Question

All of the even numbers from $2$ to $98$ inclusive, excluding those ending in $0,$ are multiplied together. What is the rightmost digit (the units digit) of the product?

$0$

$2$

$4$

$6$

$8$

Answer: D

Concepts:units digit pairing and grouping

Difficulty rating: 1580

Solution:

We only care about the units digit, which means that the tens digits don't matter.

Then we have $10$ groups of $2 \cdot 4 \cdot 6 \cdot 8 = 384.$

The units digit of each group is $4.$ We now need to find the units digit of $4^{10}.$

The units digit of $4^2 = 16$ is $6.$ This means we only need to find the units digit of $6^5.$

Note that every power of $6$ always ends in a $6$ (e.g. $6, 36, 216, \cdots$ ).

Thus, D is the correct answer.

1997 AMC 8 Problem 25

Answer: D

Difficulty rating: 1580

Solution:

Problem 25 in Other Years