Holy jumpin, toritoribe, you're right! I misread the answer key, it actually should read:
[sono hon-o doko-de katta]-ka oboete imasu ka
My inability to read aside, I still would have expected this to use "-to". Using "-ka" makes sense I suppose, as a complete Wh-clause embedded in place of an object, but... my question is still: how do you know which verbs take "-to"? Is the difference that a verb like oboeru expects an object as complement, while verbs like omou necessarily take a clause as complement, marking them all with "-to"?
If that is the case with oboeru, what happens when the complement is not Wh-? For example, "I remember to brush my teeth every day":
*mainichi ha-o migaku-[???] oboete imasu