Discussion Forum—A Way with Words, a fun radio show and podcast about language

Welcome.

Your instinct is correct that the verbs in both sentences are right.

The quick answer to your question is that in some interrogative (question) sentences, English adds the verb do. I won't go into the reasons why do is added, but once it is added, the do is the verb that is inflected based on the subject and, in this case, takes the -s ending. That is why you wrote does (3rd person singular to agree with a record), and the form of the word exist then becomes uninflected, loses its -s ending, and looks just like the dictionary form exist.

You can look at it another way. Another place where English adds the verb do is to be emphatic. Imagine someone challenges your assertion above:
"Does a record exist in the database?"
– "Yes, a record exists in the database."
"Tom thinks you are wrong."
– "A record does exist in the database. I can prove it to you."

I hope this helps.

-G