Competition Mode Question

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.
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Total 850 million movie tickets sold.
1/5 were bought by people, aged over 50 = 170 million
4/5 were bought by people, aged less than 50 = 680 million
Question stem asked to find whether movie tickets bought by people aged less than 20 is more than 425 million? It can find if we have information above tickets bought by people aged above 20 to less than 50.

(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.
Tickets bought by people aged <20 = 2*170 to 3*170 = 340 to 510 million
Hence, it can be more than 425 million or less than million.
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.
People aged >50, spent money on movie tickets = $ x, People aged < 20, spent money on movie tickets = $ x + 2.2 million
No. of people People aged >50 = M and No. of people People aged < 20 = N
Mean of tickets bought by both people = $ 6/ticket,
6 = M*x + N* (x+2.2) /M+N. Here, one equation with three unknowns can not yield unique solution. Hence, insufficient.
1) + 2)
Still M, N and x are unknown. hence insufficient.
Ans. E.
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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?

1/5(850)=190 tickets:>50
<20:>425?

(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.
two times of 190 is 380
three times of 190 is 470
one is under 425 the other is over 425 therefore,
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.

6(190)=114million
(2200+114)/6=385.
<425
sufficient

In total, there are 850 million tickets.
—> People over 50 years old bought 850*1/5 = 170 million tickets. (20%)

Did people under 20 years old buy more than 50% percent of tickets (more than 425 million tickets) ???

Statement1: People under 20 years old bought between 2*170 and 3*170
—> 340 m<tickets( bought by people under 20)< 510 m
It could be <425 or > 425
Insufficient

Statement2:
(under20)*6 > 170(over50)*6+ 2200
—> (Under20)*6= 1020+2200=3220
(Under20)= 3220/6=536.(6)

(Under20) bought more than 50 percent (536.(6)) of tickets.
Sufficient
The answer is B

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