sagarsabnis 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.

Let me try to explain this one.

So we are asked how many seats occupied.

Statement 1 - Clearly insfficient, we only have information about 20 rows

Statement 2- Same here, we are missing information on other rows

Now both (1) and (2) together -

So we have from the 1st statement that the total number of seats for the first 20 rows that were unnocupied totaled 200.

And also the unnocpied for the back 15 rows were 300.

But we have an overlap here between rows. If we don't have more information it will be impossible to know. Imagine a venn diagram and visualize the intersection between both. As long as you don't have the exact value for the intersection it will be impossible to know the total number of unnocupied seats and hence know what the occupied seats are.

I think this will do for now.

Hope it helps