Unit Digits

GRE Quant Problem Solving
1

Hello GregMat!

I am following the overwhelmed plan and I am on the section that talks about unit digits. I am having trouble with determining the unit digit for bigger numbers, so I was hoping to get a bit more clarification before I move forward.

One of the problems is asking us to find the unit digit for 33^33. To do this, we first identified that the unit digit pattern for 3 is 3-9-7-1. To find the unit digit for 33, we looked at the unit digit for 3^32 and said that 32 is a multiple of 4 and therefore the unit digit is 1. I am confused by this part because 32 is also a multiple of 2, so how do we know that the unit digit would not be 9 instead? Thank you so much for your help!

2

You can think about it this way instead: You just need to find the remainder of the exponent when divided by the "cycle length.”

3

Since the unit digit for the digit 3 follows the series → 3-9-7-1

So now we have to find the 33rd number, from the above 4 numbers of the series.
So, if we consider the jumps of 4, 32nd number completes the set.
So, the 33rd number denotes the ‘1st’ number in the 4-number series.

Hope this helps.