What book do you remember displaying as a public prop, i.e. one that you were reasonably sure you'd never finish but carried around anyway?
The reason you held onto that prop can remain your secret, unless you're brave enough to step into the bell curve confession booth. Maybe you wanted to impress an older sibling, a smart friend, or an observant teacher. Perhaps you hoped the book - if carried with sufficient flair - would prompt some object of affection to engage you in deep conversation, with that conversation a prelude to more erotic adventures. Keep your rationale secret, but at least own up to your chicanery via telling me and others what the book was. Then let us use our imaginations to imagine why you did it.
I'm just a little embarrassed to admit I did this enough early in my reading life that several of my own bogus titles popped into my head but only after my wife admitted that "The Odyssey" was her 6th grade prop. Weeks after abandoning "The Count of Monte Cristo" - a book my beloved Father told me I must read - I carted that classic around. And as late as my undergraduate years, Thomas Pynchon's first novel "V" was a constant - though unread - companion. Pynchon was so cool - if completely inscrutable - in the wild late 60's. I'm saving my most recent book-as-prop tale until one of you comes clean.
I'm guessing there'll be readers claiming they've never acted out this harmless charade. Remind me when I next see you to have you perform that walk-on-water bit, OK?