Imac i5 will shut off randomly

I leave my mac running 24-7 If i am going to be gone several days I might just shut it off. I am usually in the middle of a project. I just bought a new i5 27" with 12 g mem. It does not appear to be related to any specific program. I will leave with my project on screen. When I return I'll hit the space bar and everything comes up. But on at least 5 occasions the mac would not awake no matter what I did or key i hit. The only way to get it started was to hold done the start button till i here the bong the let go. then I get a white screen. sometime I have to repeat this once or twice before it boots up. the computer is warm as if it were running but I could not get it to respond.

Since the machine is new, make an appointment with your local Apple store to have it looked at.

hotstarman said:

I just bought a new i5 27" with 12 g mem

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Remove 4GB of ram (quite simple to do) leaving your mac with 8GB and see if that cures the shutdowns.
If it does (or doesn't), phone the shop where you bought your iMac, explain the problem and see what they recommend.
It might be faulty ram modules or something else.
If it does work and you can live with 8GB, I'd leave the machine like that and get a refund on the unused ram.

I had this problem when I upgraded the ram from 4to16GB of ram in my iMac, and since taking out 4GB it seems to have cured the shutdowns.

Worth a try