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P=23^25-23. What is the unit digit of P ?
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03 Jan 2020, 06:28
03 Jan 2020, 06:28
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\(P=23^{25}-23\). What is the unit digit of \(P\) ?
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
Re: P=23^25-23. What is the unit digit of P ?
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03 Jan 2020, 07:33
03 Jan 2020, 07:33
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We need to find the unit digit. We can also say that finding the unit digit is finding the remainder when divided by 10.
Now for the unit digit of \(23^{25}\), we only need to focus on \(3^{25}\)
\(3^{1}\) = 3
\(3^{2}\) = 9
\(3^{3}\) = 27
\(3^{4}\) = 81
\(3^{25} = 3^{24} \times 3^{1}\)
\(3^{24}\) will have a unit digit of 1 and \(1 \times 3 = 3\)
So, the unit digit of \(3^{25} = 3\)
and \(P = 3 - 3\)
Unit digit of \(P = 0\)
OA, A
Now for the unit digit of \(23^{25}\), we only need to focus on \(3^{25}\)
\(3^{1}\) = 3
\(3^{2}\) = 9
\(3^{3}\) = 27
\(3^{4}\) = 81
\(3^{25} = 3^{24} \times 3^{1}\)
\(3^{24}\) will have a unit digit of 1 and \(1 \times 3 = 3\)
So, the unit digit of \(3^{25} = 3\)
and \(P = 3 - 3\)
Unit digit of \(P = 0\)
OA, A
Carcass wrote:
\(P=23^{25}-23\). What is the unit digit of \(P\) ?
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
Re: P=23^25-23. What is the unit digit of P ?
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03 Jan 2020, 21:09
03 Jan 2020, 21:09
1
1
Bookmarks
Carcass wrote:
\(P=23^{25}-23\). What is the unit digit of \(P\) ?
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
Here,
First we need to know the power of 3
\(3^1 = 3\) --------------unit digit = 3
\(3^2 = 9 \)--------------unit digit = 9
\(3^3 = 27\) --------------unit digit = 7
\(3^4 = 81\) --------------unit digit = 1
\(3^5 = 243\) --------------unit digit = 3
We can see in the power of 3, unit digit repeats after 3, 9, 7, 1. we have 4 terms
As per ques, it is given \(23^{25}\)
just concentrate with the unit digit 23 i.e 3.
since, after every 4th term in the power of 3, repeats itself i.e 3,9,7,1,3
so, divide \(\frac{25}{4} \) and the reminder is 1, ( 25 is the power of 23, given in the ques. If the power is 36 then we divide 36 by 4)
that means we need the 5th term
the 5 term from the 3,9,7,1,3 will be 3 (unit digit),
similarly, 6th term will be 9,
7th term will be 7
8th term will be 1 and so on...........
so, the unit digit for \(23^{25}\) = 3
and we know 3 -3 = 0 , so the unit digit for \(P=23^{25}-23 = 0 \)
