Question

The Number $31,13,11,31,13,11,31,13,11,311$ Is Divisible By both $3$ And $11$. (True / False)

• A. True
• B. False

Answer 1

The correct option is B False

The given statement is false.

The number$31,13,11,31,13,11,31,13,11,311$ is neither divisible by $3$nor by $11.$

According to the rules of divisibility:

A number is divisible by $3$ only if the sum of its digits is divisible by $3.$

Sum of digits of given number $=3+1+1+3+1+1+3+1+1+3+1+1+3+1+1+3+1+1+3+1+1=35$

Since,$35$ or$3+5=8$ is not divisible by $3$.

A number is divisible by $11$ only if the difference of the sums of alternating digits is divisible by $11$.

$(3+1+1+3+1+1+3+1+1+3+1)-(1+3+1+1+3+1+1+3+1+1)$

$=19–16=3$

$3$is not divisible by $11$.

Therefore, the number $31,13,11,31,13,11,31,13,11,311$ is neither divisible by $3$ nor by $11.$