Question

if x is a positive integer, which of the following cannot be the units digit of 7^x?

a) 1
b) 3
c) 5
d) 7
e) 9

and why?

Answer 1

Consider the integer 345 = 3×100 + 4×10 + 5×1.
5 is the unit digit because it has the weight of ones. 4 has the weight of tens and 3 has the weight of hundreds.

So, for unit digit of 7^x, we consider the first few values of x to see if there is a pattern.
When x=1, 7^x = 7. Unit digit is 7
When x=2, 7^x = 49. Unit digit is 9
When x=3, 7^x = 343. Unit digit is 3
When x=4, 7^x = 2401. Unit digit is 1
When x=5, 7^x = 16807. Unit digit is 7
and so on.

Pattern for that unit digit (last digit) is 7, 9, 3, 1.
So 0, 2, 4, 5, 6 and 8 cannot be the unit digit of 7^x