Question

A five digit number is formed by the digits 1, 2, 3, 4, 5 with out repetition then total numbers which are divisible by 4 –

• A. 24
• B. 48
• C. 72
• D. 36

Answer 1

Answer: (A)

24

Answer 2

Let a 5 digit number be a b c d e it will be divisible by 4 if 2d + e is divisible by 4.

2d + e divisible by 4 \ e must be even (even)

\mathbf{\& 2(d + e/2)divisibleby4e = 2,d = 1,3,5} \\ \mathbf{\& 4case} \\ \mathbf{\& S}\mathbf{h}\mathbf{ouldbeevene = 4,d = 2} \end{array} \right\}$$ Total number of ways = 4 × 3! = 24.