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Theater M has 25 rows with 27 seats in each row. How many of

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Theater M has 25 rows with 27 seats in each row. How many of [#permalink] New post 20 Jun 2008, 01:27
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C
D
E

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Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied
during a certain show?
(1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats
per row for the front 20 rows.
(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats
per row for the back 15 rows.

Hope you like that one! :)
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Re: DS Theater [#permalink] New post 20 Jun 2008, 01:38
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quantum wrote:
Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied
during a certain show?
(1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats
per row for the front 20 rows.
(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats
per row for the back 15 rows.

Hope you like that one! :)


1 not suff, because you have info. only about the front 20 rows, the back 5 rows, you dont know whether it is occupied?

2. the same about 10 front rows.

I think E
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Re: DS Theater [#permalink] New post 20 Jun 2008, 01:40
sondenso

Kudo to you friend!

OA is E
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Re: DS Theater [#permalink] New post 20 Jun 2008, 01:42
But can someone explain in details why C is wrong?
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Re: DS Theater [#permalink] New post 20 Jun 2008, 01:49
Yes C cannot be the case - mathematically: Let 0-10 be o1 and v1 for occupied & Vacant respectively similary for 10-20 o2 & v2 and the 20-25 as o3 & v3

From Q stem: o1+v1=270, o2+v2=270 & o3+v3=135
Target: To find o1+o2+o3

Now frm st 1: v1+v2=200 -------insuffi

St2: v2+v3=300 ---Insuffi

St1+2: We end up with eqs: o1+o2=270 & o2+o3=105 ---- no way can we find the target hence E.
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Re: DS Theater [#permalink] New post 20 Jun 2008, 02:03
quantum wrote:
But can someone explain in details why C is wrong?


Oh, just think that you can figure out! :lol:

C is combine 1 and 2. You see the intersection between group1(statement1) and group2(statement2) has NOT-fixed number of seats unoccupied. You can be sure only that the number of rows in the intersection is 5 rows, but statement1 say average per row is 10 unoccupied and statement2 says everage per row is 20 unoccupied. So the total number of seats unoccupied in 5 rows in the intersection can be 50 or 100 seats.

E
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Re: DS Theater [#permalink] New post 20 Jun 2008, 13:02
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quantum wrote:
Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied
during a certain show?
(1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats
per row for the front 20 rows.
(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats
per row for the back 15 rows.

Hope you like that one! :)


E
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Re: DS Theater [#permalink] New post 21 Jun 2008, 01:17
quantum wrote:
Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied
during a certain show?
(1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats
per row for the front 20 rows.
(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats
per row for the back 15 rows.

Hope you like that one! :)


Stem :- Total number is seats = 25 * 27 = 675
To find :- No of seats occupied 'x'.

Option1 ) Avg of 10 unoccupied seats in the front row
Number of seats unocupied in the front 20 rows = 200 seats.
Total number of occupied seats = 675 -200 = 475 .
SUFF

Option 2 ) Avg of 10 unoccupied seats in the back 15 rows:- 20
Total number of seats unoccupied = 20 *15 = 300
Total number of occupied seats = 675 -300 = 375 .
SUFF

IMO = D
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Re: DS Theater [#permalink] New post 21 Jun 2008, 05:38
Answer is E.
You were not given the mid part
Re: DS Theater   [#permalink] 21 Jun 2008, 05:38
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