[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
What is the units digit of 2^105+3^105+4^105+5^105?
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- Max@Math Revolution
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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
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
Math Revolution
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Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]