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.