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If \(n\) is a positive integer, what is the units digit of \(4^n\)?
(1) \(n^2\) is divisible by 4
(2) \(n+2\) is divisible by 6
(1) \(n^2\) is divisible by 4
(2) \(n+2\) is divisible by 6
16 Sep 2014, 01:08
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Official Solution:
If \(n\) is a positive integer, what is the units digit of \(4^n\)?
The units digit of \(4^1\) is 4.
The units digit of \(4^2\) is 6.
The units digit of \(4^3\) is again 4.
The units digit of \(4^4\) is again 6.
...
From the pattern, we can deduce that if \(n\) is a positive odd number, the units digit of \(4^n\) is 4. If \(n\) is a positive even number, the unit's digit of \(4^n\) is 6. Therefore, to answer the question, we need to determine whether \(n\) is odd or even.
(1) \(n^2\) is divisible by 4.
Since it is given that \(n\) is an integer, for \(n^2\) to be divisible by 4, \(n\) must be even. Sufficient.
(2) \(n+2\) is divisible by 6.
This statement implies that \(n+2\) is even, which means \(n\) is also even. Sufficient.
Answer: D
If \(n\) is a positive integer, what is the units digit of \(4^n\)?
The units digit of \(4^1\) is 4.
The units digit of \(4^2\) is 6.
The units digit of \(4^3\) is again 4.
The units digit of \(4^4\) is again 6.
...
From the pattern, we can deduce that if \(n\) is a positive odd number, the units digit of \(4^n\) is 4. If \(n\) is a positive even number, the unit's digit of \(4^n\) is 6. Therefore, to answer the question, we need to determine whether \(n\) is odd or even.
(1) \(n^2\) is divisible by 4.
Since it is given that \(n\) is an integer, for \(n^2\) to be divisible by 4, \(n\) must be even. Sufficient.
(2) \(n+2\) is divisible by 6.
This statement implies that \(n+2\) is even, which means \(n\) is also even. Sufficient.
Answer: D
11 Oct 2023, 23:58
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
