Question

Out of the 720 six digit numbers that can be formed by using all the six digits 2,3,4,5,7 and 8 , the number of such numbers divisible by 11 is

• A. 0
• B. 36
• C. 72
• D. 96

Answer 1

The correct option is C

72

1.Let the sum of the odd placed digits be x and the sum of the even placed digits be y.

Now x + y = 29 ; x - y = - 11, 0 or 11 since the 6 - digit numbers are divisible by 11.

Since x + y = 29, either x is odd and y is even or x is even and y is odd. Hence x - y ≠ 0. Thus from x - y = - 11 and x + y = 29 we get x = 9, y = 20 and from x - y = 11 and x + y = 29, we get x = 20,

y = 9.

The number of such possibilities for x,y from the corresponding sets of number elements {8,7,5} or {2,3,4} is 3! each.

∴ Number of such 6 - digit numbers = 2 * 3! * 3! = 72.