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Which of the following can not be the units digit of 7x if x is an int
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10 Feb 2022, 07:00
10 Feb 2022, 07:00
Expert Reply
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Question Stats:
92% (00:42) correct
7% (00:26) wrong based on 14 sessions
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Which of the following can not be the units digit of \(7^x\) if x is an integer greater than 1?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Re: Which of the following can not be the units digit of 7x if x is an int
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10 Feb 2022, 08:02
10 Feb 2022, 08:02
\(7^1=7\) (last digit is 7)
\(7^2=9\) (last digit is 9)
\(7^3=3\) (last digit is 3)
\(7^4=1\) (last digit is 1)
\(7^5=7\) (last digit is 7 again!)
...
So, the cyclicity of 7 is 4.
In the cyclicity of \(7\), the repeated digits are \(1, 3, 7, 9\)
Only \(5\) will not be there.
Answer C
\(7^2=9\) (last digit is 9)
\(7^3=3\) (last digit is 3)
\(7^4=1\) (last digit is 1)
\(7^5=7\) (last digit is 7 again!)
...
So, the cyclicity of 7 is 4.
In the cyclicity of \(7\), the repeated digits are \(1, 3, 7, 9\)
Only \(5\) will not be there.
Answer C
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Re: Which of the following can not be the units digit of 7x if x is an int
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10 Feb 2022, 11:05
10 Feb 2022, 11:05
1
Carcass wrote:
Which of the following can not be the units digit of \(7^x\) if x is an integer greater than 1?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Alternate solution....
\(7^x = (7)(7)(7)(7)....\)
Since there are no 7's in the prime factorization of \(7^x\), we can be certain that \(7^x\) is NOT divisible by 5.
Since all integers with units digit 5 ARE divisible by 5, we can be certain that the correct answer is C.
