Data Sufficiency

Can someone put this into a formula to prove why it's wrong. I understand the logic of it and guessed right but need a better evaluation.



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

I don't get it...

My answer may be overly simple... but here's a go:

Basically in value DS questions, you need specific information to find the sought quantity.

neither statement gives information about occupied seats.

Let me try!

Total number of seats = 25* 27 = 675

From eq 1 -> we know that 200 out of the first 540 seats(20 rows) are un-occupied..however, we dont know the specifics about the last 5 rows.

From eq 2 -> we know that 300 out of the last 405 seats(15 rows) are un-occupied..however, we dont know the specifics about the first 10 rows.

Now combining the results of both the equation together, we specifically do not know the average no of un-occupied seats from rows 1 to 25.

Guys, here is how got C....PLEASE PLEASE CHECK IT AND TEMME ANYTHING IS WRONG WITH MY APPROACH.....
stmt 1-> total number of unoccupied seats in first 20 seats = 20*10 = 200

stmt2-> total no. of unoccupied seats in last 15 seats = 15*20 = 300

So these two have " unoccupied seats of 8 rows in common"

Now how do you find total unoccupied seat ..is = 200+300 - "unoccupied seats of 8 rows"[ONCE]
How do you find " unoccupied seats of 8 rows" from given data...

unocupied seats in all the rows EXCEPT those in 8 common rows = 300-200 =100
[300+200 - unoccupied seats in all rows except those in common 8 rows] =2* unoccupied seats in 8 common rows
=> 500-100=2* unoccupied seats in 8 rows
=>400/2= Unoccupied seats in 8 rows =200
Now total unoccupied seats = 100 +200 =300

Is there any stupid mistake i committing in my approach ??

---- So these two have " unoccupied seats of 8 rows in common"

you arrived at the above by mixing up seats and rows.
only way i could think you would have come up with the number of unoccupied seats of "8 rows" is

first 20 rows + last 15 rows - 27 seats = 8 "rows"
and that is the mistake ....

Rashmi1804 wrote:Guys, here is how got C....PLEASE PLEASE CHECK IT AND TEMME ANYTHING IS WRONG WITH MY APPROACH.....
stmt 1-> total number of unoccupied seats in first 20 seats = 20*10 = 200

stmt2-> total no. of unoccupied seats in last 15 seats = 15*20 = 300

So these two have " unoccupied seats of 8 rows in common"

Now how do you find total unoccupied seat ..is = 200+300 - "unoccupied seats of 8 rows"[ONCE]
How do you find " unoccupied seats of 8 rows" from given data...

unocupied seats in all the rows EXCEPT those in 8 common rows = 300-200 =100
[300+200 - unoccupied seats in all rows except those in common 8 rows] =2* unoccupied seats in 8 common rows
=> 500-100=2* unoccupied seats in 8 rows
=>400/2= Unoccupied seats in 8 rows =200
Now total unoccupied seats = 100 +200 =300

Is there any stupid mistake i committing in my approach ??

HI all,

in this question we need the number of occupied seats rows * seats/row . total seats =25*27

i) number of unoccupied seats 20 rows 10 unoccupied . 20*10=200 .
so total occupied seats of 20 rows are 27*20 - 200 . need not calculate it .
but we dont kow about the last five rows .

ii) Unoccupied seats of the last 15 rows : 15 * 20 .

dont know about the first 10 seats.

Both together .. We need to calculate the unoccupied seats.
so we need to have average number of unoccupied seats of the
25 rows ..If w have that we can calculate the answer for this question . The data we have is total number of seats . Hence not sufficient .

dzinyo00 wrote:My answer may be overly simple... but here's a go:

Basically in value DS questions, you need specific information to find the sought quantity.

neither statement gives information about occupied seats.

Wish Gmat is this simple .. !! you cannot calculate purely by looking at the options ..

I discuss this DS in two posts here:
https://www.beatthegmat.com/tough-ds-que ... 70053.html