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
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What is the maximum number of arrangements in which N stud
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hemant_rajput
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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.
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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Brent@GMATPrepNow
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Hmmm, I'm not sure why the word "maximum" is needed above. That said, let's solve the question.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.
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
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hemant_rajput
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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.
