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What is the maximum number of arrangements in which N stud

Expert replies
by varun289 » Fri Jan 25, 2013 8:35 pm
What is the maximum number of arrangements in which N students can be seated in a row of N seats at a movie theater, if all students from the same college are to sit next to each other?

All students come from three colleges, X, Y, and Z that sent 12, 10, and 9 students, respectively.
N is a prime number between 30 and 40.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

EACH statement ALONE is sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

A while IMO-C
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Source: — Data Sufficiency |

by hemant_rajput » Sat Jan 26, 2013 1:59 am
IMO E

from statement 1 we know student only from 3 colleges but there might be other college involved.

from statement 2 we know either N = 31 or N = 37.

now using both statement still we are not able to decide what is the value of N, because there might be more college having total of six student or there might be none.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by Brent@GMATPrepNow » Sat Jan 26, 2013 9:37 am
varun289 wrote:What is the maximum number of arrangements in which N students can be seated in a row of N seats at a movie theater, if all students from the same college are to sit next to each other?

1) All students come from three colleges, X, Y, and Z that sent 12, 10, and 9 students, respectively.
2) N is a prime number between 30 and 40.
Hmmm, I'm not sure why the word "maximum" is needed above. That said, let's solve the question.

Target question: What is the number of arrangements in which N students can be seated in a row of N seats if all students from the same college are to sit next to each other?

Statement 1: All students come from three colleges, X, Y, and Z that sent 12, 10, and 9 students, respectively.

Okay, so we're seating a total of 31 students in 31 seats, with 12 students from college X, 10 students from college Y, and 9 students from college Z.
At this point, even if we know nothing about counting techniques, we could start listing arrangements until we've counted every possible outcome.
So, it appears that statement 1 is SUFFICIENT.

Aide: the total number of arrangements = (12!)(10!)(9!)(3!)

Statement 2: N is a prime number between 30 and 40.
This means that N=31 or N=37
Also, we don't know the number of students from each college.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by hemant_rajput » Sat Jan 26, 2013 10:39 am
OOPS!, I misinterpreted the first statement. Thanks Brent for an explanation.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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