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Tough DS question

by ani781 » Fri Sep 27, 2013 4:44 pm
Hi,

I am just not being able to visualize this one :

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.

OA: E


Please help. Also can I get some similar questions ?[/spoiler]
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by GMATGuruNY » Fri Sep 27, 2013 6:56 pm
ani781 wrote:Hi,

I am just not being able to visualize this one :

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.

OA: E


Statement 1: Of the 540 seats in the front 20 rows, the number unoccupied = 10*20 = 200, implying that the number occupied = 340.
Statement 2: Of the 405 seats in the back 15 rows, the number unoccupied = 20*15 = 300, implying that the number occupied = 105.

Let Section A = the front 10 rows, Section B = the middle 10 rows, and Section C = the back 5 rows.

Case 1:
Total occupied in Section B = 105.
Total occupied in Section A = (total occupied in the front 20 rows) - (total occupied in Section B) = 340-105 = 235.
Total occupied in Section C = (total occupied in the back 15 rows) - (total occupied in Section B) = 105-105 = 0.
Total occupied = B+A+C = 105+235+0 = 340.

Case 2:
Total occupied in Section B = 70.
Total occupied in Section A = (total occupied in the front 20 rows) - (total occupied in Section B) = 340-70 = 270.
Total occupied in Section C = (total occupied in the back 15 rows) - (total occupied in Section B) = 105-70 = 35.
Total occupied = B+A+C = 70+270+35 = 375.

Since different totals are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by ani781 » Fri Sep 27, 2013 7:10 pm
Thanks Mitch,
I understand the logic. But how do I do this in under 2mins. Imagining this would need so much of stretch of thoughts... I mean this is really difficult to think this way. Well again, for average beings is it possible to inculcate a thought process similar to this ?
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by GMATGuruNY » Fri Sep 27, 2013 7:21 pm
ani781 wrote:Thanks Mitch,
I understand the logic. But how do I do this in under 2mins. Imagining this would need so much of stretch of thoughts... I mean this is really difficult to think this way. Well again, for average beings is it possible to inculcate a thought process similar to this ?
Ideally, you would quickly see that the two statements combined are insufficient for a very important reason:
We know nothing about the OVERLAP between the front 20 rows and the back 15 rows.
Since this overlap -- the number of occupied seats in the MIDDLE 10 rows -- can take on different values, so can the TOTAL number of occupied seats.
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by theCodeToGMAT » Fri Sep 27, 2013 8:27 pm
Statement 1: No information about the last 5 rows..
INSUFFICIENT

Statement 2: No information about first 10 rows Insufficient.
INSUFFICIENT

Combining...
Lets assume to possible scenarios

Case 1:
1-15 rows = 150 seats
5-10 rows = 50 seats [ 20 x 100 = 200 ]
then,
20-25 = 250 [15 x 20 = 300 ]
Total seats = 150 + 50 + 250 = 450


Case 2:
1-15 rows = 50 seats
5-10 rows = 150 seats [ 20 x 100 = 200 ]
then,
20-25 = 150 [15 x 20 = 300 ]
Total seats = 150 + 50 + 150 = 350
INSUFFICIENT

Answer [spoiler]{E}[/spoiler]
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