Question

If an 8 digit number 30x0867y is divisible by 88 then what is the value of (3x+y)​?

Answer 1

The value of (3x+y) is 5.

• For a number to be divisible by 88, we write the factors of 88.

Factors of 88 = 11 and 8

• Now we know the divisibility rule of 11 and 8.

• Applying the divisibility test of 11

Sum of even digits - sum of digits must be divisible by 11

(7+8+x+3) - (y+6+0+0) = 11a where a is any integer.

12+x-y = 11a   ............(Equation 1)

• Applying the divisibility test of 8

Last three digits of the number must be divisible by 8.

67y = 8b where b is any integer

• By dividing 67y by 8 we get to know that y must be 2 in order to be divisible by 8.

• Value of y will be 2

• Now substituting the value of y in equation 1, we get

12 + x - 2 = 11a

10+x = 11a

• Now 10+x must be divisible by 11, where x must be a number from 0 to 9

• Therefore x must be 1 so that 10+x must be divisible by 11

• Therefore x=1 and y =2

• Now we find the value of the expression required :

3x+y = 3(1)+2 = 5