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Mathematics

If 31y5 is divisible by 3, find the value(s) of digit y.

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Answer

According to the divisibility of 3, if the sum of the digits of the number is divisible by 3 then the number is divisible by 3.

∵ 31y5 is divisible by 3

⇒ 3 + 1 + y + 5 is divisible by 3

⇒ 9 + y is divisible by 3

⇒ 9 + y = 0 , 3 , 6 , 9 , 12, ……………

⇒ y = -9 , -6 , -3 , 0 , 3, 6, 9, ……………

Since y is a digit. So, y = 0 , 3 , 6 or 9.

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