The units digit (that is, the last digit) of $7^{62}$ is
(A) 7
(B) 1
(C) 3
(D) 9
(E) 5

## Part C: Each correct answer is worth 8.
The units digit (that is, the last digit) of $7^{62}$ is
(A) 7
(B) 1
(C) 3
(D) 9
(E) 5

## Solution

If we write out the first few powers of 7 ,

$$
7^{1}=7,7^{2}=49,7^{3}=343,7^{4}=2401,7^{5}=16807, \ldots
$$

we can see that the units digit follows the pattern $7,9,3,1,7,9,3,1,7, \ldots$ (That is to say, the units digit of a product depends only on the units digits of the numbers being multiplied together. This tells us that we only need to look at the units digit of the previous power to determine the units digit of a given power.)

So the pattern $7,9,3,1$, repeats in blocks of four. Since 60 is a multiple of 4 , this means that $7^{60}$ has a units digit of 1 , and so $7^{62}$ has a units digit of 9 .

ANSWER: (D)

## Part C