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Yes, you can easily rent a 2- or 3-room HDB for this price in many locations, but probably not a Condo (which start around S$3000).
If you are alone, you may also want to consider renting just a room to save some cost (sublets start at S$800/month).

Thanks Beppi. No, I am not on my own, and so renting a room is not an option. I presume that the difference between an apartment and a Condo, is that the later is in a complex containing various facilities such as pool, gym tennis court etc?

The difference is between an HDB and Condo.
HDB flats are government-subsidized housing that locals can buy and that 80% of the population lives in. They exist all over the island (many in convenient locations), have limited facilities and can only be rented out in certain situations, so do check whether it is legal before you rent one!
Condos are much more expensive privately build apartments and usually (but not always) are bigger, more luxurious and have facilities like swimming pool, gym, etc. Many of them are in less convenient locations for public transport (most inhabitants have cars).

The soul of this small country lies in its incredible diversity: people from every walk of life can find a reason to love it here. This is reflected in the space-age skyscrapers in the Central Business District, the historic shophouses in the neighbouring Colonial District, red lanterns in Chinatown, dense jungle in Bukit Timah, and the artificial sands of Sentosa Island. Living in Singapore can be a different experience every day.

Hi JensenDrake2, not sure how your post actually answers my question, which is about how much I should be allowing for rent.

You can easily get a 2 bedroom HDB flat for rent at 2000-2500 SGD/month at places such as Ang Mo Kio, Bishan, Toa Payoh. In Yishun, you will get at 1800-1900 SGD/month