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Updated on: 05 Jan 2015, 05:04
4
13
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Difficulty:

55% (hard)

Question Stats:

61% (01:21) correct 39% (01:21) wrong based on 411 sessions

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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.

Originally posted by prashi82 on 21 Aug 2008, 21:21.
Last edited by Bunuel on 05 Jan 2015, 05:04, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: At a certain theater, the cost of each adult's ticket is $5 and cost [#permalink] Show Tags 03 Jan 2015, 12:56 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 2 adults 3(2) + 2(5) = 16/5 =$3.20 average ticket price

6 children
6(2) + 4(5) = 32/10 = $3.20 average ticket price 9 children 6 adults 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 80 adults 0 + 80(5) = 400/80 =$5 average ticket price

80 children
80(2) + 80(5) = 560/160 = $3.50 average ticket price Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ Math Expert Joined: 02 Sep 2009 Posts: 59119 Re: At a certain theater, the cost of each adult's ticket is$5 and cost  [#permalink]

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05 Jan 2015, 05:07
1
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.

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21 Aug 2008, 21:36
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.
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08 Feb 2010, 12:29
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
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08 Feb 2010, 19:07
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
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18 Oct 2016, 10:26
This is a double Matrix Question :

We know Adult price is $5 and Child Price is$2.

Option A:

The ratio of C:A is 3:2

Number Price Total
Child 3x 2 6x
Total 5x 16x

Average can be found as we have the total and individual components.

Option B: Individual component of Adult number of tickets are given, giving no clue to the number of tickets sold for the children.

Hope it helps.
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16 Feb 2017, 18:58
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
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22 Oct 2019, 08:36
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