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Remainder when 3^8n+3 + 5 is divided by 10
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01 Apr 2025, 15:27
01 Apr 2025, 15:27
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Quantity A |
Quantity B |
Remainder when \(3^{8n+3} + 5\) is divided by 10 |
Remainder when \(7^{8n+3} + 5\) is divided by 10 |
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Re: Remainder when 3^8n+3 + 5 is divided by 10
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05 Apr 2025, 04:15
05 Apr 2025, 04:15
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For all values of $n$, the units digit of $\(3^{8 n+3}\)$ is 7 .
The units digit of $\(3^{8 n+3}+5\)$ is 2 and therefore, when $\(3^{8 n+3}+5\)$ is divided by 10 , it leaves a remainder 2 .
Therefore, Column $\(\mathrm{A}=2\)$. For all values of $n$, the units digit of $\(7^{8 n+3}\)$ is 3 . So, the units digit of $\(7^{8 n+3}+5\)$ is 8 and therefore, when it is divided by 10 , it leaves a remainder 8 .
Therefore, Column $\(\mathrm{B}=8\)$.
Hence, Column B $>$ Column A.
Thus, the correct answer is $B$.
The units digit of $\(3^{8 n+3}+5\)$ is 2 and therefore, when $\(3^{8 n+3}+5\)$ is divided by 10 , it leaves a remainder 2 .
Therefore, Column $\(\mathrm{A}=2\)$. For all values of $n$, the units digit of $\(7^{8 n+3}\)$ is 3 . So, the units digit of $\(7^{8 n+3}+5\)$ is 8 and therefore, when it is divided by 10 , it leaves a remainder 8 .
Therefore, Column $\(\mathrm{B}=8\)$.
Hence, Column B $>$ Column A.
Thus, the correct answer is $B$.
gmatclubot
Re: Remainder when 3^8n+3 + 5 is divided by 10 [#permalink]
05 Apr 2025, 04:15
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