avg and ration question. how to solve?

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tj123: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Mon Dec 08, 2008 12:09 am

by tj123 » Sun Jul 12, 2009 3:57 pm

At a certain theater, the cost of each adult's ticket is $5 and the cost of each childs ticket is $2. what was the avg arithmetic mean cost of all the adults and childrens tickets sold at the theater yesterday?

1) yesterday the ratio of the number of children's tickets sold to the number of adult's ticket sold at the theater was 3to 2/

2) yesterday 80 adults tickets were sold at the theater

OA A

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 12, 2009 3:57 pm

mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Sun Jul 12, 2009 5:15 pm

IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun Jul 12, 2009 9:48 pm

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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Musicolo: Master | Next Rank: 500 Posts; Posts: 116; Joined: Sun Feb 01, 2009 10:56 am

by Musicolo » Mon Jul 13, 2009 2:15 am

mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5

Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is?

Thanks a lot

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hk: MBA Student; Posts: 532; Joined: Wed Jan 28, 2009 1:39 pmFollowed by: 9 members; Location: Barcelona; Thanked: 33 times; GMAT Score:640

by hk » Mon Jul 13, 2009 10:09 am

Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is?

Thanks a lot

The question is asking for the average cost of a ticket. In other words,

Answer = Total cost of all the tickets (cost of all adult tickets + total cost of all children's ticket) / Total number of tickets sold.

But St.1 alone is enough to calculate this answer since the ratio is given. In other words, 3/2 tells us that if 5 tickets were sold in total 3 were children's tickets and 2 were adults tickets. You can put this into the formula (above) and get the average price..

Wanna know what I'm upto? Follow me on twitter: https://twitter.com/harikrish

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Mon Jul 13, 2009 5:40 pm

Hey Musicolo,

'hk" has given a nice explanation, I hope "hk" has cleared your doubt?

Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is?

Thanks a lot

Like this post

Musicolo: Master | Next Rank: 500 Posts; Posts: 116; Joined: Sun Feb 01, 2009 10:56 am

by Musicolo » Mon Jul 13, 2009 11:16 pm

hk wrote:
Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is?

Thanks a lot
The question is asking for the average cost of a ticket. In other words,

Answer = Total cost of all the tickets (cost of all adult tickets + total cost of all children's ticket) / Total number of tickets sold.

But St.1 alone is enough to calculate this answer since the ratio is given. In other words, 3/2 tells us that if 5 tickets were sold in total 3 were children's tickets and 2 were adults tickets. You can put this into the formula (above) and get the average price..

Thanks

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