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There are a total 10 movie theaters. Minimum number of ticke

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There are a total 10 movie theaters. Minimum number of ticke

by hazelnut01 » Fri Mar 31, 2017 3:00 pm
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.

Source : Math Revolution
Official Answer : D
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by [email protected] » Sat Apr 01, 2017 9:44 am
Hi ziyuenlau,

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

Final Answer: D

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by Jay@ManhattanReview » Thu Apr 06, 2017 6:14 am
ziyuenlau 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.

Source : Math Revolution
Official Answer : D
Hi ziyuenlau,

Given: Each of the 10 movie theaters sold at least 80 tickets.

Questions: Is the average number of tickets sold by the 10 movie theaters > 90?

Rephrased question: Is the total number of tickets sold > 900?

S1: Number of movie theaters that sold at least 100 tickets were more than half of the total number of movie theaters.

Let's take the minimum scenario.

Say the number of movie theaters that sold at least 100 tickets = 6, thus they together sold a minimum of 6*100 = 600 tickets.

Thus, the remaining 4 theaters sold a minimum of 4*80 = 320 tickets.

The 10 theater sold a minimum of 600 + 320 = 920 tickets. Sufficient.

S2: In 4 movie theaters of the total number of movie theaters, the number of each ticket sold were more than 105.

Say the 4 theaters each sold minimum 106 tickets, thus they together sold 106*4 = 424 tickets

Thus, the remaining 6 theaters sold a minimum of 6*80 = 480 tickets.

The 10 theater sold a minimum of 424 + 480 = 904 tickets. Sufficient.

The correct answer: D

Hope this helps!

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