82 wrote:
Que:- At a certain theater, the cost of each adult's ticket is $5 and cost of each child's ticked is$2. What was the average (arithmetic mean) cost of all adult's and children's tickets sold at the theater yesterday.

a) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2.

b) Yesterday 80 adult's tickets were sold at the theater.

Can someone help me with this one?

Thanks
Prashi82

ratio of childre't ticket: adult tickets sold = 3:2
assume that 3 and 2 tickets are sold.

a) average = cost of adult tickets + cost of childrent tickets/total tickets sold=
( 5*2+ 2*3 )/5

sufficient

Insuffcieint

A.
_________________

Smiling wins more friends than frowning

Intern
Joined: 17 Dec 2009
Posts: 24

### Show Tags

08 Feb 2010, 11:29
But the ratio provided by A doesn't hold true if you use different values: let's say that 120 children tickets were sold and 80 adults tickets were sold (same ratio as 3 to 2) then we have:

5(120)+2(80)/200 and the average price is not the same.

I choose C for this for that reason. I know it's wrong but can someone explain. Thanks.

adamsith2010 - I think the ratio does hold true if you use other values. There is an error in your equation. If we use the 120 children tickets and 80 adult like you mentioned the equation looks as follows:

5(80)+2(120)/200 =====> 640/200 = 3.2 same average as if we used the original ration.

I hope this helps
Manager
Joined: 17 Jan 2010
Posts: 130
Concentration: General Management, Strategy
GPA: 3.78
WE: Engineering (Manufacturing)

### Show Tags

08 Feb 2010, 18:07
prashi82 wrote:
Que:- At a certain theater, the cost of each adult's ticket is $5 and cost of each child's ticked is$2. What was the average (arithmetic mean) cost of all adult's and children's tickets sold at the theater yesterday.

a) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2.

b) Yesterday 80 adult's tickets were sold at the theater.

Can someone help me with this one?

Thanks
Prashi82

(5x+2y)/(x+y) is the average. However from 1) we know that x/y = 3/2 ie 2x = 3y. use this to solve for first equation which will be 3.2 Hence Sufficent
Intern
Joined: 16 May 2009
Posts: 28

### Show Tags

03 Jan 2015, 11:56
2
Hi All,

When you're dealing with "ratio data" in a DS question, it's actually really easy to prove if a pattern exists or not - just run through a few quick TESTs...

Here, we're told:
Adult tickets cost $5 each Children's tickets cost$2 each

We're asked for the AVERAGE COST of all tickets sold yesterday.

Fact 1: The ratio of Children's tickets to Adult's tickets was 3:2 yesterday.

Some Test Takers can clearly see that this ratio IS enough information to say that Fact 1 is SUFFICIENT. Here's how you can quickly prove the consistency...

IF...
3 children
3(2) + 2(5) = 16/5 = $3.20 average ticket price 6 children 4 adults 6(2) + 4(5) = 32/10 =$3.20 average ticket price

9 children
9(2) + 6(5) = 48/15 = $3.20 average ticket price With this ratio, the average is ALWAYS$3.20
Fact 1 is SUFFICIENT

Fact 2: 80 Adult tickets were sold

Here, we don't know the number of Children's tickets, so the average ticket price would change depending on THAT number. Again, here's the proof:

0 children
0 + 80(5) = 400/80 = $5 average ticket price 80 children 80 adults 80(2) + 80(5) = 560/160 =$3.50 average ticket price
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: At a certain theater, the cost of each adult's ticket is$5 and cost  [#permalink]

### Show Tags

05 Jan 2015, 04:07
1
At a certain theater, the cost of each adult's ticket is $5 and the cost of each child's ticket is$2. What was the average cost of all the adult's and children's tickets sold at the theater yesterday?

The average cost = (2*C+5*A)/(C+A)

(1) Yesterday ratio of # of children's ticket sold to the # of adult's tickets sold was 3 to 2 --> 3A =2CA = 2C/3 --> the average cost = C(2+5*2/3)/(C(1+2/3)) --> (2+5*2/3)/(1+2/3). Sufficient.

