Question

A six digit no 4x4y96 is divisible by 88.Find the value of (x+2y)

Answer 1

The given number 4x4y96.

Since, 4x4y96 is divisible by 88 = 8 × 11 , then it is divisible by 8 and 11.

Divisibility rule of 8:

In a given number if the number formed with its last 3 digits are divisible by 8 or last 3 digits are '0' s then that number is divisible by 8 .

i ) Here , Last 3 digits are y96.

If y = 2,4,6 and 8 then y96 is divisible by 8.

Divisibility rule of 11:

If the difference between the sum of digits in odd places and sum of digits in even places of a number is a multiple of 11 or equal to zero , then the given number is divisible by 11.

The difference of (6+y+x);and ( 9 + 4 + 4 = 17 )

= 17 - ( 6 + y + x ) = 11 + y + x should be divisible by 11.

If y = 2 then x = 9

If y = 4 then x = 7

If y = 6 then x = 5

If y = 8 then x = 3

In above conditions 4x4y96 is divisible by 88.

Now ,

1 ) if (9,2) then value of (x+2y) = 13

2 ) if (7,4) then value of (x+2y) = 15

3 ) if (5,6) then value of (x+2y) = 17

4 ) if (3,8) then value of (x+2y) = 19

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