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# In 1990 850 million movie tickets were sold in the United States. One

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Math Expert
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In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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10 Oct 2019, 21:28
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25% (medium)

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80% (02:05) correct 20% (02:04) wrong based on 35 sessions

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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) 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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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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10 Oct 2019, 21:56
1
from the question stem, we know that total ticket sold = 850million. tickets bought by those aged over 50years, y, = 850/5 = 170million

we are to determine whether those aged below 20 years, x, bought more than 425million tickets.

statement 1: 2y<x<3y
which implies 340million<x<510million
not sufficient, because from the given range x can be 341 million in which case we could conclude No, those aged below 20 bought less than 425million tickets or x can be 500million in which case we could conclude Yes, those aged below 20 bought more than 425million tickets.

statement 2: x>170million + 2,200million/6
implying x>503million
this sufficient since we can conclude that those aged below 20 years bought more than 425million tickets, hence the answer is Yes to the question posed.

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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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10 Oct 2019, 22:22
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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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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11 Oct 2019, 00:53
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#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.
>50 bought ; 850/5 = 170 million tickets
so <20 age ; 170*2 ; 340 or 170*3 ; 510 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.
total money spent by >50 ; 170*6 ; 1020
so by <20 age ; 2.2+1020 ; 2.3 billion ~ ticket by <20 ; 2.3/6 = 383 million
sufficient
IMO B
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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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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11 Oct 2019, 02:01
1
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
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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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11 Oct 2019, 06:05
1
Quote:
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.

(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: insufic.

over 50 = 850/5 = 170M tickets… 2 (over 50) ≤ under 20 ≤ 3 (over 50)… 340M ≤ under 20 ≤ 510M

(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: sufi.

under 20 spending - over 50 spending = 2200M
x*\$6 - 170M*6 = 2200M… x = 2200M/6 + 170… x = (2200+1020)/6 =~ 531M > 425M

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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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12 Oct 2019, 14:17
1
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

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Re: In 1990 850 million movie tickets were sold in the United States. One  [#permalink]

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12 Oct 2019, 19:50
1
From question stem: Tickets bought by people over the age of 50 = 170 million.

We need to find whether people under age of 20 bought 425 million tickets.

Statement 1: between 2 to 3 times of 170 (can take any value from 340 million to 510 million) >>NOT SUFFICIENT

Statement 2: people under 20 spent 2.2 billion more. Per ticket price is given. From this we can find additional numbers of ticket bought by people under age of 20. SUFFICIENT

Re: In 1990 850 million movie tickets were sold in the United States. One   [#permalink] 12 Oct 2019, 19:50
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