The units (ones) digit in the product $(5+1)\left(5^{3}+1\right)\left(5^{6}+1\right)\left(5^{12}+1\right)$ is
(A) 6
(B) 5
(C) 2
(D) 1
(E) 0

## Part C: Each question is worth 8 credits.
The units (ones) digit in the product $(5+1)\left(5^{3}+1\right)\left(5^{6}+1\right)\left(5^{12}+1\right)$ is
(A) 6
(B) 5
(C) 2
(D) 1
(E) 0

## Solution

We start by observing that each of $5^{3}, 5^{6}$ and $5^{12}$ have a units digit of 5 . This implies that each of $5+1,5^{3}+1,5^{6}+1$ and $5^{12}+1$ will then have a units digit of 6 .

If we multiply any two numbers having a units digit of 6 , their product will also have a units digit of 6. Applying this to the product of four numbers, we see that the final units digit must be a 6 .

ANSWER: (A)

## Part C