Question

How many four-digit numbers, each divisible by 4 can be formed using the digits 1, 2,3,4 and 5, repetitions of digits being allowed in any number?

• A. $100$
• B. $150$
• C. $125$
• D. $75$

Answer 1

Answer: (C)

$125$

We know that the rule for divisibility is that the last $2$ digits must be divisible by $4$ as whole like $16,04,08,12$ etc.

So, our last $4$ digits can be $12,24,32,44,52,32$ only suppose we $1st$ take $12$ and then we have $5$ choice for $1st$ digit of repetition is allowed and similarly $5$ for $2nd.$

$\therefore 25$ numbers ending with, so total number $25\times 5=125$

Hence, the answer is $125.$