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N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 2. What is the remainder when N is divided by 12?

 Nov 14, 2022
 #1
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The remainder is 8.

 Nov 14, 2022
 #2
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The number N has a remainder of 2 when divided by 3 and 4, so the number will have a remainder of 2 when divided by \(3\cdot 4 = 12\). Thus, N is of the form \(N = 12x+2\). This easily shows that the remainder when N is divided by 12 is \(\boxed{2}\) . 

 

Hope this helped :P

 Nov 14, 2022

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