I absolutely know nothing about the Iconia A500 tablet (except that it's runs the Android OS) but I'm fairly sure that your PDFs are not 20 and 57 Gigabytes. 20 and 57 MegaBytes is a far more normal size for a PDF. Frankly, I don't think any device could handle a 20Gigabyte PDF. The 16Gig you talk about is not 'internal memory' but the 'hard drive' of the device. The Iconica has 1Gigabyte of internal memory.
But as for your problem ... you can be fairly sure that you do not have a hardware problem but a software problem.
I would do the following test (if possible) :
copy the PDF files back to a PC and try to open them there. This way you can check if maybe the files are corrupted somehow by attempting to open them on your PC.
However, far more likely would be that indeed the PDF software you got with the A500 can not handle the files... in that case I would go to the Android App Shop to see if you can find OTHER PDF reading software.
There's bound to be multiple choices and odds are one of the software is going to be able to read them ... providing they're not corrupted, of course.
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