Rejecting tenant on gut feeling?

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Hi all, I've been a while researching and learning about renting my first investment property and I finally posted my rental ad this afternoon. Our market is pretty good in Edmonton and I've received a phone call and 6 emails so far about the house. 

To pre-screen I've used the following minimum requirements on my reply emails/phone conversation.

-Salary must be equal to or greater than 3x rent

-No previous evictions

-Good references from all previous landlords

-Credit/Background check will be performed at applicants expense

I'm left with 3 viewings scheduled for this week. Hooray! After I get over the excitement of possibly getting a renter I start to think about some of the information I got on the phone call. 

The lady asked if the minimum salary was for an individual or household. I say household. She says "Ok, we'll be fine then....between myself, my boyfriend, his brother and his cousin we meet that". This gives me pause but I couldn't think of anything else to say/question so I went ahead and scheduled the viewing.

Now, I don't have anything concrete and the application will give me more to work off of but I'm getting a gut feeling that this won't be the best set of tenants. 

I guess my question is this, can you decline an applicant based on a feeling as long as it's not based on race, religion, age, etc. I get a bit of conflicting information when reading tenant screening blogs. For example saying to look at a tenants car condition for an indication of cleanliness but later saying that you should clearly let an applicant know why they were rejected (would you tell them it's because their car was dirty)?

Thanks for any help to this nervous newbie.