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16 Sep 2014, 00:47
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16 Sep 2014, 00:47
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Official Solution:
What is the unit's digit of \(7^{75} + 6\)?
A. 1
B. 3
C. 5
D. 7
E. 9
The unit's digit of 7 raised to a positive integer power cycles in a pattern of four: 7-9-3-1. Given that \(75 = 4 *18 + 3\), the unit's digit of \(7^{75}\) aligns with the unit's digit of \(7^3\), which is 3.
Consequently, the unit's digit of \(7^{75} + 6\) is: 3 + 6 = 9.
Answer: E
What is the unit's digit of \(7^{75} + 6\)?
A. 1
B. 3
C. 5
D. 7
E. 9
The unit's digit of 7 raised to a positive integer power cycles in a pattern of four: 7-9-3-1. Given that \(75 = 4 *18 + 3\), the unit's digit of \(7^{75}\) aligns with the unit's digit of \(7^3\), which is 3.
Consequently, the unit's digit of \(7^{75} + 6\) is: 3 + 6 = 9.
Answer: E
05 Mar 2015, 08:44
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Bunuel
I don't understand that. I assumed that 75 is a multiple of 5, and 7^5 ends in 7, so I 7 + 6 = unit digit of 3. Where does that 4*18 + 3 come from? I mean.. I could simply say 75 = 9*8 + 3? Is that how you decide what unit digit it is?
