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# There are a total 10 movie theaters. Minimum number of tickets that ea

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There are a total 10 movie theaters. Minimum number of tickets that ea  [#permalink]

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31 Mar 2017, 14:58
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There are a total 10 movie theaters. Minimum number of tickets that each movie theaters sold was 80 tickets. Is total number of average tickets sold more than 90 tickets?

1) Number of movie theaters that sold at least 100 tickets were more than half of the total number of movie theaters.
2) In 4 movie theaters of the total number of movie theaters, number of each tickets sold were more than 105.

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Senior SC Moderator
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There are a total 10 movie theaters. Minimum number of tickets that ea  [#permalink]

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01 Apr 2017, 01:31
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ziyuen wrote:
There are a total 10 movie theaters. Minimum number of tickets that each movie theaters sold was 80 tickets. Is total number of average tickets sold more than 90 tickets?

1) Number of movie theaters that sold at least 100 tickets were more than half of the total number of movie theaters.
2) In 4 movie theaters of the total number of movie theaters, number of each tickets sold were more than 105.

OFFICIAL EXPLANATION

FROM MathRevolution
If you modify the original condition and the question, the average number of tickets sold>90? And this becomes the total number of tickets sold>90(10)=900? Then, there are 10 variables (10 movie theaters) and 1 equation (minimum of 80 tickets were sold), and in order to match the number of variables to the number of equations, there must be 9 more equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2) together,

If you assume that the number of movie theaters that sold at least 100 tickets as 6 and from the 6 movie theaters, 4 of them sold 106 tickets, from the total number of tickets sold=100(6)+106(4)=1,024>900, it is always yes, hence it is sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A and B) and CMT 4 (B: if you get A or B too easily, consider D).

For con 1), even if you assume the number of theaters that sold at least 100 tickets as 5, since the rest of the 5 movie theaters sold at least 80 tickets, so the total number of tickets sold becomes 100(5)+80(5)=900. Since it said that it is half greater than the total number of movie theaters, which is 10, so it is always greater than 900, hence yes, it is sufficient.

For con 2), if you assume that from the total of 10 movie theaters, 4 movie theaters sold 105 tickets and the 6 movie theaters sold 80 tickets, then the total number of tickets sold is 105(4)+80(6)=900, and since it said that the 4 movie theaters sold more than 105 tickets each, so it is always greater than 900, hence it is yes and sufficient. Therefore, the answer is D.
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Re: There are a total 10 movie theaters. Minimum number of tickets that ea  [#permalink]

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21 Dec 2017, 11:07
Hi All,

While this question is awkwardly-worded, it is essentially a 'limit' question. From the prompt, we know that each of the 10 theaters sold AT LEAST 80 tickets. We're asked if the average number of tickets sold for each theater was GREATER than 90? We can 'rewrite' this prompt - it's asking "Is the TOTAL number of tickets sold greater than 900?" This is a YES/NO question.

1) Number of movie theaters that sold at least 100 tickets were more than half of the total number of movie theaters.

This Fact tells us that MORE than half of the theaters sold at least 100 tickets. That would be at least 6 theaters (at the minimum)...

(6 theaters)(100 tickets each) = 600 tickets

From the prompt, we know that each theater sold AT LEAST 80 tickets, so we can find the minimum total that the other 4 theaters sold...

(4 theaters)(80 tickets each) = 320 tickets

Total MINIMUM number of tickets sold = 600 + 320 = 920 tickets. Increasing the number of theaters that sold at least 100 tickets would increase the total number of tickets sold. Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) In 4 movie theaters of the total number of movie theaters, number of each tickets sold were more than 105.

We can deal with Fact 2 in the same general way that we dealt with Fact 1...

(4 theaters)(more than 105 tickets each) = more than 420 tickets

Each of the other theaters sold AT LEAST 80 tickets, so we can find the minimum total that the other 6 theaters sold...

(6 theaters)(80 tickets each) = 480 tickets

Total MINIMUM number of tickets sold = (more than 420) + 480 = more than 900 tickets. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

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Re: There are a total 10 movie theaters. Minimum number of tickets that ea   [#permalink] 21 Dec 2017, 11:07

# There are a total 10 movie theaters. Minimum number of tickets that ea

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