Question

Determine which one of the following numbers is divisible by 2, 9 and 11.

• A. 101
• B. 132
• C. 200
• D. 198

Answer 1

The correct option is D 198

101 is not even, so it is not divisible by 2.
132 - divisible by 2(even)
$\Rightarrow$ sum of digits = 1 + 3 + 2 = 6, which is not divisible by 9. Hence 132 is not divisible by 9.

200 - divisible by 2(even)
$\Rightarrow$ sum of digits = 2 + 0 + 0 = 2, which is not divisible by 9. Hence 200 is not divisible by 9.

198 - divisible by 2(even)
$\Rightarrow$ sum of digits = 1 + 9 + 8 = 18, which is divisible by 9. Hence 198 is divisible by 9.
$\Rightarrow$ starting from the right and adding up all digits at odd position O = 8 + 1 = 9, starting from the right and adding up all digits at even position E = 9; O - E = 9 - 9 = 0,

Hence 198 is divisible by 11 (If the difference [O–E] is either 0 or 11, the number is divisible by 11)