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22 March, 14:13

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

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  1. 22 March, 15:08
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    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
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