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Is N an integer? 1) 2N is an integer 2) 5N is an integer (DS)

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Is N an integer? 1) 2N is an integer 2) 5N is an integer (DS)  [#permalink]

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New post 09 Sep 2018, 09:19
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Is N an integer? 1) 2N is an integer 2) 5N is an integer

I read a related post at following link - https://gmatclub.com/forum/is-n-an-inte ... 61417.html
But somehow i could not figure out how they have concluded C as an answer option.

Thanks in advance!!
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Re: Is N an integer? 1) 2N is an integer 2) 5N is an integer (DS)  [#permalink]

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New post 09 Sep 2018, 10:11
divyajoshi12 wrote:
Is N an integer? 1) 2N is an integer 2) 5N is an integer

I read a related post at following link - https://gmatclub.com/forum/is-n-an-inte ... 61417.html
But somehow i could not figure out how they have concluded C as an answer option.

Thanks in advance!!


1) 2N is an integer
this is possible when N = 1/2 , 3/2,5/2(basically divided by 2) ,0 , any other +ve of -ve integers
insufficient

2) 5N is an integer
same as above
N = 1/5 , 2/5,3/5,4/5(basically divided by 5) , 0 , any other +ve of -ve integers
insufficient

using both

we can have N = either 0 or any other +ve of -ve integers
in both the cases N should be an integer
sufficient
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Re: Is N an integer? 1) 2N is an integer 2) 5N is an integer (DS)  [#permalink]

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New post 09 Sep 2018, 11:36
divyajoshi12 wrote:
Is N an integer?
1) 2N is an integer
2) 5N is an integer


\(N\,\mathop = \limits^? \,\,\operatorname{int}\)

\(\left( 1 \right)\,\,2N = \operatorname{int} \,\,\,\,\left\{ \begin{gathered}
\,N = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,N = \frac{1}{2}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,5N = \operatorname{int} \,\,\,\,\left\{ \begin{gathered}
\,N = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,N = \frac{1}{5}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\end{gathered} \right.\)

\(\left( {1 + 2} \right)\,\,\,N = 5N - 2\left( {2N} \right)\,\,\,\mathop = \limits^{\left( 1 \right)\,\,{\text{and}}\,\,\,\left( 2 \right)} \,\,\,\operatorname{int} - 2 \cdot \operatorname{int} = \operatorname{int} - \operatorname{int} = \operatorname{int} \,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
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Re: Is N an integer? 1) 2N is an integer 2) 5N is an integer (DS) &nbs [#permalink] 09 Sep 2018, 11:36
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