Question

the sum of all the numbers formed by the digits x,y and z of the number xyz is divisible by
a. 11
b. 33
c. 37
d. 74

Answer 1

Answer:

Step-by-step explanation:

all the different numbers formed by  x y and z are:

    x   y   z    =  100 x + 10 y + z

   x    z   y    =  100 x + 10 z + y

   y   x   z    =  100 y  +  10 x + z

   y   z   x    = 100 y  + 10 z  + x

   z   x  y      = 100 z  + 10 x + y

   z   y  x      = 100 z + 10 y + x

               

sum =  200 x  + 200 y + 200 z  +  20y + 20 x + 20 z + 2 z + 2 x + 3 y

      = 222 x  + 222 y + 222 z

      = 3 * 37 * 2 * (x + y + z)

So the sum is divisible by  37  and 74