Question

A number is divisible by $8$ if the number formed by the digit in .….. placed is divisible by $8$.
(A) units and tens
(B) tens and hundred
(C) units
(D) units, tens and hundred

Answer 1

Hint:
Use the divisibility rule of eight, that says “if the number formed by the last three digits of a number is divisible by eight, then that number will also be divisible “. The last three places in a number are also named as units of one's place, tens place and hundreds place respectively. Use this information to check for the correct option.

Complete step by step solution:
Here in this problem, we need to find the correct option according to the divisibility rule of eight.
A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base ten, numbers.
For any number that can be written as $'abcde'$ where $a, b, c, d{\text{ and }}e$ are the digits of this five-digit number, $'e'$ is considered to be at units or one's place, $'d'$ is considered to be at tens place, $'c'$ is at the hundreds place, $'b'$ is at thousands place and so on.
According to the rule of eight, if the number formed by the last three digits of a number is exactly divisible by eight then the number itself will also be divisible by eight.
$ \Rightarrow $ The number formed from ones or units place, tens place and hundreds place of a number will determine the divisibility of the number.
So the statement should be: “: A number is divisible by $8$ if the number formed by the digits in units, tens and hundreds placed is divisible by $8$ “.

Hence, the option (D) is the correct answer.

Note:
For example, in $30248$ the number formed from the last three digits or units, tens and hundreds place is $248$. This can be written as $248 = 31 \times 8$ i.e. it is a multiple of eight. Therefore, according to the divisibility rule of eight, we can say the number $30248$ is divisible by $8$.
Similar to this, the divisibility rule for $2$ is to check divisibility of units placed with $2$. And the divisibility rule for ${2^2} = 4$ is to check divisibility of units and tens place with $4$.