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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
95% (01:15) correct
5%
(00:45)
wrong
based on 178
sessions
History
Date
Time
Result
Not Attempted Yet
What is the unit digit of \(7^2 8^9 3^9 5^{203}\)?
A. 0
B. 1
C. 2
D. 3
E. 6
A. 0
B. 1
C. 2
D. 3
E. 6
Asked: What is the unit digit of \(7^2 8^9 3^9 5^{203}\)?
The unit digit of \(7^2 8^9 3^9 5^{203}\)
= the unit digit of 9* 8 *3 *5
= the unit digit of 2*5
=0
IMO A
The unit digit of \(7^2 8^9 3^9 5^{203}\)
= the unit digit of 9* 8 *3 *5
= the unit digit of 2*5
=0
IMO A
09 Jul 2021, 09:44
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Solution:
Unit digit of \(7^2 \times 8^9 \times 3^9 \times 5^{203}\) = Unit digit of \(7^2 \times\) Unit digit of \(8^9 \times\) Unit digit of \(3^9 \times\) Unit digit of \(5^{203}\)
Unit digit of \(7^2=9\)
For Unit digit of \(8^9\):
We know the cyclicity of \(8\) is \(4\).
On dividing \(9\) by \(4\). we get the remainder \(1\).
Thus, unit digit of \(8^9 = 8^1 = 8\)
For Unit digit of \(3^9\):
We know the cyclicity of \(3\) is \(4\).
On dividing \(9\) by \(4\). we get the remainder \(1\).
Thus, unit digit of \(3^9 = 3^1 = 3\)
Unit digit of \(5^{203} = 5\)
Hence Unit digit of \(7^2 \times 8^9 \times 3^9 \times 5^{203}\) = Unit digit of \(7^2 \times\) Unit digit of \(8^9 \times\) Unit digit of \(3^9 \times\) Unit digit of \(5^{203} = 9\times 8\times 3\times 5 = 0\)
Hence the right answer is Option A.
Unit digit of \(7^2 \times 8^9 \times 3^9 \times 5^{203}\) = Unit digit of \(7^2 \times\) Unit digit of \(8^9 \times\) Unit digit of \(3^9 \times\) Unit digit of \(5^{203}\)
Unit digit of \(7^2=9\)
For Unit digit of \(8^9\):
We know the cyclicity of \(8\) is \(4\).
On dividing \(9\) by \(4\). we get the remainder \(1\).
Thus, unit digit of \(8^9 = 8^1 = 8\)
For Unit digit of \(3^9\):
We know the cyclicity of \(3\) is \(4\).
On dividing \(9\) by \(4\). we get the remainder \(1\).
Thus, unit digit of \(3^9 = 3^1 = 3\)
Unit digit of \(5^{203} = 5\)
Hence Unit digit of \(7^2 \times 8^9 \times 3^9 \times 5^{203}\) = Unit digit of \(7^2 \times\) Unit digit of \(8^9 \times\) Unit digit of \(3^9 \times\) Unit digit of \(5^{203} = 9\times 8\times 3\times 5 = 0\)
Hence the right answer is Option A.
