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Permutations and Combination

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Permutations and Combination

by BTGmoderatorRO » Sun Dec 17, 2017 5:13 am
If three students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then two rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?

A. 0
B.1
C. 4
D. 5
E. 9

OA is C

I would employ the help of an expert here to give the mathematical approach to solve this question.
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by Jay@ManhattanReview » Mon Dec 18, 2017 3:12 am
Roland2rule wrote:If three students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then two rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?

A. 0
B.1
C. 4
D. 5
E. 9

OA is C

I would employ the help of an expert here to give the mathematical approach to solve this question.
Say there are n numbers of rows.

Thus from the first arrangement, we have the total number of students = 3n + 6 and from the second arrangement, we have 6n - 6*2 = 6n - 12

Thus, 3n + 6 = 6n - 12 => n = 6 rows and the total number of students = 3*6 + 6 = 24

The number of students that have to sit a row such that each row has equal number of students and all the students are seated

= Total number of students/number of rows = 24/6 = 4

The correct answer: C

Hope this helps!

-Jay
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