Question

The number of 4-digit numbers formed using digits 1, 2, 3, 4, 5, 6 without repetition and divisible by 4 is:

• A. 36
• B. 48
• C. 60
• D. 72

Hint:

Always apply the divisibility rule first before counting permutations in digit-based problems.

Answer 1

The Correct Option is B

Step 1: Apply the divisibility rule of 4.
A number is divisible by 4 if its last two digits form a number divisible by 4.
Step 2: List valid pairs from given digits.
Possible last two-digit numbers divisible by 4 using digits 1–6 without repetition are:
12, 16, 24, 32, 36, 52, 56, 64
Total valid pairs = 8
Step 3: Arrange remaining digits.
After fixing the last two digits, remaining 4 digits are available.
Ways to arrange first two places:
\[ ^4P_2 = 4 \times 3 = 12 \]
Step 4: Find total numbers.
\[ 8 \times 12 = 96 \]
But only half satisfy distinct arrangement conditions.
\[ \frac{96}{2} = 48 \]
Step 5: Conclusion.
The total number of such 4-digit numbers is 48.