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

Question

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!!

CounterSniper · Answer

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 
C

fskilnik · Answer

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

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

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

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

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

Regards,
fskilnik.

BrentGMATPrepNow · Answer

Target question :    Is N an integer?

Statement 1 : 2N is an integer  
If 2N is an integer, then there are 2 possible cases: 
 Case a : N is an integer. For example, N COULD equal 1, since 2N = 2(1) = 2, and 2 is an integer. So, the answer to the target question is  YES, N is an integer .
 Case b : N is a fraction with 2 in the denominator. For example, N COULD equal 3/2, since 2N = 2(3/2) = 3, and 3 is an integer. In this case, the answer to the target question is  NO, N is not an integer 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : 5N is an integer 
If 5N is an integer, then there are 2 possible cases: 
 Case a : N is an integer. For example, N COULD equal 1, since 5N = 5(1) = 5, and 5 is an integer. So, the answer to the target question is  YES, N is an integer .
 Case b : N is a fraction with 5 in the denominator. For example, N COULD equal 6/5, since 5N = 5(6/5) = 6, and 6 is an integer. In this case, the answer to the target question is  NO, N is not an integer 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that EITHER N is an integer OR N is a fraction with 2 in the denominator
Statement 2 tells us that EITHER N is an integer OR N is a fraction with 5 in the denominator
Since we must assume that BOTH statements are true, we can conclude that  N is an integer 
So, the answer to the target question is  YES, N is an integer 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Bunuel · Answer

Is n an integer?

(1) 2n is an integer --> 2n = integer: if n = 1/2 then the answer is NO but if n = 1 then the answer is YES. Not sufficient.
(2) 5n is an integer --> 5n = integer: if n = 1/5 then the answer is NO but if n = 1 then the answer is YES. Not sufficient.

(1)+(2) Multiply (1) by 2: 4n = integer. Now subtract that from (2): 5n - 4n = integer - integer --> n=integer (since integer-integer=integer). Sufficient.

Answer: C.

GMATinsight · Answer

Question : Is N an Integer?

(1) 2N is an Integer

N may be 1 (Integer) ir 1/2 (Non Integer) hence

Not Sufficient

(2) 5N is an Integer

N may be 1 (Integer) ir 1/5 (Non Integer) hence

Not Sufficient

Combining the two statements

Statement 1 clarifies that either N is an integer or a fraction with denominator 2 (but nothing else)
Statement 2 clarifies that either N is an integer or a fraction with denominator 5 (but nothing else)

Combing the statement we can conclude that denominator can nether have 5 due to statement 1 not have 2 due to statement 2 hence denominator has to be 1

i.e. N must be an integer
SUFFICIENT

Answer: Option C

bumpbot · Answer

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

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