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

Question

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.

MHIKER · Answer

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.

SonalSinha803 · Answer

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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sudarshan22 · Answer

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  .

KSBGC · Answer

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.

BrentGMATPrepNow · Answer

APPROACH #1:

Notice that ALL even integers can be written as 2k, where k is an integer. 
For example, 14 = 2(14), and 20 = 2(10), and 66 = 2(33), etc

So, if -m/19 is an even integer, we can write: -m/19 = 2k (for some integer k)
Multiply both sides by 19 to get: -m = 38k
Multiply both sides by -1 to get: m = -38k

Since -38 is EVEN, we know that -38k MUST be even

Answer: E

Cheers,
Brent

BrentGMATPrepNow · Answer

APPROACH #2

Since the question asks "What  MUST  be true?", we can eliminate any answer choice that need not be true.

For example, if m =  38 , then -m/19 = - 38 /19 = -2, which is EVEN. 
So, m COULD equal  38 
Check the answer choices...
A)  38  is a negative number. Not true ELIMINATE.
B)  38  is a positive number. True. KEEP
C)  38  is a prime number. Not true ELIMINATE. 
D)  38  is an odd integer. Not true ELIMINATE.
E)  38  is an even integer. True. KEEP

We're left B and E. 
So, let's find another value of m that meets the given conditions.

If m =  -38 , then -m/19 = - (-38) /19 = 38/19 = 2, which is EVEN. 
So, m COULD equal  -38 
Check the remaining answer choices...
B)  -38  is a positive number. Not true ELIMINATE.

By the  process of elimination (POE) , the correct answer is E.

Cheers,
Brent

Chibvike · Answer

We get an even number when we do the following multiplication
1.Even*Odd = EVEN
2. Even*Even = EVEN

Given that 19 is odd, the only situation where a multiplication with an odd number gives us even is when the multiplier is even

Hence, from our statement 1. above;
Even*Odd=EVEN

To have an Odd denominator like we do in the question stem, divide both sides by Odd and we get
EVEN = Even/Odd
This agrees with the question stem of an odd denominator

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

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GMAT Problem Solving (PS) Questions

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

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