Buy and Hold ~ $50k property. Do lenders loan small mortgages?

[Ryan Jones]

To at least achieve the 1% rule, I'm looking in areas of the country where $50k properties bring in at least $500/month; $100k properties at least $1,000/month, etc.  

If I find a good $50k property and put 20% down, will lenders loan $40k?  On one hand you think they would be more likely too since it's a smaller amount, but I know even credit unions don't want to waste their time with such small loans.  

So in some podcasts I'm seeing the return on cash investment, but for these low dollar properties if no one will loan you small numbers, you'd have to buy it outright in cash it seems.

I'm curious about those of you who are looking at cheap properties if you are able to put 20-25% down or are you buying it all cash?