I imagine the conversation that led to the choice of wording, perhaps in the staff room: "Kids today don't know what it means to study. When we were young, we studied. We studied hard. These kids need some motivation. We need to put something on the sign - something that clearly states what's expected of them. We've always gone with 'Good luck,' which was entirely the wrong message. Let's go with 'Study hard' and wait for the exam results to skyrocket. I don't know why we didn't think of this before!"
And I imagine a student walking or driving past the sign and reading its advice, soaking it in. "My God. Study hard. Why have I not thought of this before? All this time I've been slacking off and skipping class and not studying and wondering why I'm flunking out. It's so clear to me now. I just need to study hard. That's it. I'm cancelling all of my plans, telling my friends I am out for that party on the weekend. I am going to study, study, study. And not just a little. I'm going to study hard, just like the sign says. Someday I'll look back and say, 'That sign changed my life.'"
And I imagine the parent seeing the sign and confronting their teenager after school. "Why aren't you studying for exams?" Their child replies, "These aren't the types of exams you're supposed to study for. They call them 'exams' but they're not 'exam exams.' No one expects you to study for them." To which the parent replies, "Don't you try to pull one over on me, young man. I saw the sign. It says right there in black and white: Study hard."
So to those who chose the wording for the sign, thank you. And to all those students writing exams this week, study hard. And while you're at it, good luck.