Let x = (433)24 - (377)38 + (166)54. What is the units digit of x?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8
Unit digit of (433)24 = unit digit of 324
Cyclicity of 3,
31 ends with 3
32 ends with 9
33 ends with 7
34 ends with 1
324 = 24/4 = 6 completely divisible, it ends with with 1
unit digit of (377)38 = unit digit of 738
71 ends with 7
72 ends with 9
73 ends with 3
74 ends with 1
738 = 38/4 = 2 rem.
Ends with 9.
(166)54 = 654
Any power of 6 ends with 6.
Unit digit of 654 = 6
x = 1 - 9 + 6 = 7 - 9
x = 17 - 9 = 8.