If you are in twenties or early thirties and remain single, earn $3,000 after tax per month, you will probably save $1,000 if you, let's say, spend $500 to $800 on rental, a guest bedroom in a shared house/apartment, $500 on food, $50 on utilities, $150 on phone/internet bills, $400 on commuting costs or gas/maintainance if you have a used car, $200 on occasional entertainment or others. This $1,000 savings will allow you to invest or place a house down payment when time is ripe. Is this possible based on where you live ?
It depends a lot by where one lives. If I'd be earning $3k from salary (after tax), it would be wonderful. But I don't.
Also the expenses differ greatly from country to country.
So the math you've done, although nice, doesn't apply in most parts of the world.
It also depends on lifestyle and choices made.