Question

How many integers are there between
1 and 100 which have 4 as a digit but
are not divisible by 4?​

Answer 1

Numbers containing 4 but not divisible by 4 are : 14, 34, 41, 42, 43, 45, 46, 47, 49, 54, 74, and 94, that is 12 numbers from 1 to 100.

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Answer 2

Given,

The number is having $\[4\]$ as a digit and is not divisible by $\[4\].$

Solution,

Know that the divisibility test of $\[4\]$ is that the last two digits of the number formed is divisible by $\[4\].$

Now, when the unit place is having $\[4\]$ at unit place and an odd number at the tens place.

$\[\begin{array}{l} \Rightarrow 5 \times 1\\ \Rightarrow 5\end{array}\]$

Now, when the unit place is having $\[4\]$ at tens place and an odd number at the units place.

$\[\begin{array}{l} \Rightarrow 5 \times 1\\ \Rightarrow 5\end{array}\]$

Know that here $\[42\,{\rm{and}}\,46\]$ are two even numbers having $\[4\]$ but are not divisible by $\[4\].$

Therefore,

$\[\begin{array}{l} \Rightarrow 5 + 5 + 2\\ \Rightarrow 12\end{array}\]$

Hence, there are $\[12\]$ integers are there between  $\[1\]$ and $\[100\]$ which have $\[4\]$ as a digit but  are not divisible by $\[4\].$