a museum sold admission tickets

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue May 31, 2016 1:40 am
Thanked: 3 times

a museum sold admission tickets

by Needgmat » Fri Oct 21, 2016 9:23 am
for a certain art exhibit, a museum sold admission tickets to group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of 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

OA E

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Oct 21, 2016 9:28 am
Needgmat wrote:for a certain art exhibit, a museum sold admission tickets to group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of 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
Of every 4 tickets sold, 3 are $10 regular tickets and 1 is a $6 student ticket:
3(10) + 6 = 36.

30 tickets are sold every 5 minutes.
Thus, in 60 minutes -- 12 times as long -- the number of tickets sold = 12*30 = 360.

Every 4 of these tickets brings in $36.
Thus, the amount earned every hour by 360 tickets = 360/4 * 36 = 90*36 = 3240.

Thus, in the 9 hours between 9 and 6pm, the total earnings = 9*3240 = 29,160.

The correct answer is E.

Please note that the last set of 30 tickets is sold at 5:55pm.
Thus, even in the last hour, a total of 360 tickets are sold.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue May 31, 2016 1:40 am
Thanked: 3 times

by Needgmat » Fri Oct 21, 2016 9:39 am
Hi Sir ,

Can you please check and advise, whats wrong in my approach.

From 9 to 5:00 we have 8 hrs

so in minutes it will be 8*60 = 480 +55 = 535 right?

It is given that tickets sold in every 5 minutes so it will be 535/5 = 107.

now 107*30 = 3210.

Let the regular admission tickets be R and students tickets be S.

The equation will be R+S = 3210.

it is given that R=3S

3S+S = 3210

4S=3210

The result will not be an integer, but it has to be an integer.

Please advise..

Many thanks in advance.

Kavin

Master | Next Rank: 500 Posts
Posts: 415
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

by regor60 » Fri Oct 21, 2016 10:24 am
Needgmat wrote:Hi Sir ,

Can you please check and advise, whats wrong in my approach.

From 9 to 5:00 we have 8 hrs

so in minutes it will be 8*60 = 480 +55 = 535 right?

It is given that tickets sold in every 5 minutes so it will be 535/5 = 107.

now 107*30 = 3210.

Let the regular admission tickets be R and students tickets be S.

The equation will be R+S = 3210.

it is given that R=3S

3S+S = 3210

4S=3210

The result will not be an integer, but it has to be an integer.

Please advise..

Many thanks in advance.

Kavin
You are missing the prompt in the question indicating that the ticket interval is inclusive of both the start time and the end time.

Your approach includes just the end time in the interval and misses the 30 tickets sold at 9:00.

For example, the question could read 1 pm to 3 pm inclusive. The naive approach is just to subtract 1 from 3 to equal 2.

Well, if you count two up from 1, your first number is 2 and the second is 3.

But you would have missed the activity that takes place at 1.

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Oct 21, 2016 4:00 pm
Hi All,

The math 'steps' behind this question can be done in a couple of different 'orders', depending on how you choose to think about the given information. Here's an approach that accounts for the difference in the price of the two types of tickets at the end of the calculation:

We're told that 30 tickets are sold every 5 minutes; there are 12 'groups' of 5 minutes in each hour, so...

(30)(12) = 360 tickets sold per hour (meaning from 9:00 to 9:55)

From 10:00 to 10:55, another 360 tickets are sold, etc. From 9:00am to 5:55pm, we have 9 hours worth of sales...

(9)(360) = 3240 total tickets

IF every ticket sold cost $10, then we'd have...

(3240)(10) = $32,400

HOWEVER, 1 out of every 4 tickets was actually a student ticket (which costs $6 instead of $10), so we have to subtract $4 for every student ticket in the total.

(3240 total tickets)(1/4) = 820 student tickets
(820 student tickets)($4) = $3280

Total revenue = $32,400 = $3280 = $29,160

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image