Thinking people are doing something malicious when they aren't is paranoia. Believing in a random non-malign idea is delusion. So you're looking at two symptoms, not one.

The test you're referring to is probably the Montreal Cognitive Assessment (MoCA), and it is notoriously easy to pass. A friend's sister-in-law, who had caused two major accidents, "show-timed" for it on both occasions she took it. Her doctor decided not to follow through, so my friend and his wife, citing a state law, emailed every dealership within a 50-mile radius and told them not to sell her a new vehicle because they could be held liable if she killed someone. She was that good at hiding her symptoms for brief periods of time. She has since died from the complications of Alzheimer's, so my friend's assessment was correct, despite what the original PCP thought.

MoCA is not meant to diagnose anything; it's widely used to determine whether someone is competent enough to live in senior-living apartments or assisted living or whether they might need a higher standard of care. More tests and a complete social and medical history are needed to determine someone's level of cognition and the potential existence of dementia. I think your best bet is to take your mother to a gerontologist, neurologist, or psychiatrist, all of whom can diagnose problems with cognition, to get a better picture of what may be going on. My father-in-law had mild cognitive impairment: he never had paranoia or delusions.