Question

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
• B. 6
• C. 9
• D. 12

Hint:

For divisibility by 4 rules, always focus exclusively on the last two digits. Once those are fixed, just permute the remaining digits.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are tasked with forming 4-digit numbers using the digits 1, 2, 3, and 4 without repetition such that the resulting number is divisible by 4.
Step 2: Key Formula or Approach:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Step 3: Detailed Explanation:
We have the digits \{1, 2, 3, 4\}.
Let's find all possible two-digit combinations (without repetition) from this set that are divisible by 4.
The possible two-digit numbers ending the 4-digit number can be: 12, 24, 32.
(Other combinations like 14, 21, 23, 31, 34, 41, 42, 43 are not divisible by 4).
Now, let's consider each valid case for the last two digits:
Case 1: The number ends in 12.
The remaining digits are \{3, 4\}. They can be arranged in the first two positions in $2! = 2$ ways (3412, 4312).
Case 2: The number ends in 24.
The remaining digits are \{1, 3\}. They can be arranged in the first two positions in $2! = 2$ ways (1324, 3124).
Case 3: The number ends in 32.
The remaining digits are \{1, 4\}. They can be arranged in the first two positions in $2! = 2$ ways (1432, 4132).
Total possible 4-digit numbers = $2 + 2 + 2 = 6$.
Step 4: Final Answer:
The number of such 4-digit numbers is 6.