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.