Question : Let $x$ = (433)24 – (377)38 + (166)54. What is the unit digit of $x$ ?
Option 1: 8
Option 2: 9
Option 3: 7
Option 4: 6
Correct Answer: 8
Solution :
Given: $x$ = (433)
24
– (377)
38
+ (166)
54
We can write 433
24
= 433
(4 × 5) + 4
, 377
38
= 377
(4 × 9) + 2
So, the unit digit of 433
4
= 1 and the unit digit of 377
2
= 9
The last digit for the(166)
54
will always be 6 as the unit digit of a power of a number having the last digit 6 will always be 6.
$\therefore$ $x$ = 1 – 9 + 6 = 7 – 9 → Unit digit = 17 – 9 = 8
Hence, the correct answer is 8.
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