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If \(M\) and \(N\) are positive integers greater than \(1,\) what is the remainder when the expression

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If \(M\) and \(N\) are positive integers greater than \(1,\) what is the remainder when the expression

by M7MBA » Wed Sep 09, 2020 1:24 am

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If \(M\) and \(N\) are positive integers greater than \(1,\) what is the remainder when the expression \(22^{3M}\cdot 39^{2N}+14^{2(M+N)}\) is divided by \(5?\)

(1) \(M = 13\)
(2) \(N = 14\)

Answer: A

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: If \(M\) and \(N\) are positive integers greater than \(1,\) what is the remainder when the expression

by swerve » Wed Sep 09, 2020 6:24 am

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M7MBA wrote: ↑
Wed Sep 09, 2020 1:24 am
 If \(M\) and \(N\) are positive integers greater than \(1,\) what is the remainder when the expression \(22^{3M}\cdot 39^{2N}+14^{2(M+N)}\) is divided by \(5?\)

(1) \(M = 13\)
(2) \(N = 14\)

Answer: A

Source: e-GMAT
\(22^{3M} \cdot 39^{2N} + 14^{2(M+N)}mod5= (6MN+2M+2N)mod5\); \(2(3MN+M+N)mod5;\)

1) \(M=13\);
\(2(39N+13+N)mod5 = (80N+26)mod5 = 1\);
SUFFICIENT \(\Large{\color{green}\checkmark}\)

2) \(N=14\);
\(2(42M+14+M)mod5 = (86M + 28)mod5 = (M+3)mod5\);
NOT SUFFICIENT \(\Large{\color{red}\chi}\)

Therefore, A is the correct answer.
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