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A comedian is playing two shows at a certain comedy club,

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A comedian is playing two shows at a certain comedy club,

by BTGmoderatorLU » Wed Sep 11, 2019 2:04 am

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Source: Princeton Review

A comedian is playing two shows at a certain comedy club, and twice as many tickets have been issued for the evening show as for the afternoon show. Of the total number of tickets issued for both shows, what percentage has been sold?

1) A total of 450 tickets have been issued for both shows.
2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold.

The OA is B
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Sep 12, 2019 9:49 pm

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BTGmoderatorLU wrote:Source: Princeton Review

A comedian is playing two shows at a certain comedy club, and twice as many tickets have been issued for the evening show as for the afternoon show. Of the total number of tickets issued for both shows, what percentage has been sold?

1) A total of 450 tickets have been issued for both shows.
2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold.

The OA is B
Say x tickets issues for the afternoon show; thus, 2x tickets issues for the evening show.

We have to find out what percent of total tickets x + 2x = 3x were sold.

Let's take each statement one by one.

1) A total of 450 tickets have been issued for both shows.

=> 3x = 450 => x = 150. We don't have any information about sales. Insufficient

2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold.

# of tickets sold for the afternoon show = 3/5 of x = 3x/5;
# of tickets sold for the afternoon show = 1/5 of 2x = 2x/5

Total no. of tickets sold = 3x/5 + 2x/5 = x

Percentage of tickets sold = (x/3x)*100% = 33.33%. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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by deloitte247 » Fri Sep 13, 2019 2:19 pm

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let total ticket issued for afternoon show = T
Therefore Tickets issued for evening show will be = 2T
Question = Of the total number of tickets issued for both shows. What percentage has been sold ?
Statement 1=
A total number of 450 tickets have been issued for both shows.
T+2T = 450 tickets
$$\frac{3T}{T}=\frac{450}{3}$$
$$T=150\ ticket\ and\ 2T=150\cdot2=300 Tickets$$
But this does not give any information on the ticket sold we only have total ticket issued so we cannot find the percentage sold from the ticket issued. Statement 1 is NOT SUFFICIENT.

Statement 2: Exactly 3/5 of tickets issued for the afternoon show have been sold and exactly 1/5 of the tickets issued for the evening show have been sold.

Total Tickets = T+2T = 3T
$$Tickets\ sold\ in\ the\ afternoon\ =\left(\frac{3}{5}\right)T$$
$$Tickets\ sold\ in\ the\ evening\ =\left(\frac{1}{5}\right)2T=\left(\frac{2}{5}\right)T$$
$$Total\ ticket\ sold=\left(\frac{3}{5}+\frac{2}{5}\right)T$$
$$Total\ ticket\ sold=\frac{\left(3+2\right)}{5}T=\left(\frac{5}{5}\right)T=T$$
$$Total\ \%sold=\frac{\left(Total\ ticket\ sold\right)}{Total\ ticket\ sold}\cdot100$$
$$\frac{T}{3T}\cdot100=\frac{1}{3}\cdot100=33.33\% of\tickets\sold$$
Statement 2 alone id SUFFICIENT.

$$answer\ is\ OPTION\ B.$$
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