A SCOUNTMASTER WANTED HIS 72 CADETS TO TAKE PART IN PARADE,MARCHING IN RECTANGULAR FORMATION.HE WANTED THAT THE COLUMNS AS WELL AS THE ROWS MUST HAVE MORE THAN 6 STUDENTS.IF EACH ROW HAS FEWER STUDENTS THAN THE NUMBER OF THE COLUMNS ,HOW MANY ROWS WILL HE BE ABLE TI MAKE IN THE FORMATION HE WISHES?

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Solution

Answer :

To arrange cadets in desired arrangement we make prime factors of 72 ( Number of cadets ) .

72 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3

So,

We can see that only at

8 $\times$ 9 = 72

We get , Number of column and number of rows have more than 6 cadets .

And

Column = 9 So, rows = 8 , So, That is also satisfied the second condition .

So,

Number of rows = 8 ( Ans )

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