Weighted Averages

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Aug 11, 2012 11:39 pm

Hello,

Can you please help with this problem?

Tickets to a play cost $10 for children and $25 for adults. If 100 tickets were sold, were more adult tickets sold than children's tickets?

1) The average revenue per ticket was $18
2) The revenue from ticket sales exceeded $1750

OA: D

Thanks for your valuable time and help.

Best Regards,
Sri

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 11, 2012 11:39 pm

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Sat Aug 11, 2012 11:56 pm

gmattesttaker2 wrote:Hello,

Tickets to a play cost $10 for children and $25 for adults. If 100 tickets were sold, were more adult tickets sold than children's tickets?

1) The average revenue per ticket was $18
2) The revenue from ticket sales exceeded $1750

# of children tickets = c
# of adult tickets = a

a+c = 100
Total revenue = 10*c + 25*a
If equal tickets were sold, then the revenue would be = 10*50 + 25*50 = $1750
From this we can conclude that if a>c, then revenue > $1750
Rephrased question : was the revenue > $1750

Statement 1:
avg revenue per ticket = revenue / # of tickets sold
=> total revenue = 18*100 = 1800 > 1750
Hence the statement is sufficient

Statement 2:
revenue > $1750

It answers our question
Hence the statement is sufficient

The correct answer is D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Aug 12, 2012 3:22 am

gmattesttaker2 wrote:Hello,

Can you please help with this problem?

Tickets to a play cost $10 for children and $25 for adults. If 100 tickets were sold, were more adult tickets sold than children's tickets?

1) The average revenue per ticket was $18
2) The revenue from ticket sales exceeded $1750

OA: D

Thanks for your valuable time and help.

Best Regards,
Sri

Statement 1: The average revenue per ticket was $18.
The average cost (18) is closer to the cost of an adult ticket (25) than to the cost of a children's ticket (10).
Thus, the number of adult tickets sold must have been greater than the number of children's tickets sold.
SUFFICIENT.

Statement 2: The revenue from ticket sales exceeded $1750.
Plug in the THRESHOLD: 50 of each type of ticket sold.
50(10) + 50(25) = 1750.
The equation above implies the following: for the total revenue to have EXCEEDED 1750, a greater number of the more expensive tickets -- the ADULT tickets -- must have been sold.
SUFFICIENT.

The correct answer is D.

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good_dn: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun May 05, 2013 6:03 pm

by good_dn » Sun May 05, 2013 6:07 pm

Is it possible for the average to be 18$???

If that is the case then 25a+10c = 1800 (since total tickets was 100)
and a+c =100 (a=number of adult tickets and c is number of children tickets)

a and c will have non integer values. That is not possible

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good_dn: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun May 05, 2013 6:03 pm

by good_dn » Sun May 05, 2013 6:08 pm

GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please help with this problem?

Tickets to a play cost $10 for children and $25 for adults. If 100 tickets were sold, were more adult tickets sold than children's tickets?

1) The average revenue per ticket was $18
2) The revenue from ticket sales exceeded $1750

OA: D

Thanks for your valuable time and help.

Best Regards,
Sri
Statement 1: The average revenue per ticket was $18.
The average cost (18) is closer to the cost of an adult ticket (25) than to the cost of a children's ticket (10).
Thus, the number of adult tickets sold must have been greater than the number of children's tickets sold.
SUFFICIENT.

Statement 2: The revenue from ticket sales exceeded $1750.
Plug in the THRESHOLD: 50 of each type of ticket sold.
50(10) + 50(25) = 1750.
The equation above implies the following: for the total revenue to have EXCEEDED 1750, a greater number of the more expensive tickets -- the ADULT tickets -- must have been sold.
SUFFICIENT.

The correct answer is D.

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