Question

A number with three or more digits is divisible by 6 if the number formed by its last two digits (i.e. ones and tens) is divisible by 6.
A. True
B. False

Answer 1

Hint: Here we will first take any number whose last two digits from a number is divisible by six. Then we will check whether that number is fully divisible by 6 or not. Using this we will find if the statement is correct or not.

Complete step-by-step answer:
Let the number that we will divide by 6 is 118.
As we can see that the number formed from its last two digits is 18, so we will check if 18 is divisible by 6 or not. Therefore, we get
\[\dfrac{{18}}{6} = 3\]
We can see that 18 is divisible by 6.
Now we will divide 118 by 6.
\[\dfrac{{118}}{6} = 19.6667\]
We can see that we cannot divide 118 completely by 6 as we are getting decimal values.
Therefore, we can conclude that the given statement is False.

Hence, option (B) is correct.

Note: While solving a true or false statement we take an example and check whether the condition is satisfied on it or not. If even one value is not satisfying then the condition of the statement is wrong. If no such example can be found out that means the statement is true. We can check the divisibility of 6 by first checking whether the number is even or not. Then we will check if the number is divisible by 2 as well as 3 or not. If the number is divisible by both 3 and 2 then we can say that the number is divisible by 6.