DW,
The question is actually pretty much verbatim a genuine JAR question... I had it 6 months ago, and had previously seen it in the feedback.
SOB's answer is correct. The easiest way to understand what's going on is to draw it out in little triangles (which I can't do on this screen!!)
After the first hour, the gyro has drifted 0.01 degrees, giving a track error of (500 / 60 * 0.01)(using the 1 in 60 rule), or 5/60nm.
By the end of the second hour, the drift has increased to 0.02 degrees, i.e. a FURTHER track error of (2 * 5/60)nm, in addition to the 5/60 already incurred. So the cumulative track error is now (1+2) * 5/60.
Similarly over the remaining 10 hours. The final cumulative track error is (1+2+3+...+11+12) * 5/60, or about 6nm.
A truly ridiculous question. Learn the answer, rather than the method, and it'll be an easy mark!!