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Math Expert V
Joined: 02 Sep 2009
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If -m/19 is an even integer, which of the following must be true?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (00:46) correct 11% (00:45) wrong based on 53 sessions

### HideShow timer Statistics 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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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, 09:08.
Last edited by Baten80 on 15 Jul 2018, 09:37, edited 1 time in total.
Senior Manager  G
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Re: If -m/19 is an even integer, which of the following must be true?  [#permalink]

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1
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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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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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. Re: If -m/19 is an even integer, which of the following must be true?   [#permalink] 15 Jul 2018, 09:52
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# If -m/19 is an even integer, which of the following must be true?  