(2) Yesterday 80 adult's tickets were sold at the theater --> A = 80. We know nothing about C. Not sufficient.

_________________
Intern
Joined: 21 Dec 2015
Posts: 25
WE: Account Management (Commercial Banking)

### Show Tags

20 Oct 2016, 15:56
1
prashi82 wrote:
At a certain theater, the cost of each adult's ticket is $5 and cost of each child's ticked is$2. What was the average (arithmetic mean) cost of all adult's and children's tickets sold at the theater yesterday.

(1) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2.

(2) Yesterday 80 adult's tickets were sold at the theater.

We are given that the cost of each adult's ticket is $5 and cost of each child's ticket is$2. We need to determine the average (arithmetic mean) cost of all adults’ and children's tickets sold at the theater yesterday. If we let a = the number of adults’ tickets sold and c = the number of children’s tickets sold, we can create the following average equation:

Average = (5a + 2c)/(a + c)

Statement One Alone:

Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2.

Using the information in statement one, we can create the following equation:

c/a = 3/2

2c = 3a

c = 1.5a

Since c = 1.5a, we can substitute 1.5a for c in our average equation and we have:

Average = (5a + 2 x 1.5a)/(a + 1.5a)

Average = (5a + 3a)/2.5a

Average = 8a/2.5a

Average = 3.2

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Yesterday 80 adult's tickets were sold at the theater.

Only knowing the number of adults’ tickets sold yesterday is not enough information to determine the average cost of all tickets sold. Statement two alone is not sufficient to answer the question.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Manager
Joined: 23 Apr 2014
Posts: 63
Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75

### Show Tags

16 Feb 2017, 17:58
Here is another approach.

Assume that a adults and c children tickets were sold.
The Question can be modified as follows
(5a +2c)/(a+c) = ?

stmt says c/a = 3/2
ie c = 3a/2 ----------(1)

substitute this ie the question.
(5a + 3a)/(a +3a/2)
simplifying,
16a/5a = 16/5 .. a definite answer
So sufficient.

Stmt 2 is not sufficient.

hence A
_________________

Thanks & Regards,
Anaira Mitch

Senior Manager
Joined: 22 Feb 2018
Posts: 416
Re: At a certain theater, the cost of each adult's ticket is $5 and cost [#permalink] ### Show Tags 01 Sep 2018, 08:22 prashi82 wrote: At a certain theater, the cost of each adult's ticket is$5 and cost of each child's ticked is $2. What was the average (arithmetic mean) cost of all adult's and children's tickets sold at the theater yesterday. (1) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2. (2) Yesterday 80 adult's tickets were sold at the theater. OA: A Let the Adult's ticket price be $$T_{Adult}$$ and Child's ticket price be $$T_{Child}$$ $$T_{Adult}=5 \qquad T_{Child}=2$$ Let the number of Adults be $$A$$ and the number of children be $$C$$. We have to find out the average cost of all tickets sold at the theater i.e We have to find $$\frac{A*T_{Adult}+C*T_{Child}}{A+C}......(1)$$ 1) Yesterday the ratio of the number of children's tickets sold at the theater to the number of adult's tickets sold at the theater was 3 to 2. $$\frac{C}{A}=\frac{3}{2}$$ ;$$C = \frac{{3A}}{2}......(2)$$ putting (2) and $$T_{Adult}=5 ; T_{Child}=2$$ in (1), we get Average cost of all tickets sold $$= \frac{A*T_{Adult}+C*T_{Child}}{A+C} =\frac{A*5+\frac{3A}{2}*2}{A+\frac{3A}{2}} =\frac{8A}{\frac{5A}{2}}=\frac{16}{5}$$ Statement 1 alone is sufficient. 2)Yesterday 80 adult's tickets were sold at the theater. We know about the number of Adult's ticket sold but are not aware about the number of children ticket sold. Statement 2 alone is not sufficient _________________ Good, good Let the kudos flow through you Re: At a certain theater, the cost of each adult's ticket is$5 and cost &nbs [#permalink] 01 Sep 2018, 08:22
Display posts from previous: Sort by