ExplanationThe remainder when dividing an integer by 10 always equals the units digit. You can also ignore all but the units digits, so the question can be rephrased as: What is the units digit of \(3^{17} + 7^{13}\)?
The pattern for the units digits of 3 is [3, 9, 7, 1]. Every fourth term is the same. The 17th power is 1 past the end of the repeat: 17 – 16 = 1. Thus, \(3^{17}\) must end in 3.
The pattern for the units digits of 7 is [7, 9, 3, 1]. Every fourth term is the same. The 13th power is 1 past the end of the repeat: 13 – 12 = 1. Thus, \(7^{13}\) must end in 7. The sum of these units digits is 3 + 7 = 10. Thus, the units digit is 0.
_________________
SandyIf you found this post useful, please let me know by pressing the Kudos ButtonTry our free Online GRE Test