When we compute with remainders, we can either take the remainder first and then compute, or compute first and then take the remainder.

7^2 = 49 has remainder 49 when it is divided by 50.
When numbers are divided by 50, a remainder of 49 can be thought of as a remainder of -1.
Therefore, 7^100 ~ (7^2)^50 ~ (49)^50 ~ (-1)^50 ~ 1.

When 7^100 is divided by 50, it has remainder 1.

Therefore, A is the answer.