Question 252882
<pre>
I.     {{{2n < n^2}}}

is always true if {{{n < 0}}}, because if we divided both sides
by n, a negative number, the inequality would be reversed 
and we'd have

      {{{2 > n}}}

and 2 is always greater than any negative number n.

II.    {{{2n < n}}} 

is always true because if we divided both sides by n,
which is a negative number, the inequality would be
reversed and we'd have 

      {{{2 > 1}}}

and that is always true.



III.   {{{n^2<-n}}}

That's true sometimnes but not always.  If we divided through
by n, which is a negative number, the inequality would be
reversed and we'd have

        {{{n > -1}}}

So that would be true sometimes, like when {{{n=-1/2}}}

       {{{-1/2> -1}}}

but would be false, like when {{{n = -2}}}

But since the word is "could be true" and not
"always true", we have to include it too,

so the answer is (E) I, II, and III

It it had says "always" instead of "could" then the
answer would have been C.  But since it's "could" 
it's E.

Edwin</pre>