AAPL wrote:Princeton Review

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.

OA B.

# of tickets bought by ppl over 50 years = 1/5 of 850 = 170 M

# of tickets bought by ppl ≤ 50 yrs = 850 - 170 = 680

Question: Did people under the age of 20 buy more than 425 million movie tickets?

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*170M < # of tkts under 20 bought < 3*170M
340M < # of tkts under 20 bought < 510M
Can't find the unique value.

# of tkts under 20 bought could be less than 425M or 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.

Given the average price of $6 per ticket, the amount spent on tickets by ppl over 50 = 170*6 = $1020M

=> the amount spent on tickets by ppl under 20 = 2.2B + 1020M = a finite number

# of tkts bought by ppl under 20 = A finite number / 6 = Another finite number, say x.

Since x is comparable to 425M, the answer would be unique: either yes or no. Sufficient.

We need not calculate the actual value till we are sure that we would get a unique value.

The correct answer: B

Hope this helps!

-Jay
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