As was said above, Its not uncommon for a magnet to stick to Military FMJ bullets, but that does not necessarily mean they are AP.
I would sacrifice one bullet and cut it in half with a dremel tool or something like that. It should be easy enough to tell then, as the true AP will have a hard center core, like a short rod, and a file will not touch it, and the regular FMJ just a lead core.
I have a couple hundred rounds of 3006 FMJ from the late 40's. They were in pretty bad cosmetic condition, and pre 1953 so corrosive primed. I broke them down, and saved the bullets, loaded them into modern cases, and new 4895 powder, for use in my Garand. A magnet will stick to them, but they are not AP. They weigh in the 150 grain range, and are flat based.
Earlier ammo, such as what your bullets came from were from the Pre- Garand WW2, and were boat tail, and weigh in the range of what your bullets do, so I suspect your's are from this era.
Bullet weight was reduced when the Garand was in the development phase, in an effort to make it easier on the new rifles. The Garand, was was not quite as tough as the 03's and Pattern 17 rifles were.
Regular FMJ ammo in the 3006 with go through mild steel plate up to about 3/8 inch thick at close range, so the steel test may not yield the results you expect.
Has some WW2 era 8mm mauser AP ammo once, when I was way... younger, and dumber. We shot it up pretty quickly, and had fun with it. We noticed that it would at 50 - 75 yards go through an "I" beam that a bit under 3/4 thick but heavier than 1/2 inch. I wont say for sure how thick, as this was years ago, and I dont remember for sure. I do remember it was over 1/2 inch, and we were impressed, as the holes looked like they were drilled.. I would not shoot at anything like that today, but at 18 - 20 my judgement was not always perfect.
