The Units Digit Whisperer

'What is the units digit of...' or 'units digit of x^n' or any question where only the final digit matters.

Trying to compute the full number. Wastes time, invites errors.

1. Identify only the last digit of each number involved.
2. For powers, units digits cycle. Memorize these cycles by length:
3. • Length 1 (constant): bases ending in 0, 1, 5, 6 → units digit stays the same forever.
4. • Length 2: bases ending in 4 cycle (4, 6); bases ending in 9 cycle (9, 1).
5. • Length 4: bases ending in 2 cycle (2, 4, 8, 6); bases ending in 3 cycle (3, 9, 7, 1); bases ending in 7 cycle (7, 9, 3, 1); bases ending in 8 cycle (8, 4, 2, 6).
6. To find x^n's units digit: take n mod (cycle length) and look up where you land.
7. Multiply only the units digits. Take only the units digit of the result.

Free points if you spot the pattern. Units digit questions appeared 8-11 times each across real GRE exams from 2019-2025.