If k is a positive integer, what is the remainder when 2^k is divided by 10?
1) k is divisible by 10
2) k is divisible by 4
1) k is divisible by 10
2) k is divisible by 4
The problem is asking for the remainder when 2^k is divided by 10. You need to realize that the problem lies with the last digit of 2^k, since the remainder of dividing a number by 10 will always be its last digit.
You should know that there is a certain regularity to the last digit, depending on the nature of k.
Let's start with the basics:
2^1 = 2 - last digit 2
2^2 = 4 - last digit 4
2^3 = 8 - last digit 8
2^4 = 16 - last digit 6
2^5 = 32 - last digit 2 - and the last digit repeats from now on.
This forms a pattern for 2^k:
a. when k = 4n + 1, last digit = 2
b. when k = 4n + 2, last digit = 4
c. when k = 4n + 3, last digit = 8
d. when k = 4n, last digit = 6.
This means that the last digit of 2^k is linked to whether k is divisible or not by 4, thus making the second stmt sufficient, with answer B
