Question

Choose the correct option to be filled in the blank:
The number (xyz - zyx) is always divisble by _______.

• A. 9 only
• B. 11 only
• C. both 9 and 11
• D. 101 only.

Answer 1

The correct option is C both 9 and 11

The generalised form of number xyz can be written as (100×x + 10×y + 1×z)
Similarly, zyx is written as (100×z + 10×y + 1×x).
Subtracting these two numbers, we get
(100×x + 10×y + 1×z) - (100×z + 10×y + 1×x)
(100-1)×x + (10-10)×y + (1-100)×z
99x - 99z
99(x-z)
99 can be further factorised as 9×11.
So, 99(x-z) = 9×11(x-z)
Therefore, (xyz - zyx) is divisble by both 9 and 11.
So, option c is correct.