Q168 / 270 · NDA 2025 (Phase 2) · Mathematics
How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?
- A$3$
- Correct answerB$6$
- C$9$
- D$12$
Solution
A number is divisible by $4$ if the number formed by its last two digits is divisible by $4$.
Using the digits $1, 2, 3, 4$ without repetition, the possible two-digit numbers at the end that are divisible by $4$ are $12, 24$, and $32$.
For each of these endings, the remaining two digits can be arranged in the first two places in $2! = 2$ ways.
Total number of such $4$-digit numbers is $3 \times 2 = 6$.
Answer: $6$
Using the digits $1, 2, 3, 4$ without repetition, the possible two-digit numbers at the end that are divisible by $4$ are $12, 24$, and $32$.
For each of these endings, the remaining two digits can be arranged in the first two places in $2! = 2$ ways.
Total number of such $4$-digit numbers is $3 \times 2 = 6$.
Answer: $6$
Hence, the correct answer is option: 'B'.