If it looks good, it likely is...
However, its no guarantee. If you are talking about ammo from one of the major makers, 30-40 years is nothing. Hell, I have some of my own reloads that are getting nearly that old! And yes, they still work fine.
.22LR more than a few decades old might give you a bit more trouble than fresh stuff, or it might not. As long as the cases look clean, its probably fine. RF ammo (even from major makers) has a higher expected percentage of misfires than centerfire ammo, its the nature of the beast. Budget .22RF ammo is often less reliable than their premium stuff.
Remington Golden Bullets were their high end .22 round, back before the "hyper velocity" .22s came out. Stingers, Vipers, Yellowjackets, etc. are hyper velocity, and Golden Bullets are "high velocity". This is compared to the "standard velocity" rounds from generations before. Today most standard velocity ammo is target/match ammo, and "high velocity" is what is more or less standard (i.e. commonly found).
I have seen .22s so old their bullets had oxidized (turned white on the surface) that still shot fine. I have seen cheap stuff I bought last year have multiple duds. If your Rem ammo is in the old red and white (1960s eras) packaging, and is in pristine condition, it might be worth a little more than new ammo, to the right collector. Might. A Little. Maybe.