Aptitude - Numbers - Discussion

By solving through divisibility method we can aslo get value X = 5 and Y = 2. Is it correct?

5 and 2 are not there in the answers given. Hence 8 and 5 selected.

Please can anyone explain from (0 + x + 7) - (y + 6 + 4) =x - y - 3. Must be either 0 or 11?

Thank you @Tanya.

Thank you @Tanya Mazumdar.

Thanks @Tanya Mazumdar.

Thanks @Tanya.

How can come x=2 or 8?

Please explain.

Divisibility by 3 condition is sum of all the digits are divisible by 3.
Divisibility by 11 condition is diff of sum of odd and even place digits should be equal to zero.

Let the missing digits be x and y.
Then given value becomes 476xy0.
For divisible by 11: (4+6+y)-(7+x+0)=0
=> 10+y=7+x.
=> y = (7-10)+x.
=> y = x-3 ------> (1).

Now for divisibility by 3: 4+6+7+x+y+0 => 17+x+y.
=> 17+x+x-3 => 14+2x should be divisible by 3,
now try substuiting values:
x=1: 16 not div by 3,
x=2: 18 div by 3,
x=3: 20 not div by 3.
.
.
x=5: 24 div by 3.

So for x=2
=> y= -1 which is not valid.
=> for x= 5
=> y=2. then 10+y =7+x
so the answer 2 and 5.
It will work for 8 and 5.

The sum of the numbers should be divisible by 3 in order for the number to be completely divisible by 3.

So 4+7+6+0=17.

Adding the numbers in the options so that the total number is divisible by 3.

17+ 8+5 = 30.
Hence option C is correct.