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60 percent of movie theatres in Town X have 3 screens or l

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60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   15 Feb 2013, 12:25
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60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?

A. 12
B. 18
C. 32
D. 40
E. 44
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C
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   15 Feb 2013, 22:29
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emmak wrote:
60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?

A. 12
B. 18
C. 32
D. 40
E. 44


Answer is C. Data given are in black and data inferred are in red.
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   15 Feb 2013, 21:44
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Lets take numbers here.
Assume that the total number of movie theaters in the town = 100

Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12

Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44

Of these 44 theaters, 12 are those with 3 screens or less
Therefore 32 (44-12) must be those with four screens or more

C is the answer
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   07 Jan 2016, 01:56
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emmak wrote:
60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?

A. 12
B. 18
C. 32
D. 40
E. 44


Assume the total theaters to be 100x (We assume this to avoid unitary method or decimals)

Given:
60x have 3 screens or less
Hence, 40x have 4 screens or more

20% of 60x sell more than $300 popcorn = 12x theaters.
56% of all sell less than $300 popcorn = 56x theaters. Hence 44x sell more than $300 popcorn.

Required: Percentage of theaters with 4 or more screens and more than $300 popcorn sale?
Of the 44x theaters that sell more than $300 popcorn, 12 have 3 screens of less
Total theaters with 4 or more screens and ore than $300 sale = 32x

Percentage = 32x/100x * 100 = 32%
Option C
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   25 Mar 2017, 22:13
emmak wrote:
60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?

A. 12
B. 18
C. 32
D. 40
E. 44


Setting the number of movie theatres as 100:

60 have 3 screens or less. 40 have 4 screens or more.

20% of the theatres that have 3 screens or less sell an average of more than $300 worth of popcorn per showing: 12. So 48 of the theatres that have 3 screens or less sell an average of $300 or less worth of popcorn per showing.

56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing: 56

Number of movie theatres in Town X that have 4 or more screens and sell more than $300 worth of popcorn per showing: 40-8=32.
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60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   02 Jan 2020, 11:35
official explanation

The correct response is (C).

This is a great question to pick a starting value for the number of movie theatres. Let’s say there are 100 theatres in town X. We can also choose 100 for unknown starting values in percent questions to make the math easier. Now let’s shorthand the given information from the question-stem:

60 have 3 or less screens.
12 have 3 or less screens AND sell more than $300.
56 sell $300 or less, which means 44 sells more than $300, of which we know 12 also have 3 or less screens.
That means that 44 – 12 = 32 movie theatres will have 4+ screens AND will sell more than $300 worth of popcorn
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink] New post   19 Jul 2022, 05:01
Since 60% of the movie theatres have 3 screens or less, then 40% of the theatres will have 4 screens and more.

Let the total number of theatres be 1000.
600 will be with three screens or less. Out of 600, 20%, i.e., 120, sell more than $300 worth of popcorn.
Now, 56 percent of all theatres sell less than or equal to $300.
So, 560 of total sell for less than or equal to $300.
80 are from the group of 4 screens or more.
The required percentage = (320/1000)*100 = 32

Thus, the correct option is C.
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Re: 60 percent of movie theatres in Town X have 3 screens or l [#permalink]
19 Jul 2022, 05:01
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