(updated with solutions) If the hole saws do NOT cut but just rotate and create a small amount of sawdust, you probably have an MDF door. It's like plywood, very durable. You need a CMT 550-025 multifunction hole saw for cutting. Many interior doors only have an MDF frame and its trim around the doorknob. Tap the line above the handle. If the sound changes, gets muffled, then it's probably just delusion. You can probably use an Irwin hole saw to poke a hole here. But it won't be as strong as if you place it closer to the handle in the MDF area. Also important to note - you do NOT need a 2 1/8 hole. You just need a 1 inch hole in the narrow side of the door first. This will hold your latch mechanism. Then on the main face of the door you just need to scrape off enough wood to attach the tongue and plates to the latch mechanism. 3 overlapping 1" holes on each surface will do. So all you have to do is buy a good quality 1" hole saw (this method also eliminates the need for a plastic template if you're brave and know where the bolt mechanism is).
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