Wow, it's been a long time since I've done any physics, but my sister asked me for help on a question and I am stumped.

The problem is:

What I remember is since the two charges have different signs, the third charge must be placed outside of the other two. It cannot lie in-between the other two.

Other than that... I'm drawing a blank. Any help / helpful hints would be much appreciated!

Great! That's correct physical thinking, in my opinion. Another idea is that, as a consequence of symmetry, the desired position must lie on the line connecting the 2 charges. Now, since the force decreases with distance, the desired position must be further away from the big charge than fom the small charge. To solve, remember the 'inverse square law'...