UPSC NDA I 2024 Mathematics Paper

To determine the units digit of a number raised to a power, we only need to look at the units digit of the base number. The units digit of 77 is 7 . Let's see what happens when we raise 7 to different powers:
71=7
72=49
73=343
74=2401
Notice a pattern in the units digits: 7,9,3,1. This pattern repeats. The units digit of any power of 7 will be one of these four digits.
Since the units digit cycles through four values, the probability that the units digit of 77n is 1 is 1 out of 4 .