Question 55

If the nine-digit number 708x6y8z9 is divisible by 99, then whatis the value of x + y + z?

Solution

To be divisible by 99, the number has to be divisible by 11 and 9 both.

For divisibility by 11,

7 + 8 + 6 + 8 + 9 - 0 + x + y + z

(38 - x + y + z) has to be divisible by 11.

For divisibility by 9,

(38 + x + y + z) has to be divisible by 9.

By option C),

x + y + z = 16

(38 - x + y + z) = 38 - 16 = 22 is divisible by 11.

(38 + x + y + z) = 38 + 16 = 54 is divisible by 9.

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