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If -m/19 is an even integer, which of the following must be true?

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If -m/19 is an even integer, which of the following must be true?  [#permalink]

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New post 15 Jul 2018, 08:03
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E

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If \(\frac{-m}{19}\) is an even integer, which of the following must be true?

A. m is a negative number.
B. m is a positive number.
C. m is a prime number.
D. m is an odd integer.
E. m is an even integer.

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If -m/19 is an even integer, which of the following must be true?  [#permalink]

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New post Updated on: 15 Jul 2018, 08:37
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Bunuel wrote:
If \(\frac{-m}{19}\) is an even integer, which of the following must be true?

A. m is a negative number. Yes, IMO, as the result of the fraction is even integer so an even integer is a number too.
B. m is a positive number. m must be negative as denominator 19 is positive and numerator m is negative
C. m is a prime number. it is given the the fraction's result is an even integer, so it must be a prime number.
D. m is an odd integer. Same as C, it is given that the fraction's result is an even integer

E. m is an even integer.
[Yes, to fulfill the condition m is an even integer]

I am confused about option a and b.

I chose Answer A, because any way it is negative number.

I failed figure out plausible explanation for option E.
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Originally posted by Baten80 on 15 Jul 2018, 08:08.
Last edited by Baten80 on 15 Jul 2018, 08:37, edited 1 time in total.
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Re: If -m/19 is an even integer, which of the following must be true?  [#permalink]

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New post 15 Jul 2018, 08:12
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The answer should be E. m must be an even integer. It cannot be just any number. If it is odd, then the resultant can never be even. Thus, m must be even.

Hence, E is the right answer.

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Re: If -m/19 is an even integer, which of the following must be true?  [#permalink]

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New post 15 Jul 2018, 08:27
Bunuel wrote:
If \(\frac{-m}{19}\) is an even integer, which of the following must be true?

A. m is a negative number.
B. m is a positive number.
C. m is a prime number.
D. m is an odd integer.
E. m is an even integer.


Since,
-m/19 = even integer

It is only possible when m is even multiple of 19(prime number) e.g. 19*2, 19*4, 19*6,....and so on, which is always even

Hence, E.
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Re: If -m/19 is an even integer, which of the following must be true?  [#permalink]

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New post 15 Jul 2018, 08:52
1
Bunuel wrote:
If \(\frac{-m}{19}\) is an even integer, which of the following must be true?

A. m is a negative number.
B. m is a positive number.
C. m is a prime number.
D. m is an odd integer.
E. m is an even integer.



Given

\(\frac{-m}{19}\) = even integer

-m = 19 * even integer.

We know if we multiply a integer by an even integer , it will also yield a even integer.

Thus m surely is an even integer.

The best answer is E.
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Re: If -m/19 is an even integer, which of the following must be true? &nbs [#permalink] 15 Jul 2018, 08:52
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If -m/19 is an even integer, which of the following must be true?

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