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What is the units digit of 2^105+3^105+4^105+5^105?

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by Max@Math Revolution » Thu Feb 22, 2018 1:05 am
[GMAT math practice question]

What is the units digit of $$2^{105}+3^{105}+4^{105}+5^{105}?$$

A. 3
B. 4
C. 5
D. 6
E. 7
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by Max@Math Revolution » Sun Feb 25, 2018 5:29 pm
=>

The units digit of any integer raised to the exponent 5 is the same as the units digit of the integer:
0^1 and 0^5 have remainder 0
1^1 and 1^5 have remainder 1
2^1 and 2^5 have remainder 2
...
9^1 and 9^5 have remainder 9
when divided by 10.

Therefore, the units digit of 2^105+3^105+4^105+5^105 is same as the units digit of 2 + 3 + 4 + 5 = 14.
It is 4

Therefore, B is the answer.

Answer: B
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