Question

If the number 654xy is divisible by 90 then ( x + y ) = ?

explain

Answer 1

We can obtain results by hit & trial method easily.

For instance

90 * 700=63000
90*750= 67500

Now 654xy /90 lies between 700 and 750.

Try one more guess

90*725= 65250
90*726=65340
90*727= 65430 ✔
90*728=65520

Hence we have found a number divisible by 90 and has it's first three digits as 6,5,4.

Now comparing with given number ;

654xy= 65430

We get x =3, y=0.

Now, ( x + y) = 3 + 0 =3.

As we know there are numerous methods of solving, we may get the solution in other ways using basic algebra. But in that process goes very long. Hence, Preferably this method was used.

∴ ( x + y) =3

Answer 2

Given that the number 654xy is divisible by 90.

For a number to be divisible by 90 it must be divisible by 9 and 10.

Now for 654xy to be divisible by 90, The sum of digits in the number must be divisible by 9 and the last digit should be zero because the number should also be divisible by 10.

Hence,

6 + 5 + 4 + x + y 

The last digit should be 0 i.e y = 0

= > 6 + 5 + 4 + x + 0

  So, (6 + 5 + 4 + x + 0) = (15 + x) 

if x is 3 then the sum will be divisible by 9.

        = (15 + 3)

        = 18. (Divisible by 9).


Therefore x + y = 3 + 0

                           = 3.


The result is x + y = 3.


Hope this helps!