M and N are both nonzero integers. Is M/N a prime number?

First, I am quite sure that negative number can't be prime.
For this question, I get E.
For M/N to be a prime, M must equal a prime and N equals 1

(1) |M| = -M
if M>0, M = -M
If M<0, -M = -M => M=M
So M can be either negative or positive, but we still don't know N.
INSUFFICIENT

(2) |N|=N
if N>0, N=N
if N<0, N=-N
Don't know M.
INSUFFICIENT

Together, I still can't draw any conclusion.

1. M must be negative. Since |M| must be a positive then - M must be positive as well. The only way for - M to be positive is if M is negative itself.

2. If a negative number cannot be prime than the answer would be C. M/N is 100% for certain a negative number in this problem. If negatives cannot be primes and it's asking if M/N is prime we can answer this 100% no. So if the GMAT takes the stance that there cannot be negative primes the answer would be C.

3. "for M/N to be a prime, M must equal a prime and N must equal 1" this isn't true at all. 14/2 = 7 which is a prime. 33/3 = 11 which is a prime. There are tons of ways to divide two numbers and come up with a prime. The only way you can get a prime number through multiplication is if one number is prime and the other is one (this is the very definition of a prime number).

Yea, I think I need to. When I do the math problems too fast or at work or both, I make really stupid mistakes. Then I look back and I am like, what? I did this? Happened to me twice today.

Regarding negative prime, my understanding is that any negative number (except -1) has at least 3 factors. Say -3 = 1*3*-1, which violates the definition of prime number. For -1, we can have multiple factors:
-1 = -1*-1*-1*1 and so on; hence, not a prime either.

but in gmat, -ve is not considered prime.
can any one confirm?
thanx.

St1:
Modula of any number is always positive, so M must be negative. We have no idea about N, so st1 is insufficient.

St2:
N must be a positive integer, but nothing M is known, so st2 is insufficient.

Using both,
M/N will always be negative, so M/N is not a prime number since the smallest prime number is a positive number. Sufficient.

Ans C

If |M| = -M doesn't it mean that we still are not sure whether -M is negative or positive?
if M=-2 then -M=2
if M=2 then -M=-2

Correct me if I'm wrong

I had never heard about negative primes. And in fact they do not exist by definition:
A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself.

https://mathworld.wolfram.com/PrimeNumber.html

|M| by definition must be a positive number since all absolute values are positive. So the left side of the equation is positive here. That means the right side of the equation must be positive as well. Plug in numbers into -M and see what you get. -(10) = -10 but -(-10) = 10

Example 1: (negative number)

|-10| = - (-10)
10 = 10
CORRECT

Example 2: (positive number)

|10| = -(10)
10 = -10
INCORRECT

M has no choice but to be negative here.

I am with C on this...

there is no such thing as a negative prime number...

yes negative numbers cant be prime numbers, Manhatten GMAT books confirm that

I will go with C .


1) it just tells us "M " is a negative or 0 . because |M| is a positive so -M must be positive . in order to do so , M must be negative .

here we are told that M is not zero so M is negative .

we do not know anything about N so it is not sufficient




2) it tells us N is postive . but no info about M . hence not sufficient




1 + 2 together


M/N is a negative number . A negative number can not be a prime so M/N is not a prime . hence sufficient .



correct answer = C

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Just to close discussion about negative primes. There is NO such thing. Primes are positive integers by definition.

Check more tips on Number Properties here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

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