Find the value of A if the 4-digit number 3A5A is divisible by both 3 and 5.

The value of A is 5

Step-by-step explanation:

- The number is divisible by 3 if the sum of its digits is a number

divisible by 3

- Ex: 126 is divisible by 3 because the sum of its digits = 1 + 2 + 3 = 6

and 6 is divisible by 3

- The number is divisible by 5 if its ones digit is zero or 5

- Ex: 675 is divisible by 5 because its ones digit is 5

890 is divisible by 5 because its ones digit is 0

- We are looking for the value of A in the 4-digit number 3A5A which

makes the number divisible by both 3 and 5

∵ A is in the ones position

∴ A must be zero or 5

- Let us try A = 0

∵ A = 0

∴ The number is 3050

∵ The sum of the digits of the number = 3 + 0 + 5 + 0 = 8

∵ 8 is not divisible by 3

∴ 3050 is not divisible by both 3 and 5

∴ A can not be zero

- Let us try A = 5

∵ A = 5

∴ The number is 3555

∵ The sum of the digits of the number = 3 + 5 + 5 + 5 = 18

∵ 18 is divisible by 3

∴ 3555 is divisible by both 3 and 5

∴ A must be equal 5

* The value of A is 5