If |n| is a positive number, then n is a negative number which of the following would be a counterexample?

Question

The answer has to be either -10, -4, -1, or 10 please help me 

Answer 1

"If |n| is a positive number" -- and it is! (except for |0|=0 which is neither positive nor negative.  This is  what absolute value does -- it produces a positive number when n is not 0.

 

"then n is a negative number"  -- Well, it might be or it might not be.

 

|n| is a positive number for all the values listed (and for any others we might think of).

 

But, in the case of n=+10, n is not negative.  Yet, |n| is positive (it always is).  This disproves the statement that "n is a negative number" -- because we found one that isn't!!

Answer 2

forget about |n| , it's always not a negative number.

now, the question is if n<0 ??? answer is no, of course.

from your set of possible answers, look at n=10.

Answer 3

This is a problem of words and it sounds confusing but it really isn't. It reads "if |n| is a positive number", |n| is an absolute value so |n| is always a positive number so forget that for a moment.  It says "then n is a negative number", so this is it tell. 

 

It's telling you that n is a negative number.  

 

So this statement is trying to say only negative numbers put between the absolute value symbols will come out positive.

 

is this true? not by definition of an absolute value.

 

Then the question asks for a counterexample

 

Definition of a counter example:

 

A counterexample is a special kind of example that disproves a statement or proposition.

 

so lets disprove the statement

 

so if we substitute -10 in for "n" we get |-10| = ?

 

the absolute value of -10 is 10.  That proves the statement.  right?

 

we could do this for the other 2 negative answers if you'd like but that would be redundant. 

 

The only number you have listed that can "disprove" the statement that "n" has to be a negative number for |n| to be positive is the "10"

 

So if we substitute 10 in for n we get |10| = ?

 

What is the absolute value of 10?  It is also 10.

 

In this example, 10 was not a negative number but the absolute value was still the same positive number which disproves the statement and give you your answer

 

Answer being 10

 

If you have any questions, please feel free to contact me.  Shane

Answer 4

What is the opposite of a negative number?  Pick the number that has a sign opposite to a negative.