Question

All the even numbers from 2 to 98 inclusive, except those ending in
0, are multiplied together. What is the rightmost digit, that is,
the units digit of the product?
(a) 0 (b) 2 (c) 4 (d) 6 (e) 8

Answer 1

"Math is the study of patterns"

our multipliers are:
2,4,6,8,12,14,16,18,22,24,....94,96,98

multiplying them starting with 2x4 we get answers that end in
8,8,4,8,2,2,6,2, and then the same sequence repeats.
You will also notice that after each multiplier that ends in 8, like 18 or our last one 98, the answer ends in either 6 or 4.

So all we have to do is decide if it's a 4 or 6

Here is my reasoning for that.
There are 48 even numbers up to the 98, but we have to exclude mulipliers ending in 0 such as 10,20,..
there are 10 of these, so we are down to 40 multipliers resulting in <b>39</b> answers
Our loop of last numbers has a length of 8
39÷8 = 4.875 wich is near the end of the loop of reapeating digits,
<b>so it must be the 6</b>