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

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

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.

Oh, just think that you can figure out!

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

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

we know that there were 17*20 people in the first 20 rows

and

7*15 people in the last 15 rows


however there is an overlap of 10 rows between the first 20 and the last 15 rows.

to know how many people occupied those 10 rows, additional information is needed.

hence answer is E

a venn diagram will help in this question

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.
Clearly not sufficient, no info about other rows

(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows.
Clearly not sufficient, no info about other rows

1+2)With 1 we know that there are 200 unoccupied in the first 20 rows, with 2 we know that there are 300 unoccupied in the last 15 rows.
Because we don't know how many seats there are in the common part (rows 10-20) both statements are still not sufficient.
E

Hope it's clear, let me know

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

E

Try seeing extremes.... statements didnt concretize the seating pattern so

divide rows into 3 parts first 10 + 10 + 5 rows

extreme 1: Middle set takes average of say 30 (higher side)

first 10 has average of <10 unoccupied (say 5..u can calculate actual possibility) + next 10 say abt 30 + last 5 has average of <20 unoccupied => would have a overall count on lower side

extreme 2: Middle set takes average of say 5

first 10 has average of >10 unoccupied (say 20..u can calculate actual possibility) + next 10 say abt 5 + last 5 has average of >20 unoccupied => would have a overall count on higher side

The logic is the middle set can act as cushion so we have a range of possibilities

Had their been no overlap....then we can find the total

Hope it helps..!

E

Try seeing extremes.... statements didnt concretize the seating pattern so

divide rows into 3 parts first 10 + 10 + 5 rows

extreme 1: Middle set takes average of say 30 (higher side)

first 10 has average of <10 unoccupied (say 5..u can calculate actual possibility) + next 10 say abt 30 + last 5 has average of <20 unoccupied => would have a overall count on lower side

extreme 2: Middle set takes average of say 5

first 10 has average of >10 unoccupied (say 20..u can calculate actual possibility) + next 10 say abt 5 + last 5 has average of >20 unoccupied => would have a overall count on higher side

The logic is the middle set can act as cushion so we have a range of possibilities

Had their been no overlap....then we can find the total

Hope it helps..!

Bunuel ..Karishma and other experts !

Is there a faster and a more logical way to solve this problem (or similar type of problems)?

Regards,
SR

Thanks Rich, that helps!

I was looking for a logical approach to tackle such problems under 2 minutes. I think it's not always fruitful to approach such problems in pure mathematical way(because one might end up loosing precious time and energy) . That's where GMAT surprise you by throwing such problems that demand for a more logical approach.
IMO such problems and methodologies should be discussed in a greater number !

Regards,
Arun

Hi Arun,

You've hit on an important point - knowing MORE than one way to approach questions can be quite helpful on Test Day. For most of your life, you were taught just 1 way to approach a question. When you took a test in school, you were supposed to use that 1 way and so you studied just that 1 way. On the GMAT though, many questions are designed to 'reward' a Test Taker for being is a critical thinker or pattern-matcher more than for being a mathematician. During your studies, it's important to practice more than one approach so that you have the flexibility on Test Day to decide which method is easiest/fastest.

Another thing worth noting is that you should NOT be trying to answer every Quant question within 2 minutes. The AVERAGE amount of time that you'll spend per question over the course of the entire Quant section is about 2 minutes, but your GOAL is actually to work in an efficient fashion. A question might require 1 minute or 3 minutes - and that's fine as long as you're not wasting time. If this question takes you 2.5 minutes, then that's not a problem.

GMAT assassins aren't born, they're made,
Rich

(1) It is given that the front 20 rows had a total of (20)(10) unoccupied seats. Therefore, the front 20 rows had a total of (20)(27) – (20)(10) = (20)(27 – 10) = 340 occupied seats. However, nothing is known about the occupancy of the seats in back 5 rows; NOT sufficient.

(2) It is given that the back 15 rows had a total of (15)(20) unoccupied seats. Therefore, the back 15 rows had a total of (15)(27) – (15)(20) = (15)(27 – 20) = 105 occupied seats. However, nothing is known about the occupancy of the seats in front 10 rows; NOT sufficient.

Given (1) and (2) together, it is possible to vary the number of occupied seats in rows 11 through 20—the rows that belong to both the front 20 rows and the back 15 rows—to obtain different values for the total number of occupied seats. For example, suppose that rows 1 through 12 were fully occupied, row 13 had 16 occupied seats, rows 14 through 21 were unoccupied, row 22 had 24 occupied seats, row 23 had 11 occupied seats, and rows 24 and 25 were unoccupied. Then the front 20 rows would have (12)(27) + 16 = 340 occupied seats, the back 15 rows would have (2)(27) + 16 + 24 + 11= 105 occupied seats, and there would be a total of 340 + 24 + 11 = 375 occupied seats. On the other hand, suppose that row 1 was unoccupied, rows 2 through 13 were fully occupied, row 14 had 16 occupied seats, rows 15 through 24 were unoccupied, and row 25 had 8 occupied seats. Then the front 20 rows would have (12)(27) + 16 = 340 occupied seats, the back 15 rows would have (3)(27) + 16 + 8 = 105 occupied seats, and there would be a total of (12)(27) + 16 + 8 = 348 occupied seats; NOT sufficient.

The correct answer is E;
both statements together are still not sufficient.

I am still having a hard time visualizing this. According to this diagram, it seems there are actually 30 rows?
Shouldn't the overlap start at 20 (which means the sub-group in the back will 'cut' into the first 20 by 10)?

Hi CEdward,

The diagram that you're referring to has a 'typo' in it. The prompt specifically states that there are 25 rows - and the 'overlap' in the rows mentioned in Fact 1 vs. Fact 2 is actually 10 rows (not 5 rows). However, the overall logic behind that explanation is still correct.

GMAT assassins aren't born, they're made,
Rich

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