Problem Solving

[GMAT math practice question]

If a is the remainder when 1993^2021 is divided by 10, what is the value of |a - 1| + |a - 2| + |a - 3| + |a - 4| + |a - 5|?

A. 2
B. 3
C. 4
D. 5
E. 6

=>

3^1 = 3~3, 3^2 = 9~9, 3^3 = 27~7, 3^4 = 81~1, 3^5~3, …
So, the units digits of 3^n have a period of 4.
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, 3^n has the units digit of 3 if n has a remainder of 1 when it is divided by 4.
The remainder when 2021 is divided by 4 is 1, so the units digit of 1993^(2021) is 3 and a = 3.

|a - 1| + |a - 2| + |a - 3| + |a - 4| + |a - 5|
= |3 - 1| + |3 - 2| + |3 - 3| + |3 - 4| + |3 - 5|
= 2 + 1 + 0 + 1 + 2
= 6

Therefore, E is the correct answer.
Answer: E