For a certain art exhibit, a museum sold admission tickets

Question

For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?

A. $24960
B. $25920
C. $28080
D. $28500
E. $29160

A. $24960
B. $25920
C. $28080
D. $28500
E. $29160

KarishmaB · Accepted Answer

Yes, we do but the tickets are not sold during the intervals; they are sold at 9:00 am, then at 9:05 am, then at 9:10 am etc...

Read the question stem again: 
" a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive."

Take an example. 
What does this mean: "I will message you every 5 mins starting from 9:00 in the morning to 5:55 in the evening, inclusive"?
It means I will message at 9:00, at 9:05, at 9:10 and so on till 5:55.

It's exactly the same concept here. The museum sells tickets at 9:00, then at 9:05 etc. When you think of selling tickets, don't think of a long queue moving forward one person at a time, think of tons of people requesting for a ticket at the kiosks and the museum printing 30 tickets every 5 mins.

Bunuel · Answer

From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*30 tickets were sold.

Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.

Therefore, the total revenue from ticket sales that day was 27*30*6+27*90*10=$29,160.

Answer: E.

Hope it's clear.

carcass · Answer

Sorry Bunuel but our statement say: 9 Am to 5.55 PM so we have 12*8 = 96 + 11 (and not 12 because the museum sells tickets untill 5.55 PM) so = 107 Thi poin is still unclear for me. :wall

Bunuel · Answer

From 9:00 in the morning to 5:55 in the afternoon,  inclusive  there are are 9*12=108 five-minute intervals, the same way as from 9:00 to 9:55 there are 12 five-minute intervals:
9:00
9:05
9:10
9:15
9:20
9:25
9:30
9:35
9:40
9:45
9:50
9:55

Hope it's clear.

resnickd · Answer

If you assume they sell the first batch of tickets at 9:00 AM then you get to 108..... although they do not make this very clear in the question.

Sachin9 · Answer

Bunuel, 
From 9:00 to 9: 55 there are 11 intervals.. not 12 .. what am I missing?

Bunuel · Answer

Check again:
1. 9:00
2. 9:05
3. 9:10
4. 9:15
5. 9:20
6. 9:25
7. 9:30
8. 9:35
9. 9:40
10. 9:45
11. 9:50
12. 9:55

Sachin9 · Answer

From 9 until 5:55 , we have 11 intervals..

9:00
1
9:05
2
9:10
3
9:15
4
9:20
5
9:25
6
9:30
7
9:35
8
9:40
9
9:45
10
9:50
11
9:55

voodoochild · Answer

Karishma,
Do we have to assume that as soon as the clock ticks 9:00:00, 30 tickets are sold? That sounds bizarre. Realistically, I would think that 30 tickets will be sold   between    9:00 and 9:05. Isn't it? Your above example of sending message (s)  is different because a message can be sent at a particular time "x." However, sending 30 messages exactly at "x" moment doesn't sound realistic. Do we have to assume that the GMAT thinks that such a case is realistic? I am still not clear ...how will I distinguish between the two facts:-

fact a- tickets sold   between   9:00 and 9:05
fact b- tickets sold   at    9:00 and 9:05.

Please help?

Thanks

KarishmaB · Answer

It's not unrealistic at all. Think of a batch job - a machine takes first 30 requests and processes them together at some particular time. It could take a machine a few secs or a minute to spew out the 30 tickets.
But anyway, we don't have to assume that it must sell all the tickets at that instant. What we do know is that selling 30 tickets takes less than or maximum 5 mins since after 9:00, tickets will be sold at 9:05 again and so on. It's clear from the question that 30 tickets will be sold at 5:55 (whatever time it may take after that) since the word 'inclusive' is given in the question. I can understand a bit of confusion and it may take a few secs extra to understand the question. Please note that it is a GMAT Prep question (according to the tag) and hence it's official. I can only try to explain what the question setter might have imagined when he made this question. 
Take solace in the fact that every live GMAT question is closely monitored and if it causes undue confusion, it is removed.

messi10 · Answer

I guess this is not a great question. The only thing to do is guess towards the end.

If you work with the logic that there are 11 intervals in the last hour (which is what most of us did), then you reach a total value of 3210 for the number of tickets. When you try and solve for the number of regular and student tickets, you get answers in decimals, which is not possible as the number of tickets have to be integers.

At that point, there are two options:

1) Realize that there are indeed 12 intervals in the last hour as the only other possibility.

2) Carry on with the calculation which gives an answer of something around $28,845. As this falls between D and E, you guess on one and the probability of getting the question right is 50/50. Still better than nothing.

Although, the takeaway for this question is the keyword "inclusive". This word is more common when we deal with sets of consecutive integers or evenly spaced sets and are able to deal with it more easily there. But from now on, we will just have to pay more attention to it when we see it in other question types

KarishmaB · Answer

The intervals from 9 to 9:55 have been shown only to demonstrate that every hour will have 12 intervals. There are 9 such hours. So total intervals will be 12*9

sayno · Answer

hi everyone, today this question really got me confused.
and not by the "interval" nor the "inclusive" parts,

but it is the   "If on one day 3 times as many regular admissions tickets were sold as student tickets"   part,
my interpretation of that part means that for each regular tickets there three students tickets sold, not the other way around.
am I the only one here that got this wrong in this part?
and can someone help explain the logic in that sentence.

thanks

KarishmaB · Answer

Consider this:
You are 3 times as smart as me.

Who is smarter - you or me? You are smarter, right?

Similarly, "3 times as many regular admissions tickets were sold as student tickets"
Regular tickets sold were more or student tickets?
Regular tickets sold were 3 times so regular tickets sold were more. So there were 3 regular tickets sold for each student ticket.

jlgdr · Answer

Another way to solve is. 
First intervals 60/5=12intervals per hour.
Now, from 9 to 5.55 we have 9 of such intervals hence total intervals 9*12 = 108

Then, weighted average 10$ tx and 6$ tx are in the ratio 3:1 hence weighted avg is 9$.

Hence answer will be multiple of 9, (A,D are out at this point).

9*108*30=29,160.

Answer: E

sagnik2422 · Answer

Where did you get x = 27 * 30 from? and also 3x = 3* (27 * 30)? Are you factoring here?

Bunuel · Answer

x+3x=108*30 --> 4x=108*30 --> reduce by 4: x=27*30 --> multiply by 3: 3x=3*(27*30)=27*90.

I think you need to brush up fundamentals...

sagnik242 · Answer

Why are we multiplying by 9?

KarishmaB · Answer

Because there are 9 hours:
9 to 10 am
10 to 11 am
11 to 12 noon
12 to 1 pm
1 to 2 pm
2 to 3 pm
3 to 4 pm
4 to 5 pm
5 to 6 pm

In each hour there are 12 intervals.
9:00 to 9:05 am
9:05 to 9:10 am
and so on...

Hence 9*12

For a certain art exhibit, a museum sold admission tickets

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For a certain art exhibit, a museum sold admission tickets

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