Will this PSU work for my GTS 250?

Seems like the link is not working. Well it has two +12V rails 18A each.

Will it run the card?

If you can't get the link to work, why don't you tell us the brand and model so we can look it up ourselves, or at the very least the wattage on it.

Yes most likely since the card only requires 24amps on the combined +12 volt rails but which PSU is it to make sure?

You don't know that. The label says "Maximum power". We have no way of knowing what the total 12 volt power is. And because they are not telling, it's probably pretty bad.

The Apex is junk. Note the voltage selector switch. That means that it is an obsolete design without automatic PFC. Efficiency is probably around 70% instead of the 80% + that more modern PSU's have.

I'd recommend something like a
Corsair 450VX (33 amp 12 volt rail)
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

or an Antec 500 watt BASIQ
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.hardwaresecrets.com/article/792

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

That is the PSU. What do you mean by combined 12V? So does that mean this PSU have 36A since the two 12V can be added?

That is not a recommended PSU but if you have it it will work. It is not as simple as adding the two rails together usually total wattage for the +12volt is stated under neath the sticker I would be surprised if it is more than 360 watt (30amp) on yours.
If you do not already have the PSU this 400watt Corsair is a high quality unit and will run your card no problem http://www.newegg.com/Product/Product.aspx?Item=N82E168...