swerve wrote:In 1990, 850 million movie tickets were sold in the United States. One-fifth of those tickets were bought by people over the age of 50. Did people under the age of 20 buy more than 425 million movie tickets in 1990?
1) In 1990, people under the age of 20 bought between two and three times as many tickets as were bought by people over the age of fifty.
2) In 1990, people under the age of 20 spent $2.2 billion more on movie tickets than did people over the age of 50, with both groups spending an average (arithmetic mean) of $6 per ticket.
The OA is B
Source: Princeton Review
Given that a total 850M tickets were sold, the number of tickets bought by people over the age of 50 = 1/5 of 850 = 170M.
We have to determine whether people under the age of 20 bought more than 425 million movie tickets in 1990.
Let's take each statement one by one.
1) In 1990, people under the age of 20 bought between two and three times as many tickets as were bought by people over the age of fifty.
(2*170) < The number of tickets bought by people under the age of 20 < (3*170)
340 < The number of tickets bought by people under the age of 20 < 510
The number of tickets bought by people under the age of 20 may or may not be greater than 425M. Insufficient.
2) In 1990, people under the age of 20 spent $2.2 billion more on movie tickets than did people over the age of 50, with both groups spending an average (arithmetic mean) of $6 per ticket.
Say,
the number of tickets bought by people under the age of 20 = x;
the number of tickets bought by people over the age of 50 = y = 170M;
the average price of tickets bought by people under the age of 20 = p;
the average price of tickets bought by people over the age of 50 = q
As per the information, we have
xp - yq = 2.2B
Since it is given that both groups spent an average (arithmetic mean) of $6 per ticket, we have p = q = 6
Thus, xp - yq = 2.2B => x - y = 2.2B/6 => x - 170M = ~388M => x = 170M + 366M = 436M. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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