What is the remainder when 7^n + 2 is divided by 5

(1) when n is divided by 4, the remainder is 1

(2) when n is divided by 3, the remainder is 2

just wanted to confirm if this solution method is optimal

using statement 1

In case of 7^n the unit digit circles as 7,9,3,1

And in each case the unit digit of 7^n would be 7 only, which means 9 will be the unit digit, so in each case remainder is 4

using statement 2

In case of 7^n the unit digit circles as 7,9,3,1

And in each case the unit digit of 7^n can vary and we cannot pin point what is the remainder because multiple values are possible.

Therefore A is sufficient

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