Question

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____

Answer 1

Correct Answer: 21

Determining Numbers Divisible by 15

To determine numbers divisible by 15, the following conditions must be met:

• The last digit must be 5 (a condition for divisibility by 5).
• The sum of the digits must be divisible by 3 (a condition for divisibility by 3).

Possible Combinations

Combination	Numbers Formed	Sum of Digits
1215	3	9
2235	3	12
3115	3	10
1155	3	12
2355	6	15
3555	3	18

Explanation:

For each combination of digits, the number of possible arrangements (permutations) that satisfy the conditions is determined. For example, the combination 1215 has 3 valid numbers since the arrangement must end with 5 and satisfy divisibility by 3.

Similar calculations are performed for all other combinations.

Total Numbers:

Total Numbers = 3 + 3 + 3 + 3 + 6 + 3 = 21

Answer 2

The correct answer is 21.
For number to be divisible by 15, last digit should be 5 and sum of digits must be divisible by 3.