JMO

With the 5 digits 3,4,5,6 and 7, how many possible numbers can be formed which is divisible by 11.




Answer:

for the number to be divisible by 11, the difference of sum of numbers in the odd and even place must be divisible by 11.

on quick checking you may notice that if the odd terms are 5,6 and 7 and the even terms are 3 and 4
we get sum of odd terms = 5 + 6+ 7 = 18
and the sum of even terms = 3 + 4 = 7

Therefore, the difference of sum of odd and even terms = 18 - 7 = 11

Since, 11 is divisible by 11, such number is divisible by 11.

now, we can interchange the three numbers in the odd place among themselves and 2 numbers in the even place among themselves. that will not alter the divisibility of the number by 11.

53647                   54637
53746                   54736
63547                   64537
63745                   64735
73546                   74635
73645                   74536

SO, 12 numbers in total.